Quantification of heart rate variability by discrete nonstationary non-Markov stochastic processes
NASA Astrophysics Data System (ADS)
Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail
2002-04-01
We develop the statistical theory of discrete nonstationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of nonstationary effects. The developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized TCF. Using the projection operators technique we find the chain of finite-difference non-Markov kinetic equations for discrete nonstationary TCF and for the set of nonstationary discrete memory functions (MF's). The last one contains supplementary information about nonstationary properties of the complex system on the whole. Another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity, which contains some information of the nonstationarity effects. The full set of dynamic, spectral and kinetic parameters, and kinetic functions (TCF, short MF's statistical spectra of non-Markovity parameter, and statistical spectra of nonstationarity parameter) has made it possible to acquire the in-depth information about discreteness, non-Markov effects, long-range memory, and nonstationarity of the underlying processes. The developed theory is applied to analyze the long-time (Holter) series of RR intervals of human ECG's. We had two groups of patients: the healthy ones and the patients after myocardial infarction. In both groups we observed effects of fractality, standard and restricted self-organized criticality, and also a certain specific arrangement of spectral lines. The received results demonstrate that the power spectra of all orders (n=1,2,...) MF mn(t) exhibit the neatly expressed fractal features. We have found out that the full sets of non-Markov, discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can
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.
Stochastic longshore current dynamics
NASA Astrophysics Data System (ADS)
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
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
Bertagni, Matteo Bernard; Ridolfi, Luca
2016-01-01
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
Stochastic Physicochemical Dynamics
NASA Astrophysics Data System (ADS)
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Controlled Stochastic Dynamical Systems
2007-04-18
the existence of value functions of two-player zero-sum stochastic differential games Indiana Univ. Math. Journal, 38 (1989), pp 293-314. [6] George ...control problems, Adv. Appl. Prob., 15, (1983) pp 225-254. [10] Karatzas, I. Ocone, D., Wang, H. and Zervos , M., Finite fuel singular control with
Regular and stochastic behavior of Parkinsonian pathological tremor signals
NASA Astrophysics Data System (ADS)
Yulmetyev, R. M.; Demin, S. A.; Panischev, O. Yu.; Hänggi, Peter; Timashev, S. F.; Vstovsky, G. V.
2006-09-01
Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.
Stochastic Gain in Population Dynamics
NASA Astrophysics Data System (ADS)
Traulsen, Arne; Röhl, Torsten; Schuster, Heinz Georg
2004-07-01
We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.
Dynamically orthogonal field equations for stochastic flows and particle dynamics
2011-02-01
where uncertainty ‘lives’ as well as a system of Stochastic Di erential Equations that de nes how the uncertainty evolves in the time varying stochastic ... stochastic dynamical component that are both time and space dependent, we derive a system of field equations consisting of a Partial Differential Equation...a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new
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.
Variational principles for stochastic soliton dynamics
Holm, Darryl D.; Tyranowski, Tomasz M.
2016-01-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa–Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler–Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling. PMID:27118922
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Long-range memory and non-Markov statistical effects in human sensorimotor coordination
NASA Astrophysics Data System (ADS)
M. Yulmetyev, Renat; Emelyanova, Natalya; Hänggi, Peter; Gafarov, Fail; Prokhorov, Alexander
2002-12-01
In this paper, the non-Markov statistical processes and long-range memory effects in human sensorimotor coordination are investigated. The theoretical basis of this study is the statistical theory of non-stationary discrete non-Markov processes in complex systems (Phys. Rev. E 62, 6178 (2000)). The human sensorimotor coordination was experimentally studied by means of standard dynamical tapping test on the group of 32 young peoples with tap numbers up to 400. This test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere. The numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function, the memory functions of low orders and the first three points of the statistical spectrum of non-Markovity parameter. Our observations demonstrate, that with the regard to results of the standard dynamic tapping-test it is possible to divide all examinees into five different dynamic types. We have introduced the conflict coefficient to estimate quantitatively the order-disorder effects underlying life systems. The last one reflects the existence of disbalance between the nervous and the motor human coordination. The suggested classification of the neurophysiological activity represents the dynamic generalization of the well-known neuropsychological types and provides the new approach in a modern neuropsychology.
Dynamic response of mechanical systems to impulse process stochastic excitations: Markov approach
NASA Astrophysics Data System (ADS)
Iwankiewicz, R.
2016-05-01
Methods for determination of the response of mechanical dynamic systems to Poisson and non-Poisson impulse process stochastic excitations are presented. Stochastic differential and integro-differential equations of motion are introduced. For systems driven by Poisson impulse process the tools of the theory of non-diffusive Markov processes are used. These are: the generalized Itô’s differential rule which allows to derive the differential equations for response moments and the forward integro-differential Chapman-Kolmogorov equation from which the equation governing the probability density of the response is obtained. The relation of Poisson impulse process problems to the theory of diffusive Markov processes is given. For systems driven by a class of non-Poisson (Erlang renewal) impulse processes an exact conversion of the original non-Markov problem into a Markov one is based on the appended Markov chain corresponding to the introduced auxiliary pure jump stochastic process. The derivation of the set of integro-differential equations for response probability density and also a moment equations technique are based on the forward integro-differential Chapman-Kolmogorov equation. An illustrating numerical example is also included.
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. PMID:27547083
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.
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
Principal axes for stochastic dynamics
NASA Astrophysics Data System (ADS)
Vasconcelos, V. V.; Raischel, F.; Haase, M.; Peinke, J.; Wächter, M.; Lind, P. G.; Kleinhans, D.
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
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 dynamics of cholera epidemics.
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Stochastic dynamics of cholera epidemics
NASA Astrophysics Data System (ADS)
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
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 Dynamic Mixed-Integer Programming (SD-MIP)
2015-05-05
door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for stochastic dynamic mixed...project lays the foundation for stochastic dynamic mixed-integer and linear programming (SD-MIP). This project has produced several new ideas in...models. Recent research has opened the door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for
Stochastic Resonance in Protein Folding Dynamics.
Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A
2016-05-04
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.
Dynamic range of hypercubic stochastic excitable media
NASA Astrophysics Data System (ADS)
Assis, Vladimir R. V.; Copelli, Mauro
2008-01-01
We study the response properties of d -dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modeled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h . The response function (mean density of active sites ρ versus h ) is obtained via simulations (for d=1,2,3,4 ) and mean-field approximations at the single-site and pair levels (∀d) . In any dimension, the dynamic range and sensitivity of the response function are maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d .
A stochastic model of human gait dynamics
NASA Astrophysics Data System (ADS)
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
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.
Double inverse stochastic resonance with dynamic synapses
NASA Astrophysics Data System (ADS)
Uzuntarla, Muhammet; Torres, Joaquin J.; So, Paul; Ozer, Mahmut; Barreto, Ernest
2017-01-01
We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
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.
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
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.
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.
Stochastic Dynamics through Hierarchically Embedded Markov Chains
NASA Astrophysics Data System (ADS)
Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.
2017-02-01
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
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).
The stochastic search dynamics of interneuron migration.
Britto, Joanne M; Johnston, Leigh A; Tan, Seong-Seng
2009-08-05
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.
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.
Statistics and generation of non-Markov phase screens
NASA Astrophysics Data System (ADS)
Charnotskii, Mikhail; Baker, Gary
2016-09-01
Statistics of the random phase screens used for the modeling of beam propagation and imaging through the turbulent atmosphere is currently based on the Markov Approximation (MA) for wave propagation. This includes the phase structure functions of individual screens and the use of the statistically-independent screens for the multi-screen splitstep simulation of wave propagation. As the propagation modeling progresses to address the deep turbulence conditions, the increased number of phase screens is required to accurately describe the multiple scattering. This makes the MA a critical limitation, both because phase statistic of the thin turbulent layer does not follow MA, and because the closely space screens cannot be considered as statistically and functionally independent. A recently introduced Sparse-Spectrum (SS) model of statistically homogeneous random fields makes it possible to generate 3-D samples of refractive-index fluctuations with prescribed spectral density at a very reasonable computational cost. This leads to generation of samples of the phase screen sets that are free from the limitations of the MA. We investigated statistics of the individual phase screens and cross-correlations between the pairs of phase screens and found that the thickness Δz of the turbulent layer replaced by the phase screen is a new parameter defining the phase statistics in the non-Markov case. SS-based numerical algorithms for generation of the 3-D samples of the turbulent refractive index, and for the phase screen sets are presented. We also compare the split-step simulation results for the traditional MA and non-Markov screens.
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
Nonlinear and Stochastic Dynamics in the Heart.
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N
2014-10-10
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.
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.
Stochastic epidemic dynamics on extremely heterogeneous networks
NASA Astrophysics Data System (ADS)
Parra-Rojas, César; House, Thomas; McKane, Alan J.
2016-12-01
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
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.
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.
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.
Stochastic oscillatory dynamics of generalized repressilators
NASA Astrophysics Data System (ADS)
Strelkowa, Natalja; Barahona, Mauricio
2012-09-01
We explore the impact of low copy number noise on the onset and quality of oscillations in the generalized repressilator model with odd-number of elements. In our previous work [Strelkowa & Barahona, 2011] we applied deterministic complexity analysis and provided analytical conditions for the emergence of stable limit cycles via Hopf Bifurcations in odd-numbered rings. Here, we extend this analysis to the stochastic description of the model and study the influence of a biochemical design 'knob' - the gene copy number - on the onset and quality of the oscillations. The gene copy number simultaneously affects two parameters that are usually considered independently in mathematical analyses of this model: namely, the system size Ω and the deterministic bifurcation parameter c1. Here we study the dynamic properties on the (Ω,c1)-plane and characterize how the oscillation characteristics depend on both parameters. The (Ω,c1)-plane can thus provide a useful perspective for the design and control of engineered synthetic oscillators with respect to biologically meaningful design parameters.
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 Technical Reports Server (NTRS)
Carati, Daniele; Ghosal, Sandip
1994-01-01
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 single-molecule dynamics of synaptic membrane protein domains
NASA Astrophysics Data System (ADS)
Kahraman, Osman; Li, Yiwei; Haselwandter, Christoph A.
2016-09-01
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics of synaptic proteins provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the single-molecule trajectories observed for synaptic proteins, and spatially inhomogeneous protein lifetimes at the cell membrane. Our results suggest that central aspects of the single-molecule and collective dynamics observed for membrane protein domains can be understood in terms of stochastic reaction-diffusion processes at the cell membrane.
Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation
NASA Astrophysics Data System (ADS)
Ma, Juan; Chen, Jian-Jun; Gao, Wei
2006-08-01
A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper.
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.
Microtubules: dynamically unstable stochastic phase-switching polymers
NASA Astrophysics Data System (ADS)
Zakharov, P. N.; Arzhanik, V. K.; Ulyanov, E. V.; Gudimchuk, N. B.; Ataullakhanov, F. I.
2016-08-01
One of the simplest molecular motors, a biological microtubule, is reviewed as an example of a highly nonequilibrium molecular machine capable of stochastic transitions between slow growth and rapid disassembly phases. Basic properties of microtubules are described, and various approaches to simulating their dynamics, from statistical chemical kinetics models to molecular dynamics models using the Metropolis Monte Carlo and Brownian dynamics methods, are outlined.
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
Forecasting financial asset processes: stochastic dynamics via learning neural networks.
Giebel, S; Rainer, M
2010-01-01
Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.
Modeling ion channel dynamics through reflected stochastic differential equations
NASA Astrophysics Data System (ADS)
Dangerfield, Ciara E.; Kay, David; Burrage, Kevin
2012-05-01
Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the “gold standard,” but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks.
Open quantum system stochastic dynamics with and without the RWA
NASA Astrophysics Data System (ADS)
Band, Y. B.
2015-02-01
We study the dynamics of a two-level quantum system interacting with a single frequency electromagnetic field and a stochastic magnetic field, with and without making the rotating wave approximation (RWA). The transformation to the rotating frame does not commute with the stochastic Hamiltonian if the stochastic field has nonvanishing components in the transverse direction, hence, applying the RWA requires transformation of the stochastic terms in the Hamiltonian. For Gaussian white noise, the master equation is derived from the stochastic Schrödinger-Langevin equations, with and without the RWA. With the RWA, the master equation for the density matrix has Lindblad terms with coefficients that are time-dependent (i.e., the master equation is time-local). An approximate analytic expression for the density matrix is obtained with the RWA. For Ornstein-Uhlenbeck noise, as well as other types of colored noise, in contradistinction to the Gaussian white noise case, the non-commutation of the RWA transformation and the noise Hamiltonian can significantly affect the RWA dynamics when ω {{τ }corr} 1, where ω is the electromagnetic field frequency and {{τ }corr} is the stochastic magnetic field correlation time.
Fast stochastic algorithm for simulating evolutionary population dynamics
NASA Astrophysics Data System (ADS)
Tsimring, Lev; Hasty, Jeff; Mather, William
2012-02-01
Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.
NASA Astrophysics Data System (ADS)
Yulmetyev, Renat; Demin, Sergey; Emelyanova, Natalya; Gafarov, Fail; Hänggi, Peter
2003-03-01
In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes (Phys. Rev. E 62 (5) (2000) 6178, Phys. Rev. E 64 (2001) 066132, Phys. Rev. E 65 (2002) 046107, Physica A 303 (2002) 427). The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year olds), young people (from 21 up to 29 year olds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differences between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.
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.
Dynamical Epidemic Suppression Using Stochastic Prediction and Control
2004-10-28
reduce the rate of input of susceptibles. By using the PDF flux, we are able to distinguish regions used in other chaos control schemes that are...use this information in a control algo- stochastic chaos control methods that account specifically for rithm to prevent bursting dynamics (that is, to
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.
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.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time
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 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
Stochastic Circumplanetary Dynamics of Rotating Non-Spherical Dust Particles
NASA Astrophysics Data System (ADS)
Makuch, Martin; Brilliantov, N. V.; Sremcevic, M.; Spahn, F.; Krivov, A. V.
2006-12-01
Influence of stochastically fluctuating radiation pressure on the dynamics of dust grains on circumplanetary orbits was studied. Stochasticity stems from the permanent change of the particle cross-section due to rotation of nonspherical grains, exposed to the solar radiation. We found that stochasticity depends on the characteristic angular velocity of particles which, according to our estimates, spins very fast on the time scale of the orbital motion. According to this we modelled the stochastic part of the radiation pressure by a Gaussian white noise. Gauss perturbation equations with the radiation pressure being a sum of the deterministic and stochastic component have been used. We observed monotonous increasing standard deviation of the orbital elements, that is, the diffusive-like behaviour of the ensemble, which results in a spatial spreading of initially confined set of particles. By linear approximation we obtained expression for the effective diffusion coefficients and estimate their dependence on the geometrical characteristics of particles and their spin. Teoretical results were compared with numerical simulations performed for the putative dust tori of Mars. Our theory agrees fairly well with simulations for the initial period of the system evolution. The agreement however deteriorates with increasing time where impact of the non-linear terms of the perturbation equations becomes important. Analysis shows that the theoretical results may estimate the low boundary of the time-dependent standard deviation of the orbital elements. In the case of dust ejected from Martian moon Deimos we observed a change of orbital elements up to 10% of their initial values during the first 1000 years of orbital evolution. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may, together with further noise sources (shadow, planetary bowshock, charge fluctuations, etc
Stochastic dynamics and Parrondo’s paradox
NASA Astrophysics Data System (ADS)
Behrends, Ehrhard
2008-02-01
The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures. The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A1,…,Ar. For every ρ=1,…,r there is prescribed a strict contraction Γρ:Aρ→M. A random walk ( on M is then defined as follows. The starting position is X0=x0, where x0∈M is fixed, and if the walk at the m’th step is at position Xm∈M, then one chooses a ρ among the ρ with Xm∈Aρ (with equal probability, say) and defines X as Γρ(Xm). Associated with the walk is a gainφ(Xm) in every round, where φ:M→R is a continuous function. The aim of the present investigations is the study of the expectation Gm of φ(Xm) as a function of m. Our main result states that the sequence (Gm) is “eventually approximately periodic” provided that all Aρ are not only closed but also open in M: for every ε there is an l0∈N such that (Gm) is l0-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain. In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A1,A2, the contractions Γ1,Γ2 are rather simple, but the expectations of the gains are not even Cesáro convergent.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
Stochastic dynamics of invasion and fixation
NASA Astrophysics Data System (ADS)
Traulsen, Arne; Nowak, Martin A.; Pacheco, Jorge M.
2006-07-01
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive a simple closed formula that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counterintuitive results at different intensities of selection.
Solution Methods for Stochastic Dynamic Linear Programs.
1980-12-01
Linear Programming, IIASA , Laxenburg, Austria, June 2-6, 1980. [2] Aghili, P., R.H., Cramer and H.W. Thompson, "On the applicability of two- stage...Laxenburg, Austria, May, 1978. [52] Propoi, A. and V. Krivonozhko, ’The simplex method for dynamic linear programs", RR-78-14, IIASA , Vienna, Austria
Finite dimensional Markov process approximation for stochastic time-delayed dynamical systems
NASA Astrophysics Data System (ADS)
Sun, Jian-Qiao
2009-05-01
This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. A simple one-dimensional stochastic system is used to demonstrate the method and the theory. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.
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.
On the dynamical-stochastic dualism of rainfall intermittency
NASA Astrophysics Data System (ADS)
Molini, Annalisa
2013-04-01
Intermittency and its non-universal signature in rainfall scaling functions still impose limitations on the modeling of precipitation across different temporal and spatial scales. Whether rainfall intermittency can be considered (and modeled) as a dynamical phenomenon connected with the precipitation generation mechanism or a predominantly stochastic process remains in fact an open question. Fat-tail probability distributions and red-noise spectra were found characterizing the rainfall process over a wide range of scales and climatic regimes - in analogy with some classical non-linear systems displaying "dynamical" intermittency. However, stochastic processes with infinite degrees of freedom can likewise generate signals with alternating persistent laminar periods and highly bursting phases. This talk explores the dynamical-stochastic dichotomy of precipitation, by presenting some recent advancement in the description of temporal rainfall intermittency. We focus on the connection between intermittency and the rainfall generation process, as well as the dependence of intermittency statistics on different climatic regimes, with particular emphasis on arid and semi-arid climates, where intermittency and convection are the main hallmark of the rainfall regime.
Stochastic circumplanetary Dynamics of rotating non-spherical Dust Particles
NASA Astrophysics Data System (ADS)
Makuch, M.; Brilliantov, N. V.; Sremcevic, M.; Spahn, F.; Krivov, A. V.
We investigate the influence of stochastically fluctuating radiation pressure on the dynamics of dust grains on circumplanetary orbits. The stochasticity stems from the permanent change of the particle cross-section exposed to the solar radiation due to rotation of nonspherical grains. Therefore, the stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of rotating particles, such as orientational time-correlation function of an individual grain. We evaluate this function and observe that it depends on the characteristic angular velocity of particles, which according to our estimates, spin very fast on the time scale of the orbital motion. This allows to model the stochastic part of the radiation pressure by a Gaussian white noise. The parameters of the noise are expressed in terms of the particle's geometric properties and their characteristic spin. In our analytical approach we use the Gauss perturbation equations with the radiation pressure being a sum of the deterministic and stochastic component and analyse the dynamics of a grains ensemble. We observe a steadily increasing standard deviation of the orbital elements, that is, the diffusive-like behaviour of the ensemble, which results in a spatial spreading of initially confined set of particles. In the linear approximation we obtain analytical expression for the effective diffusion coefficients and estimate their dependence on the geometrical characteristics of particles and their spin. The results of our analytical theory were compared with extensive numerical simulations performed for a specific dust complex, the putative dust tori of Mars. We found that our theory agrees fairly well with simulations for the initial period of the system evolution. The agreement however deteriorates at later time when the impact of the non-linear terms of the perturbation equations, neglected in our theory, becomes important. Nevertheless, the analysis shows that the theoretical
Stochastic Population Dynamics of a Montane Ground-Dwelling Squirrel
Hostetler, Jeffrey A.; Kneip, Eva; Van Vuren, Dirk H.; Oli, Madan K.
2012-01-01
Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990–2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1) for 9 out of 18 years. The stochastic population growth rate λs was 0.92, suggesting a declining population; however, the 95% CI on λs included 1.0 (0.52–1.60). Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years) probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration. PMID:22479616
Stochastic population dynamics of a montane ground-dwelling squirrel.
Hostetler, Jeffrey A; Kneip, Eva; Van Vuren, Dirk H; Oli, Madan K
2012-01-01
Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1) for 9 out of 18 years. The stochastic population growth rate λ(s) was 0.92, suggesting a declining population; however, the 95% CI on λ(s) included 1.0 (0.52-1.60). Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years) probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.
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.
Stochastic beam dynamics in quasi-isochronous storage rings
Bai, M.; Jeon, D.; Lee, S.Y.; Ng, K.Y.; Riabko, A.; Zhao, X. |
1997-03-01
We investigate effects of quantum fluctuation, potential well distortion, quantum lifetime, and Touschek lifetime of the quasi-isochronous (QI) dynamical system. The Fokker-Planck equation is employed to study the equilibrium bunch distribution. The quantum lifetime in the moderate damping regime is compared with analytical formulae. The effects of harmonic radio-frequency phase modulation on equilibrium distribution function, quantum lifetime reduction, and the occurrence of stochastic resonance are studied. The formula for the Touschek lifetime for the QI dynamical system is derived and studied. {copyright} {ital 1997} {ital The American Physical Society}
Cycles, stochasticity and density dependence in pink salmon population dynamics
Krkošek, Martin; Hilborn, Ray; Peterman, Randall M.; Quinn, Thomas P.
2011-01-01
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
Stochastic circumplanetary dynamics of rotating non-spherical dust particles
NASA Astrophysics Data System (ADS)
Makuch, Martin; Brilliantov, Nikolai V.; Sremčević, Miodrag; Spahn, Frank; Krivov, Alexander V.
2006-08-01
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth.
Stochastic dynamics with a mesoscopic bath
NASA Astrophysics Data System (ADS)
Plyukhin, Alexander V.; Schofield, Jeremy
2001-10-01
We consider the effects of bath size on the nature of the dynamics and transport properties for two simple models in which the bath is composed of a collinear chain of harmonic oscillators. The first model consists of an untwisted rotating chain (elastic rotor) for which we obtain a non-Markovian equation analogous to the generalized Langevin equation for the rotational degrees of freedom. We demonstrate that the corresponding memory function oscillates with a frequency close to that of the lowest mode of the chain. The second model considered consists of a tagged oscillator in a finite harmonic chain. For this model, we find an additional harmonic force in the generalized Langevin equation for the terminal atom that does not appear in the equation of motion for the semi-infinite chain. It is demonstrated that the force constant for the additional harmonic force scales as 1/N, where N is the number of oscillators in the chain. Using an exact representation for the velocity correlation function, the transport properties of the model are discussed.
Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics
Molina, Ignacio; Theodoropoulos, Constantinos
2014-01-01
A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to
Modeling bacterial population growth from stochastic single-cell dynamics.
Alonso, Antonio A; Molina, Ignacio; Theodoropoulos, Constantinos
2014-09-01
A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to
Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems
NASA Astrophysics Data System (ADS)
Sun, Jian-Qiao
This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.
A stochastic boundary forcing for dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Altenhoff, Adrian M.; Walther, Jens H.; Koumoutsakos, Petros
2007-07-01
The method of dissipative particle dynamics (DPD) is an effective, coarse grained model of the hydrodynamics of complex fluids. DPD simulations of wall-bounded flows are however often associated with spurious fluctuations of the fluid properties near the wall. We present a novel stochastic boundary forcing for DPD simulations of wall-bounded flows, based on the identification of fluctuations in simulations of the corresponding homogeneous system at equilibrium. The present method is shown to enforce accurately the no-slip boundary condition, while minimizing spurious fluctuations of material properties, in a number of benchmark problems.
Hierarchy of Stochastic Pure States for Open Quantum System Dynamics
NASA Astrophysics Data System (ADS)
Suess, D.; Eisfeld, A.; Strunz, W. T.
2014-10-01
We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact reduced density operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate that HOPS provides an efficient theoretical tool and apply it to the spin-boson model, the calculation of absorption spectra of molecular aggregates, and energy transfer in a photosynthetic pigment-protein complex.
Stochastic Dynamics of Charge Fluctuations in Dusty Plasma
NASA Astrophysics Data System (ADS)
Asgari, H.; Muniandy, S. V.; Wong, C. S.
2011-11-01
Dust particles immersed in plasma acquire charge by collecting electrons and ions and also by emitting electrons. The grain charge fluctuates due to the discrete nature of the charge. The rates of ions and electrons capturing depend on the grain charge and therefore on the history of the absorption. Memory effects can be introduced into stochastic charging dynamics by generalizing the standard Langevin equation to fractional Langevin equation with shifted fractional derivative. The temporal autocorrelation function of grain charge fluctuation is derived and average amplitude of fluctuations is determined.
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
2008-05-15
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.
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
Evaluation of Electric Power Procurement Strategies by Stochastic Dynamic Programming
NASA Astrophysics Data System (ADS)
Saisho, Yuichi; Hayashi, Taketo; Fujii, Yasumasa; Yamaji, Kenji
In deregulated electricity markets, the role of a distribution company is to purchase electricity from the wholesale electricity market at randomly fluctuating prices and to provide it to its customers at a given fixed price. Therefore the company has to take risk stemming from the uncertainties of electricity prices and/or demand fluctuation instead of the customers. The way to avoid the risk is to make a bilateral contact with generating companies or install its own power generation facility. This entails the necessity to develop a certain method to make an optimal strategy for electric power procurement. In such a circumstance, this research has the purpose for proposing a mathematical method based on stochastic dynamic programming and additionally considering the characteristics of the start-up cost of electric power generation facility to evaluate strategies of combination of the bilateral contract and power auto-generation with its own facility for procuring electric power in deregulated electricity market. In the beginning we proposed two approaches to solve the stochastic dynamic programming, and they are a Monte Carlo simulation method and a finite difference method to derive the solution of a partial differential equation of the total procurement cost of electric power. Finally we discussed the influences of the price uncertainty on optimal strategies of power procurement.
A Stochastic-Dynamic Model for Real Time Flood Forecasting
NASA Astrophysics Data System (ADS)
Chow, K. C. A.; Watt, W. E.; Watts, D. G.
1983-06-01
A stochastic-dynamic model for real time flood forecasting was developed using Box-Jenkins modelling techniques. The purpose of the forecasting system is to forecast flood levels of the Saint John River at Fredericton, New Brunswick. The model consists of two submodels: an upstream model used to forecast the headpond level at the Mactaquac Dam and a downstream model to forecast the water level at Fredericton. Inputs to the system are recorded values of the water level at East Florenceville, the headpond level and gate position at Mactaquac, and the water level at Fredericton. The model was calibrated for the spring floods of 1973, 1974, 1977, and 1978, and its usefulness was verified for the 1979 flood. The forecasting results indicated that the stochastic-dynamic model produces reasonably accurate forecasts for lead times up to two days. These forecasts were then compared to those from the existing forecasting system and were found to be as reliable as those from the existing system.
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.
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.
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.
Stochastic cellular automata model for stock market dynamics
NASA Astrophysics Data System (ADS)
Bartolozzi, M.; Thomas, A. W.
2004-04-01
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, σi (t)=+1 , or sell, σi (t)=-1 , a stock at a certain discrete time step. The remaining cells are inactive, σi (t)=0 . The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P500 index.
Stochastic cellular automata model for stock market dynamics.
Bartolozzi, M; Thomas, A W
2004-04-01
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, sigma(i) (t)=+1, or sell, sigma(i) (t)=-1, a stock at a certain discrete time step. The remaining cells are inactive, sigma(i) (t)=0. The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P 500 index.
NASA Astrophysics Data System (ADS)
Abramov, Rafail V.
2017-03-01
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.
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.
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.
Stochastic dynamics of particles trapped in turbulent flows.
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 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.
The stochastic system approach for estimating dynamic treatments effect.
Commenges, Daniel; Gégout-Petit, Anne
2015-10-01
The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.
Efficient stochastic thermostatting of path integral molecular dynamics.
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E
2010-09-28
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Efficient stochastic thermostatting of path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-09-01
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
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
Setting development goals using stochastic dynamical system models
Nicolis, Stamatios C.; Bali Swain, Ranjula; Sumpter, David J. T.
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers. PMID:28241057
Application of stochastic processes in random growth and evolutionary dynamics
NASA Astrophysics Data System (ADS)
Oikonomou, Panagiotis
We study the effect of power-law distributed randomness on the dynamical behavior of processes such as stochastic growth patterns and evolution. First, we examine the geometrical properties of random shapes produced by a generalized stochastic Loewner Evolution driven by a superposition of a Brownian motion and a stable Levy process. The situation is defined by the usual stochastic Loewner Evolution parameter, kappa, as well as alpha which defines the power-law tail of the stable Levy distribution. We show that the properties of these patterns change qualitatively and singularly at critical values of kappa and alpha. It is reasonable to call such changes "phase transitions". These transitions occur as kappa passes through four and as alpha passes through one. Numerical simulations are used to explore the global scaling behavior of these patterns in each "phase". We show both analytically and numerically that the growth continues indefinitely in the vertical direction for alpha greater than 1, goes as logarithmically with time for alpha equals to 1, and saturates for alpha smaller than 1. The probability density has two different scales corresponding to directions along and perpendicular to the boundary. Scaling functions for the probability density are given for various limiting cases. Second, we study the effect of the architecture of biological networks on their evolutionary dynamics. In recent years, studies of the architecture of large networks have unveiled a common topology, called scale-free, in which a majority of the elements are poorly connected except for a small fraction of highly connected components. We ask how networks with distinct topologies can evolve towards a pre-established target phenotype through a process of random mutations and selection. We use networks of Boolean components as a framework to model a large class of phenotypes. Within this approach, we find that homogeneous random networks and scale-free networks exhibit drastically
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
2015-06-07
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.
Nonlinear dynamic characteristics of SMA intravascular stent under radial stochastic loads.
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-01-01
Nonlinear dynamic characteristics of shape memory alloy (SMA) intravascular stent under radial stochastic loads were studied in this paper. Von de Pol item was improved to interpret the hysteretic phenomena of SMA, and the nonlinear dynamic model of SMA intravascular stent under radial stochastic loads was developed. The conditions of stochastic stability of the system were obtained in singular boundary theory. The steady-state probability density function of the dynamic response of the system was given, and the stochastic Hopf bifurcation characteristics of the system were analyzed. Theoretical analysis and numerical simulation show that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process, which can cause stent fracture or loss. The results of this paper are helpful to application of SMA intravascular stent in biomedical engineering fields.
Stochastic dynamics of the prisoner's dilemma with cooperation facilitators.
Mobilia, Mauro
2012-07-01
In the framework of the paradigmatic prisoner's dilemma game, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators." In our model, cooperators and defectors interact as in the classical prisoner's dilemma, where selection favors defection. However, here the presence of a small number of cooperation facilitators enhances the fitness (reproductive potential) of cooperators, while it does not alter that of defectors. In a finite population of size N, the dynamics of the prisoner's dilemma with facilitators is characterized by the probability that cooperation takes over (fixation probability) by the mean times to reach the absorbing states. These quantities are computed exactly using Fokker-Planck equations. Our findings, corroborated by stochastic simulations, demonstrate that the influence of facilitators crucially depends on the difference between their density z and the game's cost-to-benefit ratio r. When z > r, the fixation of cooperators is likely in a large population and, under weak selection pressure, invasion and replacement of defection by cooperation is favored by selection if b(z - r)(1 - z) > N(-1), where 0
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.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
NASA Astrophysics Data System (ADS)
Zeng, Caibin; Yang, Qigui
2015-12-01
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.
Transition probability estimates for non-Markov multi-state models.
Titman, Andrew C
2015-12-01
Non-parametric estimation of the transition probabilities in multi-state models is considered for non-Markov processes. Firstly, a generalization of the estimator of Pepe et al., (1991) (Statistics in Medicine) is given for a class of progressive multi-state models based on the difference between Kaplan-Meier estimators. Secondly, a general estimator for progressive or non-progressive models is proposed based upon constructed univariate survival or competing risks processes which retain the Markov property. The properties of the estimators and their associated standard errors are investigated through simulation. The estimators are demonstrated on datasets relating to survival and recurrence in patients with colon cancer and prothrombin levels in liver cirrhosis patients.
Stochastic dynamics of interacting haematopoietic stem cell niche lineages.
Székely, Tamás; Burrage, Kevin; Mangel, Marc; Bonsall, Michael B
2014-09-01
Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.
Filtering nonlinear dynamical systems with linear stochastic models
NASA Astrophysics Data System (ADS)
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
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.
Stochastic modeling of stem-cell dynamics with control.
Sun, Zheng; Komarova, Natalia L
2012-12-01
Tissue development and homeostasis are thought to be regulated endogenously by control loops that ensure that the numbers of stem cells and daughter cells are maintained at desired levels, and that the cell dynamics are robust to perturbations. In this paper we consider several classes of stochastic models that describe stem/daughter cell dynamics in a population of constant size, which are generalizations of the Moran process that include negative control loops that affect differentiation probabilities for stem cells. We present analytical solutions for the steady-state expectations and variances of the numbers of stem and daughter cells; these results remain valid for non-constant cell populations. We show that in the absence of differentiation/proliferation control, the number of stem cells is subject to extinction or overflow. In the presence of linear control, a steady state may be maintained but no tunable parameters are available to control the mean and the spread of the cell population sizes. Two types of nonlinear control considered here incorporate tunable parameters that allow specification of the expected number of stem cells and also provide control over the size of the standard deviation. We show that under a hyperbolic control law, there is a trade-off between minimizing standard deviations and maintaining the system robustness against external perturbations. For the Hill-type control, the standard deviation is inversely proportional to the Hill coefficient of the control loop. Biologically this means that ultrasensitive response that is observed in a number of regulatory loops may have evolved in order to reduce fluctuations while maintaining the desired population levels.
Point Set Registration via Particle Filtering and Stochastic Dynamics
Sandhu, Romeil; Dambreville, Samuel; Tannenbaum, Allen
2013-01-01
In this paper, we propose a particle filtering approach for the problem of registering two point sets that differ by a rigid body transformation. Typically, registration algorithms compute the transformation parameters by maximizing a metric given an estimate of the correspondence between points across the two sets of interest. This can be viewed as a posterior estimation problem, in which the corresponding distribution can naturally be estimated using a particle filter. In this work, we treat motion as a local variation in pose parameters obtained by running a few iterations of a certain local optimizer. Employing this idea, we introduce stochastic motion dynamics to widen the narrow band of convergence often found in local optimizer approaches for registration. Thus, the novelty of our method is threefold: First, we employ a particle filtering scheme to drive the point set registration process. Second, we present a local optimizer that is motivated by the correlation measure. Third, we increase the robustness of the registration performance by introducing a dynamic model of uncertainty for the transformation parameters. In contrast with other techniques, our approach requires no annealing schedule, which results in a reduction in computational complexity (with respect to particle size) as well as maintains the temporal coherency of the state (no loss of information). Also unlike some alternative approaches for point set registration, we make no geometric assumptions on the two data sets. Experimental results are provided that demonstrate the robustness of the algorithm to initialization, noise, missing structures, and/or differing point densities in each set, on several challenging 2D and 3D registration scenarios. PMID:20558877
a Stochastic Newmark Method for Engineering Dynamical Systems
NASA Astrophysics Data System (ADS)
ROY, D.; DASH, M. K.
2002-01-01
The purpose of this study is to develop a stochastic Newmark integration principle based on an implicit stochastic Taylor (Ito-Taylor or Stratonovich-Taylor) expansion of the vector field. As in the deterministic case, implicitness in stochastic Taylor expansions for the displacement and velocity vectors is achieved by introducing a couple of non-unique integration parameters, α and β. A rigorous error analysis is performed to put bounds on the local and global errors in computing displacements and velocities. The stochastic Newmark method is elegantly adaptable for obtaining strong sample-path solutions of linear and non-linear multi-degree-of freedom (m.d.o.f.) stochastic engineering systems with continuous and Lipschitz-bounded vector fields under (filtered) white-noise inputs. The method has presently been numerically illustrated, to a limited extent, for sample-path integration of a hardening Duffing oscillator under additive and multiplicative white-noise excitations. The results are indicative of consistency, convergence and stochastic numerical stability of the stochastic Newmark method (SNM).
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.
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.
Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales
Xiu, Dongbin
2016-06-21
The focus of the project is the development of mathematical methods and high-performance com- putational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly e cient and scalable numer- ical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.
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
Dynamics of semi-flexible tethered sheets : a simulation study using stochastic rotation dynamics.
Babu, S B; Stark, H
2011-12-01
The dynamics of a semi-flexible sheet or tethered membrane in a solvent is studied using the method of stochastic rotation dynamics. Hydrodynamic interactions between different parts of the sheet are naturally included in this method. We confirm the scaling law for the radius of gyration versus sheet size predicted for a self-avoiding tethered membrane. The mean-square displacement shows both sub-diffusive and diffusive behavior similar to linear polymers. In the intermediate scattering function the sub-diffusive behavior appears as stretched exponential which we reproduce in our simulations. Thereby, we confirm an early prediction between the roughness and the sub-diffusion exponent derived from Zimm dynamics (E. Frey, D.R. Nelson, J. Phys. I 1, 1715 (1991)). Finally, we show that the diffusion coefficient of the square sheet is inversely proportional to the edge length of the sheet again in good agreement with theoretical predictions.
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination.
Wang, Lei; Teng, Zhidong; Tang, Tingting; Li, Zhiming
2017-01-01
In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.
Dynamics of stochastic SEIS epidemic model with varying population size
NASA Astrophysics Data System (ADS)
Liu, Jiamin; Wei, Fengying
2016-12-01
We introduce the stochasticity into a deterministic model which has state variables susceptible-exposed-infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô's formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.
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.
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)
Modeling of stochastic dynamics of time-dependent flows under high-dimensional random forcing
NASA Astrophysics Data System (ADS)
Babaee, Hessam; Karniadakis, George
2016-11-01
In this numerical study the effect of high-dimensional stochastic forcing in time-dependent flows is investigated. To efficiently quantify the evolution of stochasticity in such a system, the dynamically orthogonal method is used. In this methodology, the solution is approximated by a generalized Karhunen-Loeve (KL) expansion in the form of u (x , t ω) = u ̲ (x , t) + ∑ i = 1 N yi (t ω)ui (x , t) , in which u ̲ (x , t) is the stochastic mean, the set of ui (x , t) 's is a deterministic orthogonal basis and yi (t ω) 's are the stochastic coefficients. Explicit evolution equations for u ̲ , ui and yi are formulated. The elements of the basis ui (x , t) 's remain orthogonal for all times and they evolve according to the system dynamics to capture the energetically dominant stochastic subspace. We consider two classical fluid dynamics problems: (1) flow over a cylinder, and (2) flow over an airfoil under up to one-hundred dimensional random forcing. We explore the interaction of intrinsic with extrinsic stochasticity in these flows. DARPA N66001-15-2-4055, Office of Naval Research N00014-14-1-0166.
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…
Dynamically Active Compartments Coupled by a Stochastically Gated Gap Junction
NASA Astrophysics Data System (ADS)
Bressloff, Paul C.; Lawley, Sean D.
2017-03-01
We analyze a one-dimensional PDE-ODE system representing the diffusion of signaling molecules between two cells coupled by a stochastically gated gap junction. We assume that signaling molecules diffuse within the cytoplasm of each cell and then either bind to some active region of the cell's membrane (treated as a well-mixed compartment) or pass through the gap junction to the interior of the other cell. We treat the gap junction as a randomly fluctuating gate that switches between an open and a closed state according to a two-state Markov process. This means that the resulting PDE-ODE is stochastic due to the presence of a randomly switching boundary in the interior of the domain. It is assumed that each membrane compartment acts as a conditional oscillator, that is, it sits below a supercritical Hopf bifurcation. In the ungated case (gap junction always open), the system supports diffusion-induced oscillations, in which the concentration of signaling molecules within the two compartments is either in-phase or anti-phase. The presence of a reflection symmetry (for identical cells) means that the stochastic gate only affects the existence of anti-phase oscillations. In particular, there exist parameter choices where the gated system supports oscillations, but the ungated system does not, and vice versa. The existence of oscillations is investigated by solving a spectral problem obtained by averaging over realizations of the stochastic gate.
Identifying type I excitability using dynamics of stochastic neural firing patterns.
Jia, Bing; Gu, Huaguang
2012-12-01
The stochastic firing patterns are simulated near saddle-node bifurcation on an invariant cycle corresponding to type I excitability in stochastic Morris-Lecar model. In absence of external periodic signal, the stochastic firing manifests continuous distribution in ISI histogram (ISIH), whose amplitude at first increases sharply and then decreases exponentially. In presence of the external periodic signal, stochastic firing patterns appear as two cases of integer multiple firing with multiple discrete peaks in ISIH. One manifests perfect exponential decay in all peaks and the other imperfect exponential decay except a lower first peak. These stochastic firing patterns simulated with or without external periodic signal can be demonstrated in the experiments on rat hippocampal CA1 pyramidal neurons. The exponential decay laws in the multiple peaks are also acquired using probability analysis method. The perfect decay law is determined by the independent characteristic within the firing while the imperfect decay law is from the inhibitory effect. In addition, the stochastic firing patterns corresponding to type I excitability are compared to those of type II excitability. The results not only reveal the dynamics of stochastic firing patterns with or without external signal corresponding to type I excitability, but also provide practical indicators to availably identify type I excitability.
Rosenbaum, Robert; Rubin, Jonathan E; Doiron, Brent
2013-01-01
Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.
Wang, Weikang; Quan, Yi; Fu, Qibin; Liu, Yu; Liang, Ying; Wu, Jingwen; Yang, Gen; Luo, Chunxiong; Ouyang, Qi; Wang, Yugang
2014-01-01
Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy. PMID:24416258
Mixed quantal-semiquantal dynamics with stochastic particles for backreaction
Ando, Koji
2014-10-14
A mixed quantal-semiquantal theory is presented in which the semiquantal squeezed-state wave packet describes the heavy degrees of freedom. Starting from the mean-field equations of motion that are naturally derived from the time-dependent variational principle, we introduce the stochastic particle description for both the quantal and semiquantal parts in an aim to take into account the interparticle correlation, in particular the “quantum backreaction” beyond the mean-field approximation. A numerical application on a model of O{sub 2} scattering from a Pt surface demonstrates that the proposed scheme gives correct asymptotic behavior of the scattering probability, with improvement over the mixed quantum-classical scheme with Bohmian particles, which is comprehended by comparing the Bohmian and the stochastic trajectories.
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.
Dynamic data integration and stochastic inversion of a confined aquifer
NASA Astrophysics Data System (ADS)
Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.
2013-12-01
Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing
Sampling-Based RBDO Using Stochastic Sensitivity and Dynamic Kriging for Broader Army Applications
2011-08-09
AND DYNAMIC KRIGING FOR BROADER ARMY APPLICATIONS K.K. Choi, Ikjin Lee, Liang Zhao, and Yoojeong Noh Department of Mechanical and Industrial...Thus, for broader Army applications, a sampling-based RBDO method using surrogate model has been developed recently. The Dynamic Kriging (DKG) method...Uuing Stochastic Sensitivity and Dynamic Kriging for Broader Army Applications 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
Lacroix, Denis
2005-06-01
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
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.
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>
Stochastic Modeling of the Persistence of HIV: Early Population Dynamics
2013-05-10
also given to the Trident Committee, especially Prof Kidwell , for their support. Finally, I owe a debt of gratitude to friends and family for their...Code 50 4 List of Figures 1.1 Illustration of 3CM 7 2.1 Graphs of R < 1, R > 1 15 2.2 A flow chart representation of the functions involved in...A simulation of the stochastic model with R =8.18 43 6.1 Histograms of end state values from ODE w/ RV coefficients 45 6.2 Histograms of end state
Stochastic dynamics of the chlorite-iodide reaction
NASA Astrophysics Data System (ADS)
Sagués, F.; Ramírez-Piscina, L.; Sancho, J. M.
1990-04-01
A recently proposed theoretical framework appropriate to the study of the stochastic behavior of several chemical systems is used to analyze the irreproducibility of the observed reaction times in the chlorite-iodide clock reaction. Noise terms are incorporated through the kinetic constants and their intensity is further correlated with the inverse of the stirring rate. Analytical and simulation results are obtained for the first moments of the reaction time distribution. These results are compared with recent experimental data obtained by Nagypál and Epstein.
Stochastic modeling of uncertain mass characteristics in rigid body dynamics
NASA Astrophysics Data System (ADS)
Richter, Lanae A.; Mignolet, Marc P.
2017-03-01
This paper focuses on the formulation, assessment, and application of a modeling strategy of uncertainty on the mass characteristics of rigid bodies, i.e. mass, position of center of mass, and inertia tensor. These characteristics are regrouped into a 4×4 matrix the elements of which are represented as random variables with joint probability density function derived following the maximum entropy framework. This stochastic model is first shown to satisfy all properties expected of the mass and tensor of inertia of rigid bodies. Its usefulness and computational efficiency are next demonstrated on the behavior of a rigid body in pure rotation exhibiting significant uncertainty in mass distribution.
Stochastic dynamics and a power law for measles variability.
Keeling, M; Grenfell, B
1999-01-01
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size. PMID:10365402
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)
Liu, Jie; Sun, Xingsheng; Han, Xu; Jiang, Chao; Yu, Dejie
2015-05-01
Based on the Gegenbauer polynomial expansion theory and regularization method, an analytical method is proposed to identify dynamic loads acting on stochastic structures. Dynamic loads are expressed as functions of time and random parameters in time domain and the forward model of dynamic load identification is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions of system. Random parameters are approximated through the random variables with λ-probability density function (PDFs) or their derivative PDFs. For this kind of random variables, Gegenbauer polynomial expansion is the unique correct choice to transform the problem of load identification for a stochastic structure into its equivalent deterministic system. Just via its equivalent deterministic system, the load identification problem of a stochastic structure can be solved by any available deterministic methods. With measured responses containing noise, the improved regularization operator is adopted to overcome the ill-posedness of load reconstruction and to obtain the stable and approximate solutions of certain inverse problems and the valid assessments of the statistics of identified loads. Numerical simulations demonstrate that with regard to stochastic structures, the identification and assessment of dynamic loads are achieved steadily and effectively by the presented method.
NASA Astrophysics Data System (ADS)
Caraballo, Tomás; Morillas, F.; Valero, J.
In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.
Adaptive and Distributed Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment
2010-11-18
stochastic and dynamic vehicle routing problems,” PhD Thesis, Dept. of Civil and Environmental Engineering , Massachusetts Institute of Technology ... Technology (MIT), Cam- bridge, in 2001. From 2001 to 2004, he was an Assistant Professor of aerospace engineering at the University of Illinois at Urbana...system. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known con- trol algorithms rely on
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.
Simulation of Quantum Dynamics Based on the Quantum Stochastic Differential Equation
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
Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.
Li, Xiao-Jian; Yang, Guang-Hong
2017-02-01
This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.
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.
Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits.
Soltani, Mohammad; Vargas-Garcia, Cesar Augusto; Singh, Abhyudai
2015-08-01
Inside individual cells, stochastic expression drives random fluctuations in gene product copy numbers, which corrupts functioning of both natural and synthetic genetic circuits. Dynamic models of genetic circuits are formulated stochastically using the chemical master equation framework. Since obtaining probability distributions can be computationally expensive in these models, noise is typically investigated through lower-order statistical moments (mean, variance, correlation, skewness, etc.) of mRNA/proteins levels. However, due to the nonlinearities in genetic circuits, this moment dynamics is typically not closed, in the sense that the time derivative of the lower-order statistical moments depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. We provide a new moment closure scheme for studying stochastic dynamics of genetic circuits, where genes randomly toggle between transcriptionally active and inactive states. The method is based on conditioning protein levels on active states of genes and then expressing higher-order moments as functions of lower-order conditional moments. The conditional closure scheme is illustrated on different circuit motifs and found to outperform existing closure techniques. Rapid computation of stochasticity through closure methods will enable improved characterization and design of synthetic circuits that exhibit robust performance in spite of noisy expression of underlying genes.
Characterizing the dynamics of rubella relative to measles: the role of stochasticity
Rozhnova, Ganna; Metcalf, C. Jessica E.; Grenfell, Bryan T.
2013-01-01
Rubella is a completely immunizing and mild infection in children. Understanding its behaviour is of considerable public health importance because of congenital rubella syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The recurrent dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behaviour of a stochastic seasonally forced susceptible–infected–recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the recurrent patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections. PMID:24026472
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; ...
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
2015-10-06
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.
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.
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
Wang, Lei; Tang, Tingting
2017-01-01
In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed. PMID:28194223
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
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.
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.
Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports
Schilde, M.; Doerner, K.F.; Hartl, R.F.
2011-01-01
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
Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.
Venturi, D; Karniadakis, G E
2014-06-08
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.
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.
Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module.
Gonzalez-Navarrete, Manuel
2016-10-01
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression. We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator.
Generalized principles of stochasticity can be used to control dynamic heterogeneity
Liao, David; Estévez-Salmerón, Luis; Tlsty, Thea D.
2012-01-01
It is increasingly appreciated that phenotypic stochasticity plays fundamental roles in biological systems at the cellular level and that a variety of mechanisms generates phenotypic interconversion over a broad range of time scales. The ensuing dynamic heterogeneity can be used to understand biological and clinical processes involving diverse phenotypes in different cell populations. The same principles can be applied, not only to populations composed of cells, but also to populations composed of molecules, tissues, and multicellular organisms. Stochastic units generating dynamic heterogeneity can be integrated across various length scales. We propose that a graphical tool we have developed, called a metronomogram, will allow us to identify factors that suitably influence the restoration of homeostatic heterogeneity so as to modulate the consequences of dynamic heterogeneity for desired outcomes. PMID:23197162
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.
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
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.
Research on Nonlinear and Stochastic Dynamics with Defense Applications
2009-03-30
Y.-C. Lai, " Fractal dimension in dissipative chaotic scatter- ing," Physical Review E 76, 016208(1-6) (2007). • J. M. Seoane, L. Huang, M. A. F...complex basin topology. We have also investigated how the fractal dimension of the set of singularities in scattering function varies as the system...exponents and fractal dimensions are developed for stationary dynamical systems. We have proposed a framework to characterize nonstationary dynamical
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
Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics.
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.
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.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
NASA Astrophysics Data System (ADS)
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-01
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.
Stochastic dynamics of model proteins on a directed graph.
Bongini, Lorenzo; Casetti, Lapo; Livi, Roberto; Politi, Antonio; Torcini, Alessandro
2009-06-01
A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs" while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between "fast" and "slow" folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.
NASA Astrophysics Data System (ADS)
Gu, Anhui; Li, Yangrong
The paper is devoted to establishing a combination of sufficient criterion for the existence and upper semi-continuity of random attractors for stochastic lattice dynamical systems. By relying on a family of random systems itself, we first set up the abstract result when it is convergent, uniformly absorbing and uniformly random when asymptotically null in the phase space. Then we apply the results to the second-order lattice dynamical system driven by multiplicative white noise. It is indicated that the criterion depending on the dynamical system itself seems more applicable than the existing ones to lattice differential models.
Passler, Peter P; Hofer, Thomas S
2017-02-15
Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short-coming has little impact on structural and short-time dynamic properties, it can be shown that dynamics in the long-time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD-region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard-Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose-Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self-diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc.
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.
Equilibrium solutions for microscopic stochastic systems in population dynamics.
Lachowicz, Mirosław; Ryabukha, Tatiana
2013-06-01
The present paper deals with the problem of existence of equilibrium solutions of equations describing the general population dynamics at the microscopic level of modified Liouville equation (individually--based model) corresponding to a Markov jump process. We show the existence of factorized equilibrium solutions and discuss uniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposed under the assumption of periodic structures.
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.
Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion
NASA Astrophysics Data System (ADS)
Chotorlishvili, L.; Toklikishvili, Z.; Berakdar, J.
2009-09-01
We study a chain of nonlinear interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semiclassical dynamics is chaotic. This is achievable by tuning the external field parameters according to the method described in this paper. We show analytically for a finite spin chain that Arnold diffusion is the underlying mechanism for the present stochastic control. Quantum mechanically we consider the regime where the classical dynamics is regular or chaotic. For the latter we utilize the random matrix theory. The efficiency and the stability of the non-equilibrium quantum spin states are quantified by the time dependence of the Bargmann angle related to the geometric phases of the states.
NASA Astrophysics Data System (ADS)
Yu, Xin; Xie, Xue-Jun; Wu, Yu-Qiang
2010-10-01
This article further discusses the problem of output-feedback regulation for more general stochastic nonlinear systems with stochastic integral input-to-state stable inverse dynamics, and focuses on solving the important and unsolved problem proposed in Yu and Xie (Yu, X., and Xie, X.J. (2010), 'Output Feedback Regulation of Stochastic Nonlinear Systems with Stochastic iISS Inverse Dynamics', IEEE Transactions on Automatic Control, 55, 304-320): How to weaken the conditions on nonlinearities in drift and diffusion vector fields? Under the weaker conditions, how to make full use of the known information of stochastic nonlinear systems to design an adaptive output-feedback controller such that all the closed-loop signals are almost surely bounded and the output is driven to zero almost surely?
NASA Astrophysics Data System (ADS)
Ma, Juan; Gao, Wei; Wriggers, Peter; Wu, Tao; Sahraee, Shahab
2010-04-01
A new two-factor method based on the probability and the fuzzy sets theory is used for the analyses of the dynamic response and reliability of fuzzy-random truss systems under the stationary stochastic excitation. Considering the fuzzy-randomness of the structural physical parameters and geometric dimensions simultaneously, the fuzzy-random correlation function matrix of structural displacement response in time domain and the fuzzy-random mean square values of structural dynamic response in frequency domain are developed by using the two-factor method, and the fuzzy numerical characteristics of dynamic responses are then derived. Based on numerical characteristics of structural fuzzy-random dynamic responses, the structural fuzzy-random dynamic reliability and its fuzzy numerical characteristic are obtained from the Poisson equation. The effects of the uncertainty of the structural parameters on structural dynamic response and reliability are illustrated via two engineering examples and some important conclusions are obtained.
Path integral methods for the dynamics of stochastic and disordered systems
NASA Astrophysics Data System (ADS)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.
Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps
NASA Astrophysics Data System (ADS)
Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir
2017-04-01
This paper is to investigate the dynamics of a stochastic SIS epidemic model with saturated incidence rate and double epidemic diseases which make the research more complex. The environment variability in this study is characterized by white noise and jump noise. Sufficient conditions for the extinction and persistence in the mean of two epidemic diseases are obtained. It is shown that the two diseases can coexist under appropriate conditions. Finally, numerical simulations are introduced to illustrate the results developed.
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.
A stochastic microscopic model for the dynamics of antigenic variation.
Guerberoff, Gustavo; Alvarez-Valin, Fernando
2015-09-07
We present a novel model that describes the within-host evolutionary dynamics of parasites undergoing antigenic variation. The approach uses a multi-type branching process with two types of entities defined according to their relationship with the immune system: clans of resistant parasitic cells (i.e. groups of cells sharing the same antigen not yet recognized by the immune system) that may become sensitive, and individual sensitive cells that can acquire a new resistance thus giving rise to the emergence of a new clan. The simplicity of the model allows analytical treatment to determine the subcritical and supercritical regimes in the space of parameters. By incorporating a density-dependent mechanism the model is able to capture additional relevant features observed in experimental data, such as the characteristic parasitemia waves. In summary our approach provides a new general framework to address the dynamics of antigenic variation which can be easily adapted to cope with broader and more complex situations.
Stochastic models of cover class dynamics. [remote sensing of vegetation
NASA Technical Reports Server (NTRS)
Barringer, T. H.; Robinson, V. B.
1981-01-01
Investigations related to satellite remote sensing of vegetation have been concerned with questions of signature identification and extension, cover inventory accuracy, and change detection and monitoring. Attention is given to models of ecological succession, present directions in successional modeling and analysis, nondynamic spatial models, issues in the analysis of spatial data, and aspects of spatial modeling. Issues in time-series analysis are considered along with dynamic spatial models, and problems of model specification and identification.
Dynamic Correlation Functions of Adsorption Stochastic Systems with Diffusional Relaxation
NASA Astrophysics Data System (ADS)
Grynberg, Marcelo D.; Stinchcombe, Robin B.
1995-02-01
We investigate the nonequilibrium behavior of dynamic correlation functions of random sequential adsorption processes with diffusional relaxation. Depending on the relative values of the transition probability rates, in one dimension these systems reduce to a soluble problem of many fermions. In contrast to the standard diffusive relaxation of the macroscopic density, the correlation functions exhibit a faster decay. Our results are supported and compared with Monte Carlo simulations.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.
Daunizeau, J; Friston, K J; Kiebel, S J
2009-11-01
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.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
NASA Astrophysics Data System (ADS)
Daunizeau, J.; Friston, K. J.; Kiebel, S. J.
2009-11-01
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.
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
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.
NASA Astrophysics Data System (ADS)
Kapranov, Sergey V.; Kouzaev, Guennadi A.
2013-06-01
The motion of a dipole in external electric fields is considered in the framework of nonlinear pendulum dynamics. A stochastic layer is formed near the separatrix of the dipole pendulum in a restoring static electric field under the periodic perturbation by plane-polarized electric fields. The width of the stochastic layer depends on the direction of the forcing field variation, and this width can be evaluated as a function of perturbation frequency, amplitude, and duration. A numerical simulation of the approximate stochastic layer width of a perturbed pendulum yields a multi-peak frequency spectrum. It is described well enough at high perturbation amplitudes by an analytical estimation based on the separatrix map with an introduced expression of the most effective perturbation phase. The difference in the fractal dimensions of the phase spaces calculated geometrically and using the time-delay reconstruction is attributed to the predominant development of periodic and chaotic orbits, respectively. The correlation of the stochastic layer width with the phase space fractal dimensions is discussed.
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.
NASA Astrophysics Data System (ADS)
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2016-08-01
In this work, a non-linear dynamics of a simple three-dimensional climate model in the presence of stochastic forcing is studied. We demonstrate that a dynamic scenario of mixed-mode stochastic oscillations of the climate system near its equilibrium can be formed. As this takes place, a growth of noise intensity increases the frequency of interspike intervals responsible for the abrupt climate changes. In addition, a certain enhancement of stochastic forcing abruptly increases the atmospheric carbon dioxide and decreases the Earth's ice mass. A transition from order to chaos occurring at a critical noise is shown.
Stochastic actions for diffusive dynamics: reweighting, sampling, and minimization.
Adib, Artur B
2008-05-15
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requires the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the nondifferentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.
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.
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.
Population dynamics of wild rodents induce stochastic fadeouts of a zoonotic pathogen.
Guzzetta, Giorgio; Tagliapietra, Valentina; Perkins, Sarah E; Hauffe, Heidi C; Poletti, Piero; Merler, Stefano; Rizzoli, Annapaola
2017-02-19
Stochastic processes play an important role in the infectious disease dynamics of wildlife, especially in species subject to large population oscillations. Here we study the case of a free ranging population of yellow-necked mice (Apodemus flavicollis) in northern Italy, where circulation of Dobrava-Belgrade hantavirus (DOBV) has been detected intermittently since 2001, until an outbreak emerged in 2010. We analyzed the transmission dynamics of the recent outbreak using a computational model that accounts for seasonal changes of the host population and territorial behavior. Model parameters were informed by capture-mark-recapture data collected over 14 years and longitudinal seroprevalence data from 2010 to 2013. The intermittent observation of DOBV before 2010 can be interpreted as repeated stochastic fadeouts after multiple introductions of infectious rodents migrating from neighboring areas. We estimated that only 20% of introductions in a naïve host population results in sustained transmission after two years, despite an effective reproduction number well above the epidemic threshold (mean 4.5, 95% credible intervals, CI: 0.65-15.8). Following the 2010 outbreak, DOBV has become endemic in the study area, but we predict a constant probability of about 4.7% per year that infection dies out, following large population drops in winter. In the absence of stochastic fadeout, viral prevalence is predicted to continue its growth to an oscillating equilibrium around a value of 24% (95% CI: 3-57%). We presented an example of invasion dynamics of a zoonotic virus where stochastic fadeout have played a major role and may induce future extinction of the endemic infection. This article is protected by copyright. All rights reserved.
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
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.
Non-autonomous and stochastic dynamics of oceanic gravity currents
NASA Astrophysics Data System (ADS)
Bongolan-Walsh, Vena Pearl
The incompressible Navier-Stokes equations (the momentum, continuity and scalar transport equations) are the fundamental equations of fluid mechanics. Of great importance to weather and climate studies is the thermohaline circulation, which is affected by gravity currents, hence we chose it as our application. First, we studied the Navier-Stokes equations (without scalar transport) using non-autonomous dynamical systems techniques, and showed the existence of recurrent or Poisson stable motions under recurrent or Poisson stable forcing, respectively. This was motivated by observed periodic and recurrent motions in nature. Next, we investigated the coupled Navier-Stokes and scalar transport equations (we may take the scalar to be salinity, say), with spatially correlated white noise on the boundary. We employed random dynamical system ideas, and showed that this system is ergodic under suitable conditions for mean salinity input flux on the boundary, Prandtl number and covariance of the noise. This addition of a random term to the boundary conditions was motivated by observed seasonal variations in the salinity flux in gravity currents. The final part of this thesis are numerical simulations studying the effects of different boundary conditions on the entrainment behavior, salinity distribution and salinity transport properties of gravity currents. The finding is that gravity currents developing under Neumann and Dirichlet boundary conditions differ most in the way they transport salinity from the middle salinity parts (roughly the middle of the current) towards the fresher part (roughly the top of the current). This study contributes to understanding the behavior of the Navier-Stokes Equations under time-periodic forcings, uncertain boundary conditions, and how gravity currents are affected by different boundary conditions.
Stochastic demography and population dynamics in the red kangaroo Macropus rufus.
Jonzén, Niclas; Pople, Tony; Knape, Jonas; Sköld, Martin
2010-01-01
1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.
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)
Zhu, Z. W.; Zhang, W. D.; Xu, J.
2014-03-01
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.
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.
Sahoo, Avimanyu; Jagannathan, Sarangapani
2017-02-01
In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.
NASA Astrophysics Data System (ADS)
Nataraju, Madhura; Johnson, Timothy J.; Adams, Douglas E.
2003-07-01
Environmental and operational variability due to changes in the excitation or any other variable can mimic or altogether obscure evidence of structural defects in measured data leading to false positive/negative diagnoses of damage and conservative/tolerant predictions of remaining useful life in structural health monitoring system. Diagnostic and prognostic errors like these in many types of commercial and defense-related applications must be eliminated if health monitoring is to be widely implemented in these applications. A theoretical framework of "dynamic similiarity" in which two sets of mathematical operators are utilized in one system/data model to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish damage from nonlinear, time-varying and stochastic events in the measured data is discussed in this paper. Because structural damage initiation, evolution and accumulation are nonlinear processes, the challenge here is to distinguish abnormal from normal nonlinear dynamics, which are accentuated by physically or statistically non-stationary events in the operating environment. After discussing several examples of structural diagnosis and prognosis involving dynamic similarity, a simplifeid numerical finite element model of a helicopter blade with time-varying flexural stiffness on a nonlinear aerodynamic elastic foundation that is subjected to a stochastic base excitation is utilized to introduce and examine the effects of dynamic similarity on health monitoring systems. It is shown that environmental variability can be distinguished from structural damage using a physics-based model in conjunction with the dynamic similarity operators to develop more robust damage detection algorithms, which may prove to be more accurate and precise when operating conditions fluctuate.
Using stochastic dynamics to validate runtimes of protein simulations
NASA Astrophysics Data System (ADS)
Hicks, Stephen D.; Henley, Christopher L.
2009-03-01
We use short molecular dynamics simulations (˜200 cpu-hr, using NAMD) of individual bonds between capsid proteins to microscopically determine coarse-grained elastic parameters of entire virus capsids. In particular, we treat each protein (or for larger proteins, each domain) as a rigid body described by a 6-vector of translational and orientational degrees of freedom, xi(t). We then model the evolution of the relative positions as an overdamped random walk, xi(t) = -γijKjk(xk(t)-xk) + ζi(t), where ζi(t) are random variables satisfying <ζi(t)ζj(t')>= 2γijTδ(t-t'). Our goal is to determine the stiffness matrix Kij, but this requires long-time data to measure accurately. We therefore measure the noise matrix 2γijT, which depends on much shorter timescales, and compute the relaxation times by diagonalizing 12̂K12̂. Although we use biologically relevant configurations in each simulation, we have taken the domains out of their full context by simulating one pair at a time, and therefore external stresses are missing, which we measure from the drift and compensate for in subsequent simulations. Finally, we apply this technique to the HIV capsid protein.
Adsorbed polymers under flow. A stochastic dynamical system approach
NASA Astrophysics Data System (ADS)
Armstrong, Robert; Jhon, Myung S.
1985-09-01
Recent experiments have shown that porous filters preadsorbed with polymer molecules exhibit an anomalously high pressure drop at high rates of flow. We have modeled the adsorbed polymers as dynamical systems and have found that the introduction of hydrodynamic interaction between molecules destabilizes at a high applied shear. As a direct result this instability will cause the molecules to unravel and stretch far into the cross section of the pore, and thus by inference, cause the observed anomalously high pressure drop. Although much of this paper is devoted to the stability characteristics of the deterministic system, Brownian motion is also considered, and an account of the statistics of the Brownian system when the deterministic system becomes unstable is given. The examples revealed in this paper are not of sufficient complexity to calculate with any accuracy the magnitude of this anomalous pressure drop. We simply present a procedure by which a large variety of more complex models could be undertaken and their ultimate effect clearly understood.
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.
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.
Dynamics of an electric dipole moment in a stochastic electric field.
Band, Y B
2013-08-01
The mean-field dynamics of an electric dipole moment in a deterministic and a fluctuating electric field is solved to obtain the average over fluctuations of the dipole moment and the angular momentum as a function of time for a Gaussian white-noise stochastic electric field. The components of the average electric dipole moment and the average angular momentum along the deterministic electric-field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with Gaussian white noise in all three components. The components of the average electric dipole moment and the average angular momentum perpendicular to the deterministic electric-field direction oscillate with time but decay to zero, and their variance grows with time.
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.
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
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.
Beyond the quasi-particle: stochastic domain wall dynamics in soft ferromagnetic nanowires
NASA Astrophysics Data System (ADS)
Hayward, T. J.; Omari, K. A.
2017-03-01
We study the physical origins of stochastic domain wall pinning in soft ferromagnetic nanowires using focused magneto-optic Kerr effect measurements and dynamic micromagnetic simulations. Our results illustrate the ubiquitous nature of these effects in Ni80Fe20 nanowires, and show that they are not only a result of the magnetisation history of the system (i.e. the magnetisation structure of the injected domain walls), and the onset of non-linear propagation dynamics above the Walker breakdown field, but also a complex interplay between the two. We show that this means that, while micromagnetics can be used to make qualitative predictions of the behaviour of domain walls at defect sites, making quantitative predictions is much more challenging. Together, our results reinforce the view that even in these simple pseudo-one dimensional nanomagnets, domain walls must be considered as complex, dynamically evolving objects rather than simple quasi-particles.
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; AnophelesSpatially-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
Wang, Xin-Fan; Wang, Jian-Qiang; Deng, Sheng-Yue
2013-01-01
We investigate the dynamic stochastic multicriteria decision making (SMCDM) problems, in which the criterion values take the form of log-normally distributed random variables, and the argument information is collected from different periods. We propose two new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG) operator and the dynamic log-normal distribution weighted geometric (DLNDWG) operator, and develop a method for dynamic SMCDM with log-normally distributed random variables. This method uses the DLNDWG operator and the LNDWG operator to aggregate the log-normally distributed criterion values, utilizes the entropy model of Shannon to generate the time weight vector, and utilizes the expectation values and variances of log-normal distributions to rank the alternatives and select the best one. Finally, an example is given to illustrate the feasibility and effectiveness of this developed method.
A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization.
Waliszewski, Przemyslaw
2005-10-01
The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.
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.
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.
Stochastic ratcheting of two-dimensional colloids: Directed current and dynamical transitions
NASA Astrophysics Data System (ADS)
Chakraborty, Dipanjan; Chaudhuri, Debasish
2015-05-01
We present results of molecular dynamics simulations for two-dimensional repulsively interacting colloids driven by a one-dimensional asymmetric and commensurate ratchet potential, switching on and off stochastically. This drives a time-averaged directed current of colloids, exhibiting resonance with change in ratcheting frequency, where the resonance frequency itself depends nonmonotonically on density. Using scaling arguments, we obtain analytic results that show good agreement with numerical simulations. With increasing ratcheting frequency, we find nonequilibrium reentrant transitions between solid and modulated liquid phases.
Simulation of DNA motion in a microchannel using stochastic rotation dynamics.
Watari, Nobuhiko; Makino, Masato; Kikuchi, Norio; Larson, Ronald G; Doi, Masao
2007-03-07
The authors propose a method to simulate the DNA motion in microchannels of complex geometry. It is based on stochastic rotation dynamics using a new scheme for the boundary condition. The method enables them to define a boundary wall of arbitrary shape and to describe a wall moving at an arbitrary velocity. As an application, they simulate the motion of DNA in Poiseuille flow between two parallel planes and show that DNA molecules tend to concentrate near the center of the channel in agreement with experimental results.
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.
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.
The Influence of Ecohydrologic Dynamics on Landscape Evolution: a Stochastic Approach
NASA Astrophysics Data System (ADS)
Deal, E.; Favre Pugin, A. C.; Botter, G.; Braun, J.
2015-12-01
The stream power incision model (SPIM) has a long history of use in modeling landscape evolution. Despite simplifications made in its formulation, it has emerged over the last 30 years as a powerful tool to interpret the histories of tectonically active landscapes and to understand how they evolve over millions of years. However, intense interest in the relationship between climate and erosion has revealed that the standard SPIM has some significant shortcomings. First, it fails to account for the role of erosion thresholds, which have been shown to be important and require an approach that addresses the variable or stochastic nature of erosion processes and drivers. Second, the standard SPIM does not address the influence of catchment hydrology, which modulates the incoming precipitation to produce discharge that in turn drives fluvial erosion. Hydrological processes alter in particular the frequency and magnitude of extreme events which are highly relevant for landscape erosion. To address these weaknesses we introduce a new analytical stochastic-threshold formulation of the stream power incision model that is driven by probabilistic hydrology. The hydrological model incorporates a stochastic description of soil moisture which takes into account the random nature of the rainfall forcing and the dynamics of the soil layer. The soil layer dynamics include infiltration and evapotranspiration which are both modelled as being dependent on the time varying soil moisture level (state dependent). The stochastic approach allows us to integrate these effects over long periods of time to understand their influence on the longterm average erosion rate without the need to explicitly model processes on the short timescales where they are relevant. Our model can therefore represent the role of soil properties (thickness, porosity) and vegetation (through evapotranspiration rates) in the longterm catchment-wide water balance, and in turn the longterm erosion rate. We identify
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
Avraam, Demetris; de Magalhaes, Joao Pedro; Vasiev, Bakhtier
2013-08-01
The mortality patterns in human populations reflect biological, social and medical factors affecting our lives, and mathematical modelling is an important tool for the analysis of these patterns. It is known that the mortality rate in all human populations increases with age after sexual maturity. This increase is predominantly exponential and satisfies the Gompertz equation. Although the exponential growth of mortality rates is observed over a wide range of ages, it excludes early- and late-life intervals. In this work we accept the fact that the mortality rate is an exponential function of age and analyse possible mechanisms underlying the deviations from the exponential law across the human lifespan. We consider the effect of heterogeneity as well as stochastic factors in altering the exponential law and compare our results to publicly available age-dependent mortality data for Swedish and US populations. In a model of heterogeneous populations we study how differences in parameters of the Gompertz equation describing different subpopulations account for mortality dynamics at different ages. Particularly, we show that the mortality data on Swedish populations can be reproduced fairly well by a model comprising four subpopulations. We then analyse the influence of stochastic effects on the mortality dynamics to show that they play a role only at early and late ages, when only a few individuals contribute to mortality. We conclude that the deviations from exponential law at young ages can be explained by heterogeneity, namely by the presence of a subpopulation with high initial mortality rate presumably due to congenital defects, while those for old ages can be viewed as fluctuations and explained by stochastic effects.
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
Schilde, M; Doerner, K F; Hartl, R F
2014-10-01
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.
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.
Stochastic mean-field formulation of the dynamics of diluted neural networks.
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.
Mustafa, G.
1989-01-01
This study presents a comprehensive physically based stochastic dynamic optimization model to assist planners in making decisions concerning mine soil depths and soil mixture ratios required to achieve successful revegetation of mine lands at different probability levels of success, subject to an uncertain weather regime. A perennial grass growth model was modified and validated for predicting vegetation growth in reclaimed mine soils. The plant growth model is based on continuous relationships between plant growth, air temperature, dry length, leaf area, photoperiod and plant-soil-moisture stresses. A plant available soil moisture model was adopted to estimate daily soil moisture for mine soils. A general probability model was developed to estimate the probability of successful revegetation in a 5-year bond release period. The probability model considers five possible bond release criteria in mine soil reclamation planning. A stochastic dynamic optimization model (SDOM) was developed to find the optimum combination of soil depth and soil mixture ratios that met the successful vegetation standard under non-irrigated conditions with weather as the only random element of the system. The SDOM was applied for Wise County, Virginia, and the model found that 2:1 sandstone/siltstone soil mixture required the minimum soil depth to achieve successful revegetation. These results were also supported by field data. The developed model allows the planners to better manage lands drastically disturbed by surface mining.
A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow
NASA Astrophysics Data System (ADS)
Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.
2014-12-01
Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.
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.
NASA Astrophysics Data System (ADS)
Miyamoto, Hitoshi; Kimura, Ryo
2016-09-01
This paper proposes a stochastic evaluation method for examining tree population states in a river cross section using an integrated model with Monte Carlo simulation. The integrated model consists of four processes as submodels, i.e., tree population dynamics, flow discharge stochasticity, stream hydraulics, and channel geomorphology. A floodplain of the Kako River in Japan was examined as a test site, which is currently well vegetated and features many willows that have been growing in both individual size and overall population over the last several decades. The model was used to stochastically evaluate the effects of hydrologic and geomorphologic changes on tree population dynamics through the Monte Carlo simulation. The effects including the magnitude of flood impacts and the relative change in the floodplain level are examined using very simple scenarios for flow regulation, climate change, and channel form changes. The stochastic evaluation method revealed a tradeoff point in floodplain levels, at which the tendency of a fully vegetated state switches to that of a bare floodplain under small impacts of flood. It is concluded from these results that the states of tree population in a floodplain can be determined by the mutual interactions among flood impacts, seedling recruitment, tree growth, and channel geomorphology. These interactions make it difficult to obtain a basic understanding of tree population dynamics from a field study of a specific floodplain. The stochastic approach used in this paper could constitute an effective method for evaluating fundamental channel characteristics for a vegetated floodplain.
Wang, Xiu-Ling; Gao, Xin-Qi; Wang, Xue-Chen
2011-08-01
Actin filaments and chloroplasts in guard cells play roles in stomatal function. However, detailed actin dynamics vary, and the roles that they play in chloroplast localization during stomatal movement remain to be determined. We examined the dynamics of actin filaments and chloroplast localization in transgenic tobacco expressing green fluorescent protein (GFP)-mouse talin in guard cells by time-lapse imaging. Actin filaments showed sliding, bundling and branching dynamics in moving guard cells. During stomatal movement, long filaments can be severed into small fragments, which can form longer filaments by end-joining activities. With chloroplast movement, actin filaments near chloroplasts showed severing and elongation activity in guard cells during stomatal movement. Cytochalasin B treatment abolished elongation, bundling and branching activities of actin filaments in guard cells, and these changes of actin filaments, and as a result, more chloroplasts were localized at the centre of guard cells. However, chloroplast turning to avoid high light, and sliding of actin fragments near the chloroplast, was unaffected following cytochalasin B treatment in guard cells. We suggest that the sliding dynamics of actin may play roles in chloroplast turning in guard cells. Our results indicate that the stochastic dynamics of actin filaments in guard cells regulate chloroplast localization during stomatal movement.
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)
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.
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.
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.
The effects of spatial correlations and demographic stochasticity on population dynamics
NASA Astrophysics Data System (ADS)
Snyder, Robin Elizabeth
2001-12-01
Because of limited mobility and localized interactions, most organisms do not interact equally with all parts of their environment but instead with a limited neighborhood. The resulting spatial correlations affect population dynamics. The discreteness of organisms can also affect population dynamics. Because population size cannot change by less than one, and size-changing events such as births and deaths occur at distinct times, population dynamics are noisy. For large populations, this so-called ``demographic stochasticity'' is often ignorable, but when population size is small, either throughout the system or in a region, noise can have important consequences. This dissertation explores the combined effects of spatial correlations and population discreteness. Chapter II discusses the limitations of many traditional physics techniques in analyzing ecological models. Chapters III and IV consider grid-based models. Every grid point can be vacant or occupied by an individual, and individuals interact according to simple, probabilistic rules. In chapter III, I develop approximate equations for the population mean and variance, including the effects of demographic stochasticity, by ignoring all but very short-range spatial correlations (a moment closure scheme). I apply this to a grid model and obtain expressions for population mean and variance. In chapter IV, I develop an empirical moment closure scheme based on observed spatial correlations. This leads to expressions for population mean and variance that are both simpler and more accurate, as well as to probability distributions for how long the population will take to reach a given, low level. Subsequently, I turn to the effects of population discreteness on the spread of newly introduced species. In chapter V, I analyze a common class of one- dimensional, single-species invasion models and find three effects of population discreteness and demographic stochasticity on invasion speed. The result is that for very
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.
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.
NASA Astrophysics Data System (ADS)
Morales, Marco A.; Fernández-Cervantes, Irving; Agustín-Serrano, Ricardo; Anzo, Andrés; Sampedro, Mercedes P.
2016-08-01
A functional with interactions short-range and long-range low coarse-grained approximation is proposed. This functional satisfies models with dissipative dynamics A, B and the stochastic Swift-Hohenberg equation. Furthermore, terms associated with multiplicative noise source are added in these models. These models are solved numerically using the method known as fast Fourier transform. Results of the spatio-temporal dynamic show similarity with respect to patterns behaviour in ferrofluids phases subject to external fields (magnetic, electric and temperature), as well as with the nucleation and growth phenomena present in some solid dissolutions. As a result of the multiplicative noise effect over the dynamic, some microstructures formed by changing solid phase and composed by binary alloys of Pb-Sn, Fe-C and Cu-Ni, as well as a NiAl-Cr(Mo) eutectic composite material. The model A for active-particles with a non-potential term in form of quadratic gradient explain the formation of nanostructured particles of silver phosphate. With these models is shown that the underlying mechanisms in the patterns formation in all these systems depends of: (a) dissipative dynamics; (b) the short-range and long-range interactions and (c) the appropiate combination of quadratic and multiplicative noise terms.
Extended-Range Prediction with Low-Dimensional, Stochastic-Dynamic Models: A Data-driven Approach
2012-09-30
COVERED - 4 . TITLE AND SUBTITLE Extended-Range Prediction with Low-Dimensional, Stochastic-Dynamic Models: A Data-driven Approach 5a. CONTRACT...mwheeler/maproom/RMM/ 4 • As the Madden-Julian oscillation (MJO) moves eastward from the Indian to the Pacific ocean, it typically accelerates, becomes
Johnston, Iain G; Jones, Nick S
2015-08-08
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.
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
NASA Astrophysics Data System (ADS)
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed
2017-03-01
In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.
Dynamic response analysis of linear stochastic truss structures under stationary random excitation
NASA Astrophysics Data System (ADS)
Gao, Wei; Chen, Jianjun; Cui, Mingtao; Cheng, Yi
2005-03-01
This paper presents a new method for the dynamic response analysis of linear stochastic truss structures under stationary random excitation. Considering the randomness of the structural physical parameters and geometric dimensions, the computational expressions of the mean value, variance and variation coefficient of the mean square value of the structural displacement and stress response under the stationary random excitation are developed by means of the random variable's functional moment method and the algebra synthesis method from the expressions of structural stationary random response of the frequency domain. The influences of the randomness of the structural physical parameters and geometric dimensions on the randomness of the mean square value of the structural displacement and stress response are inspected by the engineering examples.
Stochastic dynamics and the predictability of big hits in online videos
NASA Astrophysics Data System (ADS)
Miotto, José M.; Kantz, Holger; Altmann, Eduardo G.
2017-03-01
The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 106 time series of videos' views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat's law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Lévy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models.
NASA Technical Reports Server (NTRS)
Garrett, Bruce C.; Swaminathan, P. K.; Murthy, C. S.; Redmon, Michael J.
1987-01-01
A variable time step algorithm has been implemented for solving the stochastic equations of motion for gas-surface collisions. It has been tested for a simple model of electronically inelastic collisions with an insulator surface in which the phonon manifold acts as a heat bath and electronic states are localized. In addition to reproducing the accurate nuclear dynamics of the surface atoms, numerical calculations have shown the algorithm to yield accurate ensemble averages of physical observables such as electronic transition probabilities and total energy loss of the gas atom to the surface. This new algorithm offers a gain in efficieny of up to an order of magnitude compared to fixed time step integration.
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.
Stochastic Predator-Prey Dynamics of Transposons in the Human Genome.
Xue, Chi; Goldenfeld, Nigel
2016-11-11
Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic, relying on the enzymes produced by the regular transposons. In this case, we show that a stochastic model, which takes into account the small copy numbers of the active transposons in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of the number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
Stochastic Predator-Prey Dynamics of Transposons in the Human Genome
NASA Astrophysics Data System (ADS)
Xue, Chi; Goldenfeld, Nigel
2016-11-01
Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic, relying on the enzymes produced by the regular transposons. In this case, we show that a stochastic model, which takes into account the small copy numbers of the active transposons in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of the number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
Jun, James J.; Longtin, André
2017-01-01
Abstract The neural basis of spontaneous movement generation is a fascinating open question. Long-term monitoring of fish, swimming freely in a constant sensory environment, has revealed a sequence of behavioral states that alternate randomly and spontaneously between periods of activity and inactivity. We show that key dynamical features of this sequence are captured by a 1-D diffusion process evolving in a nonlinear double well energy landscape, in which a slow variable modulates the relative depth of the wells. This combination of stochasticity, nonlinearity, and nonstationary forcing correctly captures the vastly different timescales of fluctuations observed in the data (∼1 to ∼1000 s), and yields long-tailed residence time distributions (RTDs) also consistent with the data. In fact, our model provides a simple mechanism for the emergence of long-tailed distributions in spontaneous animal behavior. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. Our main finding is thus the identification of a threshold crossing process as the mechanism governing spontaneous movement initiation and termination, and to infer the presence of underlying nonstationary agents. Another important outcome of our work is a dimensionality reduction scheme that allows similar segments of data to be grouped together. This is done by first extracting geometrical features in the dataset and then applying principal component analysis over the feature space. Our study is novel in its ability to model nonstationary behavioral data over a wide range of timescales. PMID:28374017
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
Armstrong, Cameron R; David, John A; Thompson, John R
2015-07-13
We present a simple numerical model that is used in conjunction with a systematic algorithm for parameter optimization to understand the three-dimensional stochastic intensity dynamics of stimulated Brillouin scattering in a two-mode optical fiber. The primary factors driving the complex dynamics appear to be thermal density fluctuations, transverse pump fluctuations, and asymmetric transverse mode fractions over the beam cross-section.
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.
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.
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.
Analysing animal social network dynamics: the potential of stochastic actor-oriented models.
Fisher, David N; Ilany, Amiyaal; Silk, Matthew J; Tregenza, Tom
2017-03-01
Animals are embedded in dynamically changing networks of relationships with conspecifics. These dynamic networks are fundamental aspects of their environment, creating selection on behaviours and other traits. However, most social network-based approaches in ecology are constrained to considering networks as static, despite several calls for such analyses to become more dynamic. There are a number of statistical analyses developed in the social sciences that are increasingly being applied to animal networks, of which stochastic actor-oriented models (SAOMs) are a principal example. SAOMs are a class of individual-based models designed to model transitions in networks between discrete time points, as influenced by network structure and covariates. It is not clear, however, how useful such techniques are to ecologists, and whether they are suited to animal social networks. We review the recent applications of SAOMs to animal networks, outlining findings and assessing the strengths and weaknesses of SAOMs when applied to animal rather than human networks. We go on to highlight the types of ecological and evolutionary processes that SAOMs can be used to study. SAOMs can include effects and covariates for individuals, dyads and populations, which can be constant or variable. This allows for the examination of a wide range of questions of interest to ecologists. However, high-resolution data are required, meaning SAOMs will not be useable in all study systems. It remains unclear how robust SAOMs are to missing data and uncertainty around social relationships. Ultimately, we encourage the careful application of SAOMs in appropriate systems, with dynamic network analyses likely to prove highly informative. Researchers can then extend the basic method to tackle a range of existing questions in ecology and explore novel lines of questioning.
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.
Derlet, P. M.; Gilbert, M. R.; Dudarev, S. L.
2011-10-01
Nanoscale prismatic loops are modeled via a partial stochastic differential equation that describes an overdamped continuum elastic string, with a view to describing both the internal and collective dynamics of the loop as a function of temperature. Within the framework of the Langevin equation, expressions are derived that relate the empirical parameters of the model, the friction per unit length, and the elastic stiffness per unit length, to observables that can be obtained directly via molecular-dynamics simulations of interstitial or vacancy prismatic loop mobility. The resulting expressions naturally exhibit the properties that the collective diffusion coefficient of the loop (i) scales inversely with the square root of the number of interstitials, a feature that has been observed in both atomistic simulation and in situ TEM investigations of loop mobility, and (ii) the collective diffusion coefficient is not at all dependent on the internal interactions within the loop, thus qualitatively rationalizing past simulation results showing that the characteristic migration energy barrier is comparable to that of a single interstitial, and cluster migration is a result of individual (but correlated) interstitial activity.
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.
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
NASA Astrophysics Data System (ADS)
Helbing, Dirk; Schönhof, Martin; Kern, Daniel
2002-06-01
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc, they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified methods of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems and for information service providers. One of the promising fields of application is traffic optimization.
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 (Fe{sup 3+}, He{sup +} and H{sup +}) 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
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
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.
D'Onofrio, Giuseppe; Pirozzi, Enrica
2016-09-26
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
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.
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.
Transient climate rainfall downscaling using a combined dynamic-stochastic methodology
NASA Astrophysics Data System (ADS)
Burton, Aidan; Blenkinsop, Stephen; Fowler, Hayley J.; Kilsby, Chris G.
2010-05-01
Managers of water resource systems need downscaled climate change projections that are relevant at the catchment scale and at a range of future time horizons. However, the uncertainty in future climate projections and the natural variability of the climate system affect the robustness of their decisions. Dynamic downscaling of discrete future time-slices also limits the analysis of the temporal development of climate change impacts, as only steady state scenarios are widely available. Addressing these issues a new transient (i.e. temporally non-stationary) rainfall simulation methodology has been developed which combines dynamical and statistical downscaling to generate a multi-model ensemble of transient daily point-scale rainfall timeseries. Each timeseries is sampled from a continuous stochastic simulation of the control-future time period and exhibits climatic non-stationarity in accordance with GCM/RCM projections. The ensemble as a whole represents aspects of both climate model uncertainty and natural variability and provides a basis for probabilistic time-horizon analyses such as when a particular impact will occur or when a particular threshold will be reached. The methodology is demonstrated for a case study raingauge located near the Brévilles spring in Northern France. Thirteen RCM projections from the PRUDENCE project for both control (1961-1990) and future (2071-2100) time-slices were obtained to form the basis of a multi-model representation of climate change. Each dynamically downscales the climate from either the ECHAM4/OPYC or the HadCM3 GCM. Multiplicative ‘change factors' were evaluated for a set of statistics of daily rainfall for each RCM. These quantify the future value of each statistic as a multiple of the control value for each calendar month in turn. Multiplying the case study raingauge statistics by the change factors provides future projections with an implicit correction for biases in the RCM control runs and a representation of the
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
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...
Dynamics of a stochastic HIV-1 infection model with logistic growth
NASA Astrophysics Data System (ADS)
Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan
2017-03-01
This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.
Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias
2007-11-13
We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information.
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.
Dynamic Transition States of ErbB1 Phosphorylation Predicted by Spatial Stochastic Modeling
Pryor, Meghan McCabe; Low-Nam, Shalini T.; Halász, Ádám M.; Lidke, Diane S.; Wilson, Bridget S.; Edwards, Jeremy S.
2013-01-01
ErbB1 overexpression is strongly linked to carcinogenesis, motivating better understanding of erbB1 dimerization and activation. Recent single-particle-tracking data have provided improved measures of dimer lifetimes and strong evidence that transient receptor coconfinement promotes repeated interactions between erbB1 monomers. Here, spatial stochastic simulations explore the potential impact of these parameters on erbB1 phosphorylation kinetics. This rule-based mathematical model incorporates structural evidence for conformational flux of the erbB1 extracellular domains, as well as asymmetrical orientation of erbB1 cytoplasmic kinase domains during dimerization. The asymmetric dimer model considers the theoretical consequences of restricted transactivation of erbB1 receptors within a dimer, where the N-lobe of one monomer docks with the C-lobe of the second monomer and triggers its catalytic activity. The dynamic nature of the erbB1 phosphorylation state is shown by monitoring activation states of individual monomers as they diffuse, bind, and rebind after ligand addition. The model reveals the complex interplay between interacting liganded and nonliganded species and the influence of their distribution and abundance within features of the membrane landscape. PMID:24048005
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
NASA Astrophysics Data System (ADS)
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
NASA Astrophysics Data System (ADS)
Banerjee, Kinshuk
2015-05-01
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.
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.
Dynamic Reconfiguration and Routing Algorithms for IP-Over-WDM Networks With Stochastic Traffic
NASA Astrophysics Data System (ADS)
Brzezinski, Andrew; Modiano, Eytan
2005-10-01
We develop algorithms for joint IP-layer routing and WDM logical topology reconfiguration in IP-over-WDM networks experiencing stochastic traffic. At the wavelenght division multiplexing (WDM) layer, we associate a nonnegligible overhead with WDM reconfiguration, during which time tuned transceivers cannot service backlogged data. The Internet Protocol (IP) layer is modeled as a queueing system. We demonstrate that the proposed algorithms achieve asymptotic throughput optimality by using frame-based maximum weight scheduling decisions. We study both fixed and variable frame durations. In addition to dynamically triggering WDM reconfiguration, our algorithms specify precisely how to route packets over the IP layer during the phases in which the WDM layer remains fixed. We demonstrate that optical-layer constraints do not affect the results, and provide an analysis of the specific case of WDM networks with multiple ports per node. In order to gauge the delay properties of our algorithms, we conduct a simulation study and demonstrate an important tradeoff between WDM reconfiguration and IP-layer routing. We find that multihop routing is extremely beneficial at low-throughput levels, while single-hop routing achieves improved delay at high-throughput levels. For a simple access network, we demonstrate through simulation the benefit of employing multihop IP-layer routes.
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.
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.
On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
NASA Astrophysics Data System (ADS)
Rákos, A.; Harris, R. J.
2008-05-01
We consider the fluctuations of generalized currents in stochastic Markovian dynamics. The large deviations of current fluctuations are shown to obey a Gallavotti-Cohen (GC) type symmetry in systems with a finite state space. However, this symmetry is not guaranteed to hold in systems with an infinite state space. A simple example of such a case is the zero-range process (ZRP). Here we discuss in more detail the already reported (Harris et al 2006 Europhys. Lett. 75 227) breakdown of the GC symmetry in the context of the ZRP with open boundaries and we give a physical interpretation of the phases that appear. Furthermore, the earlier analytical results for the single-site case are extended to cover multiple-site systems. We also use our exact results to test an efficient numerical algorithm of Giardinà et al (2006 Phys. Rev. Lett. 96 120603), which was developed to measure the current large deviation function directly. We find that this method breaks down in some phases which we associate with the gapless spectrum of an effective Hamiltonian.
NASA Astrophysics Data System (ADS)
Dunn, Aaron; Muntifering, Brittany; Dingreville, Rémi; Hattar, Khalid; Capolungo, Laurent
2016-11-01
Charged particle irradiation is a frequently used experimental tool to study damage accumulation in metals expected during neutron irradiation. Understanding the correspondence between displacement rate and temperature during such studies is one of several factors that must be taken into account in order to design experiments that produce equivalent damage accumulation to neutron damage conditions. In this study, spatially resolved stochastic cluster dynamics (SRSCD) is used to simulate damage evolution in α-Fe and find displacement rate/temperature pairs under 'target' and 'proxy' conditions for which the local distribution of vacancies and vacancy clusters is the same as a function of displacement damage. The SRSCD methodology is chosen for this study due to its computational efficiency and ability to simulate damage accumulation in spatially inhomogeneous materials such as thin films. Results are presented for Frenkel pair irradiation and displacement cascade damage in thin films and bulk α-Fe. Holding all other material and irradiation conditions constant, temperature adjustments are shown to successfully make up for changes in displacement rate such that defect concentrations and cluster sizes remain relatively constant. The methodology presented in this study allows for a first-order prediction of the temperature at which ion irradiation experiments ('proxy' conditions) should take place in order to approximate neutron irradiation ('target' conditions).
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations.
Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph
2012-04-01
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDEs). For large, but finite populations this allows us to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates μ are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For μN≪1 this limits the use of SDEs, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a rock-scissors-paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
NASA Astrophysics Data System (ADS)
Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph
2012-04-01
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDEs). For large, but finite populations this allows us to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates μ are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For μN≪1 this limits the use of SDEs, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a rock-scissors-paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.
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).
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.
Sindhikara, Daniel J; Kim, Seonah; Voter, Arthur F; Roitberg, Adrian E
2009-06-09
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 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 pseudorandom 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 has not been programmed to distribute initial seeds.
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
NASA Astrophysics Data System (ADS)
Drummond, Jen; Davies-Colley, Rob; Stott, Rebecca; Sukias, James; Nagels, John; Sharp, Alice; Packman, Aaron
2014-05-01
Transport dynamics of microbial cells and organic fine particles are important to stream ecology and biogeochemistry. Cells and particles continuously deposit and resuspend during downstream transport owing to a variety of processes including gravitational settling, interactions with in-stream structures or biofilms at the sediment-water interface, and hyporheic exchange and filtration within underlying sediments. Deposited cells and particles are also resuspended following increases in streamflow. Fine particle retention influences biogeochemical processing of substrates and nutrients (C, N, P), while remobilization of pathogenic microbes during flood events presents a hazard to downstream uses such as water supplies and recreation. We are conducting studies to gain insights into the dynamics of fine particles and microbes in streams, with a campaign of experiments and modeling. The results improve understanding of fine sediment transport, carbon cycling, nutrient spiraling, and microbial hazards in streams. We developed a stochastic model to describe the transport and retention of fine particles and microbes in rivers that accounts for hyporheic exchange and transport through porewaters, reversible filtration within the streambed, and microbial inactivation in the water column and subsurface. This model framework is an advance over previous work in that it incorporates detailed transport and retention processes that are amenable to measurement. Solute, particle, and microbial transport were observed both locally within sediment and at the whole-stream scale. A multi-tracer whole-stream injection experiment compared the transport and retention of a conservative solute, fluorescent fine particles, and the fecal indicator bacterium Escherichia coli. Retention occurred within both the underlying sediment bed and stands of submerged macrophytes. The results demonstrate that the combination of local measurements, whole-stream tracer experiments, and advanced modeling
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.
Vellela, Melissa; Qian, Hong
2009-10-06
Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.
Stochastic dynamics of complexation reaction in the limit of small numbers.
Ghosh, Kingshuk
2011-05-21
We study stochastic dynamics of the non-linear bimolecular reaction A + B↔AB. These reactions are common in several bio-molecular systems such as binding, complexation, protein multimerization to name a few. We use master equation to compute the full distribution of several stochastic equilibrium properties such as number of complexes formed (N(c)), equilibrium constant (K). We provide exact analytical and simpler approximate expression for equilibrium fluctuation quantities to quickly estimate the amount of noise as a function of reactant molecules and rates. We construct the phase diagram for a fluctuational quantity f, defined as the ratio of standard deviation to average (f=√
Stochastic dynamics and chaos in the 3D Hindmarsh-Rose model
NASA Astrophysics Data System (ADS)
Ryashko, Lev; Bashkirtseva, Irina; Slepukhina, Evdokia; Fedotov, Sergei
2016-12-01
We study the effect of random disturbances on the three-dimensional Hindmarsh-Rose model of neural activity. In a parametric zone, where the only attractor of the system is a stable equilibrium, a stochastic generation of bursting oscillations is observed. For a sufficiently small noise, random states concentrate near the equilibrium. With an increase of the noise intensity, along with small-amplitude oscillations around the equilibrium, bursts are observed. The relationship of the noise-induced generation of bursts with system transitions from order to chaos is discussed. For a quantitative analysis of these stochastic phenomena, an approach based on the stochastic sensitivity function technique is suggested.
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
NASA Astrophysics Data System (ADS)
Sapsis, T.
2012-04-01
We examine the geometry of the inertial manifold associated with fluid flows described by Navier-Stokes equations and we relate its nonlinear dimensionality to energy exchanges between the mean flow and stochastic modes of the flow. Specifically, we employ a stochastic framework based on the dynamically orthogonal field equations to perform efficient order-reduction in terms of time-dependent modes and describe the inertial manifold in the reduced-order phase space in terms of the associated probability measure. We introduce the notion of local fractal dimensionality and we establish a connection with the finite-time Lyapunov exponents of the reduced-order dynamics. Based on this tool we illustrate in 2D Navier-Stokes equations that the underlying mechanism responsible for the finite dimensionality of the inertial manifold is, apart from the viscous dissipation, the reverse flow of energy from the stochastic fluctuations (containing in general smaller lengthscales) back to the mean flow (which is characterized by larger spatial scales).
Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise
NASA Astrophysics Data System (ADS)
Chen, Can; Kang, Yanmei
2017-01-01
A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.
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.
Williams, D J; Hall, K B
1999-01-01
Three unrestrained stochastic dynamics simulations have been carried out on the RNA hairpin GGAC[UUCG] GUCC, using the AMBER94 force field (Cornell et al., 1995. J. Am. Chem. Soc. 117:5179-5197) in MacroModel 5.5 (Mohamadi et al., 1990. J. Comp. Chem. 11:440-467) and either the GB/SA continuum solvation model (Still et al., 1990. J. Am. Chem. Soc. 112:6127-6129) or a linear distance-dependent dielectric (1/R) treatment. The linear distance-dependent treatment results in severe distortion of the nucleic acid structure, restriction of all hydroxyl dihedrals, and collapse of the counterion atmosphere over the course of a 5-ns simulation. An additional vacuum simulation without counterions shows somewhat improved behavior. In contrast, the two GB/SA simulations (1.149 and 3.060 ns in length) give average structures within 1.2 A of the initial NMR structure and in excellent agreement with results of an earlier explicit solvent simulation (Miller and Kollman, 1997. J. Mol. Biol. 270:436-450). In a 3-ns GB/SA simulation starting with the incorrect UUCG tetraloop structure (Cheong et al., 1990. Nature. 346:680-682), this loop conformation converts to the correct loop geometry (Allain and Varani, 1995. J. Mol. Biol. 250:333-353), suggesting enhanced sampling relative to the previous explicit solvent simulation. Thermodynamic effects of 2'-deoxyribose substitutions of loop nucleotides were experimentally determined and are found to correlate with the fraction of time the ribose 2'-OH is hydrogen bonded and the distribution of the hydroxyl dihedral is observed in the GB/SA simulations. The GB/SA simulations thus appear to faithfully represent structural features of the RNA without the computational expense of explicit solvent. PMID:10354444
Huaguang, Gu; Zhiguo, Zhao; Bing, Jia; Shenggen, Chen
2015-01-01
On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris—Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to
Stochastic dynamic study of optical transition properties of single GFP-like molecules.
Lin, Hanbing; Yuan, Jian-Min
2016-03-01
Due to high fluctuations and quantum uncertainty, the processes of single-molecules should be treated by stochastic methods. To study fluorescence time series and their statistical properties, we have applied two stochastic methods, one of which is an analytic method to study the off-time distributions of certain fluorescence transitions and the other is Gillespie's method of stochastic simulations. These methods have been applied to study the optical transition properties of two single-molecule systems, GFPmut2 and a Dronpa-like molecule, to yield results in approximate agreement with experimental observations on these systems. Rigorous oscillatory time series of GFPmut2 before it unfolds in the presence of denaturants have not been obtained based on the stochastic method used, but, on the other hand, the stochastic treatment puts constraints on the conditions under which such oscillatory behavior is possible. Furthermore, a sensitivity analysis is carried out on GFPmut2 to assess the effects of transition rates on the observables, such as fluorescence intensities.
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.
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.
1990-08-31
diagonalizable matrix A satisfy 5 Xi i k for j = 1,2,...,n, Ik ki = >k 2 (2) 1 where k is an integer vector k = (k1 , ,..., kn) with k1 > 0. Furthermore...stochastic systems and secondly, to demonstrate the relationship between stochastic averaging and normal form theory for non- nilpotent systems. To this...for large k. Furthermore, since the matrix A is diagonal, the image of LA, Im(LA), and its null space, ker (LA), span the whole space. Consequently, in
NASA Astrophysics Data System (ADS)
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-02-01
We analyze the thermodynamic properties of stochastic differential equations driven by smooth Poisson-Kac fluctuations, and their convergence, in the Kac limit, towards Wiener-driven Langevin equations. Using a Markovian embedding of the stochastic work variable, it is proved that the Kac-limit convergence implies a Stratonovich formulation of the limit Langevin equations, in accordance with the Wong-Zakai theorem. Exact moment analysis applied to the case of a purely frictional system shows the occurrence of different regimes and crossover phenomena in the parameter space.
Johnson, Todd; Bartol, Tom; Sejnowski, Terrence; Mjolsness, Eric
2015-06-18
A stochastic reaction network model of Ca(2+) 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)
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)
Sakellariou, J. S.; Fassois, S. D.
2017-01-01
The identification of a single global model for a stochastic dynamical system operating under various conditions is considered. Each operating condition is assumed to have a pseudo-static effect on the dynamics and be characterized by a single measurable scheduling variable. Identification is accomplished within a recently introduced Functionally Pooled (FP) framework, which offers a number of advantages over Linear Parameter Varying (LPV) identification techniques. The focus of the work is on the extension of the framework to include the important FP-ARMAX model case. Compared to their simpler FP-ARX counterparts, FP-ARMAX models are much more general and offer improved flexibility in describing various types of stochastic noise, but at the same time lead to a more complicated, non-quadratic, estimation problem. Prediction Error (PE), Maximum Likelihood (ML), and multi-stage estimation methods are postulated, and the PE estimator optimality, in terms of consistency and asymptotic efficiency, is analytically established. The postulated estimators are numerically assessed via Monte Carlo experiments, while the effectiveness of the approach and its superiority over its FP-ARX counterpart are demonstrated via an application case study pertaining to simulated railway vehicle suspension dynamics under various mass loading conditions.
NASA Astrophysics Data System (ADS)
Zhao, Hui; Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Xiao, Jinghua; Yang, Yixian
2015-05-01
In this paper, exponential anti-synchronization in mean square of an uncertain memristor-based neural network is studied. The uncertain terms include non-modeled dynamics with boundary and stochastic perturbations. Based on the differential inclusions theory, linear matrix inequalities, Gronwall's inequality and adaptive control technique, an adaptive controller with update laws is developed to realize the exponential anti-synchronization. Adaptive controller can adjust itself behavior to get the best performance, according to the environment is changing or the environment has changed, which has the ability to adapt to environmental change. Furthermore, a numerical example is provided to validate the effectiveness of the proposed method.
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
Using stochastic dynamic programming to support catchment-scale water resources management in China
NASA Astrophysics Data System (ADS)
Davidsen, Claus; Pereira-Cardenal, Silvio Javier; Liu, Suxia; Mo, Xingguo; Rosbjerg, Dan; Bauer-Gottwein, Peter
2013-04-01
A hydro-economic modelling approach is used to optimize reservoir management at river basin level. We demonstrate the potential of this integrated approach on the Ziya River basin, a complex basin on the North China Plain south-east of Beijing. The area is subject to severe water scarcity due to low and extremely seasonal precipitation, and the intense agricultural production is highly dependent on irrigation. Large reservoirs provide water storage for dry months while groundwater and the external South-to-North Water Transfer Project are alternative sources of water. An optimization model based on stochastic dynamic programming has been developed. The objective function is to minimize the total cost of supplying water to the users, while satisfying minimum ecosystem flow constraints. Each user group (agriculture, domestic and industry) is characterized by fixed demands, fixed water allocation costs for the different water sources (surface water, groundwater and external water) and fixed costs of water supply curtailment. The multiple reservoirs in the basin are aggregated into a single reservoir to reduce the dimensions of decisions. Water availability is estimated using a hydrological model. The hydrological model is based on the Budyko framework and is forced with 51 years of observed daily rainfall and temperature data. 23 years of observed discharge from an in-situ station located downstream a remote mountainous catchment is used for model calibration. Runoff serial correlation is described by a Markov chain that is used to generate monthly runoff scenarios to the reservoir. The optimal costs at a given reservoir state and stage were calculated as the minimum sum of immediate and future costs. Based on the total costs for all states and stages, water value tables were generated which contain the marginal value of stored water as a function of the month, the inflow state and the reservoir state. The water value tables are used to guide allocation decisions in
Westerband, Andrea C; Horvitz, Carol C
2017-02-01
Temporal variability in light from gaps in the tree canopy strongly influences the vital rates of understory plants. From 2012 to 2015, we estimated the size-specific vital rates of two herbs, Calathea crotalifera and Heliconia tortuosa, over a range of light environments. We estimated maximum photosynthetic capacity (Amax ) for a subset of individuals each year during three annual censuses, and modelled future size as a linear function of current size (a plant trait that changes ontogenetically), canopy openness (an environmental variable), and Amax (a potentially plastic physiological trait). We estimated what the demographic success would be of a population comprised of individuals with a particular fixed Amax for each of several levels of canopy openness if the environment remained constant, by evaluating corresponding Integral Projection Models and their deterministic growth rates (λ). We then estimated their demographic success in the stochastic light environment (λS ) and its elasticities. As light increased, deterministic λ increased for Calathea by 33% but decreased for Heliconia by 52%, and increasing Amax had no effect on λ for Calathea but increased λ for Heliconia in low light. As Amax increased, λS increased for Heliconia, but not Calathea. We also investigated whether photosynthetic rates would influence the elasticities of λS, including its response to perturbation of vital rates in each environment (E(S)β ), vital rates over all environments (E(S) ), and variability of vital rates among environments (E(S)(σ) ). E(S) , E(S)(σ) , and E(S)β were influenced by Amax for Heliconia but not Calathea. Events that affect some vital rates in high light have a greater impact on overall fitness than events that affect the same vital rates in shady environments, and there is greater potential for selection on traits of large individuals in high light than in low light for Heliconia, while the reverse was true for Calathea. Photosynthetic rates
Drury, Kevin L S; Dwyer, Greg
2005-12-01
Stochastic models are of increasing importance in ecology but are usually only applied to observational data. Here we use a stochastic population model to combine experimental and observational data to understand the colonization of old fields by monarch butterflies Danaus plexippus. We experimentally tested for density dependence in oviposition rates when predators were excluded, and we measured predation rates under natural conditions. Significance tests on the resulting data showed that both oviposition and predation were density dependent but could not show how oviposition and mortality combine to determine egg densities in nature. We therefore used our data to calculate the Akaike Information Criterion to choose between a nested suite of stochastic models that differed in their oviposition and mortality terms. When we simply fit the models to the observational data, the best model assumed density independence in both oviposition and predation. When we instead first estimated the oviposition rate at low density from experimental data, however, the best model included density dependence in oviposition, and a model that included density dependence in both oviposition and predation performed nearly as well. This result is consistent with our experiments and suggests that experiments can enhance the usefulness of stochastic models in ecology.
NASA Astrophysics Data System (ADS)
Nome, Rene A.; Sorbello, Cecilia; Jobbágy, Matías; Barja, Beatriz C.; Sanches, Vitor; Cruz, Joyce S.; Aguiar, Vinicius F.
2017-03-01
The stochastic dynamics of individual co-doped Er:Yb upconversion nanoparticles (UCNP) were investigated from experiments and simulations. The UCNP were characterized by high-resolution scanning electron microscopy, dynamic light scattering, and zeta potential measurements. Single UCNP measurements were performed by fluorescence upconversion micro-spectroscopy and optical trapping. The mean-square displacement (MSD) from single UCNP exhibited a time-dependent diffusion coefficient which was compared with Brownian dynamics simulations of a viscoelastic model of harmonically bound spheres. Experimental time-dependent two-dimensional trajectories of individual UCNP revealed correlated two-dimensional nanoparticle motion. The measurements were compared with stochastic trajectories calculated in the presence of a non-conservative rotational force field. Overall, the complex interplay of UCNP adhesion, thermal fluctuations and optical forces led to a rich stochastic behavior of these nanoparticles.
Sheng, Li; Wang, Zidong; Zou, Lei; Alsaadi, Fuad E
2016-07-20
In this paper, the event-based finite-horizon H∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v)-dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2011-03-01
The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a "quantum system" is just a label for (so to say "prequantum") classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger's equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The "effect of entanglement" is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.
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)
Brouard, S.; Plata, J.
2011-06-01
We study the effect of noise on the axial mode of an electron in a Penning trap under parametric-resonance conditions. Our approach, based on the application of averaging techniques to the description of the dynamics, provides an understanding of the random phase flips detected in recent experiments. The observed correlation between the phase jumps and the amplitude collapses is explained. Moreover, we discuss the actual relevance of noise color to the identified phase-switching mechanism. Our approach is then generalized to analyze the persistence of the stochastic phase flips in the dynamics of a cloud of N electrons. In particular, we characterize the detected scaling of the phase-jump rate with the number of electrons.
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.
Jiménez-Hernández, Hugo; González-Barbosa, Jose-Joel; Garcia-Ramírez, Teresa
2010-01-01
This investigation demonstrates an unsupervised approach for modeling traffic flow and detecting abnormal vehicle behaviors at intersections. In the first stage, the approach reveals and records the different states of the system. These states are the result of coding and grouping the historical motion of vehicles as long binary strings. In the second stage, using sequences of the recorded states, a stochastic graph model based on a Markovian approach is built. A behavior is labeled abnormal when current motion pattern cannot be recognized as any state of the system or a particular sequence of states cannot be parsed with the stochastic model. The approach is tested with several sequences of images acquired from a vehicular intersection where the traffic flow and duration used in connection with the traffic lights are continuously changed throughout the day. Finally, the low complexity and the flexibility of the approach make it reliable for use in real time systems. PMID:22163616
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.
Analysis of bilinear stochastic systems
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Dynamics of the stochastic Leslie-Gower predator-prey system with randomized intrinsic growth rate
NASA Astrophysics Data System (ADS)
Zhao, Dianli; Yuan, Sanling
2016-11-01
This paper investigates the stochastic Leslie-Gower predator-prey system with randomized intrinsic growth rate. Existence of a unique global positive solution is proved firstly. Then we obtain the sufficient conditions for permanence in mean and almost sure extinction of the system. Furthermore, the stationary distribution is derived based on the positive equilibrium of the deterministic model, which shows the population is not only persistent but also convergent by time average under some assumptions. Finally, we illustrate our conclusions through two examples.
Numerical Schemes for Dynamically Orthogonal Equations of Stochastic Fluid and Ocean Flows
2011-11-03
stochastic subspace are given in §4. For the former, the discretization of diffusion operators is straightforward. That of advection operators requires special...Sc = ν̂/K̂ is the Schmidt number which is the ratio of kinematic viscosity ν̂ to molecular diffusivity K̂ for the density field, ĝ′ = ĝ (ρ̂max−ρ̂min... diffusion terms implicitly because they do not couple the equations and the resulting diagonal-dominant matrices can be inverted efficiently. While they
Different delays-induced regime shifts in a stochastic insect outbreak dynamics
NASA Astrophysics Data System (ADS)
Zeng, Jiakui; Zeng, Chunhua; Xie, Qingshuang; Guan, Lin; Dong, Xiaohui; Yang, Fengzao
2016-11-01
Considering time delays in the deterministic and stochastic forces, we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem. The stationary probability distribution (SPD) and mean first passage time (MFPT) are obtained, respectively. Our main results show: (i) The multiplicative noise, positive cross-correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one, but the additive noise and negative cross-correlation can induce the regime shifts from the bust outbreak state to the boom one; (ii) For the negative cross-correlation, the MFPT as a function of noise strengths exhibits one maximum, which shows the characteristic of the noise-delayed switching for the boom outbreak state, but for the no cross-correlation or positive cross-correlation, the MFPT decreases with the noise strengths; (iii) Two different types of time delays play same roles on the maximal MFPT with additive noise, and play opposite roles on the maximal MFPT with multiplicative noise. The mechanisms for noises-and delays-induced regime shifts between two states can be explained physically through the effective potential of ecological model.
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...
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.
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.
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)
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.
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.
Uncovering wind turbine properties through two-dimensional stochastic modeling of wind dynamics.
Raischel, Frank; Scholz, Teresa; Lopes, Vitor V; Lind, Pedro G
2013-10-01
Using a method for stochastic data analysis borrowed from statistical physics, we analyze synthetic data from a Markov chain model that reproduces measurements of wind speed and power production in a wind park in Portugal. We show that our analysis retrieves indeed the power performance curve, which yields the relationship between wind speed and power production, and we discuss how this procedure can be extended for extracting unknown functional relationships between pairs of physical variables in general. We also show how specific features, such as the rated speed of the wind turbine or the descriptive wind speed statistics, can be related to the equations describing the evolution of power production and wind speed at single wind turbines.
Temperature-dependent dynamics of stochastic domain-wall depinning in nanowires.
Wuth, Clemens; Lendecke, Peter; Meier, Guido
2012-01-18
The temperature dependence of domain-wall depinning in permalloy nanowires is investigated by measuring depinning fields and corresponding depinning times as a function of the external magnetic bias field. Domain walls are pinned at triangular notches in the nanowires and detected noninvasively by Hall micromagnetometry. This technique allows one to acquire depinning-field and depinning-time distributions in the temperature range between 5 and 50 K and thus to determine the stochastics of the depinning process. The results are discussed in terms of the Néel-Brown model for thermally activated magnetization reversal, assuming a single energy barrier to overcome. In general, the cases presented deviate from this description and give a clear indication that a more complex term for the energy landscape of domain-wall depinning at constrictions in nanowires is obligatory.
Wu, Zhizhang Huang, Zhongyi
2016-07-15
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.
Uncovering wind turbine properties through two-dimensional stochastic modeling of wind dynamics
NASA Astrophysics Data System (ADS)
Raischel, Frank; Scholz, Teresa; Lopes, Vitor V.; Lind, Pedro G.
2013-10-01
Using a method for stochastic data analysis borrowed from statistical physics, we analyze synthetic data from a Markov chain model that reproduces measurements of wind speed and power production in a wind park in Portugal. We show that our analysis retrieves indeed the power performance curve, which yields the relationship between wind speed and power production, and we discuss how this procedure can be extended for extracting unknown functional relationships between pairs of physical variables in general. We also show how specific features, such as the rated speed of the wind turbine or the descriptive wind speed statistics, can be related to the equations describing the evolution of power production and wind speed at single wind turbines.
Chen, Nan; Majda, Andrew J
2017-02-14
The El Niño Southern Oscillation (ENSO) has significant impact on global climate and seasonal prediction. A simple modeling framework is developed here that automatically captures the statistical diversity of ENSO. First, a stochastic parameterization of the wind bursts including both westerly and easterly winds is coupled to a simple ocean-atmosphere model that is otherwise deterministic, linear, and stable. Second, a simple nonlinear zonal advection with no ad hoc parameterization of the background sea-surface temperature (SST) gradient and a mean easterly trade wind anomaly representing the multidecadal acceleration of the trade wind are both incorporated into the coupled model that enables anomalous warm SST in the central Pacific. Then a three-state stochastic Markov jump process is used to drive the wind burst activity that depends on the strength of the western Pacific warm pool in a simple and effective fashion. It allows the coupled model to simulate the quasi-regular moderate traditional El Niño, the super El Niño, and the central Pacific (CP) El Niño as well as the La Niña with realistic features. In addition to the anomalous SST, the Walker circulation anomalies at different ENSO phases all resemble those in nature. In particular, the coupled model succeeds in reproducing the observed episode during the 1990s, where a series of 5-y CP El Niños is followed by a super El Niño and then a La Niña. Importantly, both the variance and the non-Gaussian statistical features in different Niño regions spanning from the western to the eastern Pacific are captured by the coupled model.
Chen, Nan; Majda, Andrew J.
2017-01-01
The El Niño Southern Oscillation (ENSO) has significant impact on global climate and seasonal prediction. A simple modeling framework is developed here that automatically captures the statistical diversity of ENSO. First, a stochastic parameterization of the wind bursts including both westerly and easterly winds is coupled to a simple ocean–atmosphere model that is otherwise deterministic, linear, and stable. Second, a simple nonlinear zonal advection with no ad hoc parameterization of the background sea-surface temperature (SST) gradient and a mean easterly trade wind anomaly representing the multidecadal acceleration of the trade wind are both incorporated into the coupled model that enables anomalous warm SST in the central Pacific. Then a three-state stochastic Markov jump process is used to drive the wind burst activity that depends on the strength of the western Pacific warm pool in a simple and effective fashion. It allows the coupled model to simulate the quasi-regular moderate traditional El Niño, the super El Niño, and the central Pacific (CP) El Niño as well as the La Niña with realistic features. In addition to the anomalous SST, the Walker circulation anomalies at different ENSO phases all resemble those in nature. In particular, the coupled model succeeds in reproducing the observed episode during the 1990s, where a series of 5-y CP El Niños is followed by a super El Niño and then a La Niña. Importantly, both the variance and the non-Gaussian statistical features in different Niño regions spanning from the western to the eastern Pacific are captured by the coupled model. PMID:28137886
Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson
2017-02-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
Truccolo, Wilson
2017-01-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
Markov stochasticity coordinates
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
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.
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)
Sheehan, T.; Bachelet, D. M.; Ferschweiler, K.
2015-12-01
The MC2 dynamic global vegetation model fire module simulates fire occurrence, area burned, and fire impacts including mortality, biomass burned, and nitrogen volatilization. Fire occurrence is based on fuel load levels and vegetation-specific thresholds for three calculated fire weather indices: fine fuel moisture code (FFMC) for the moisture content of fine fuels; build-up index (BUI) for the total amount of fuel available for combustion; and energy release component (ERC) for the total energy available to fire. Ignitions are assumed (i.e. the probability of an ignition source is 1). The model is run with gridded inputs and the fraction of each grid cell burned is limited by a vegetation-specific fire return period (FRP) and the number of years since the last fire occurred in the grid cell. One consequence of assumed ignitions FRP constraint is that similar fire behavior can take place over large areas with identical vegetation type. In regions where thresholds are often exceeded, fires occur frequently (annually in some instances) with a very low fraction of a cell burned. In areas where fire is infrequent, a single hot, dry climate event can result in intense fire over a large region. Both cases can potentially result in large areas with uniform vegetation type and age. To better reflect realistic fire occurrence, we have developed a stochastic fire occurrence model that: a) uses a map of relative ignition probability and a multiplier to alter overall ignition occurrence; b) adjusts the original fixed fire thresholds with ignition success probabilities based on fire weather indices; and c) calculates spread by using a probability based on slope and wind direction. A Monte Carlo method is used with all three algorithms to determine occurrence. The new stochastic ignition approach yields more variety in fire intensity, a smaller annual total of cells burned, and patchier vegetation.
Lecca, Paola; Ihekwaba, Adaoha E C; Dematté, Lorenzo; Priami, Corrado
2010-11-23
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.
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.
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.
2013-01-01
Background Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic? Results Here, we use a related mathematical modeling approach to demonstrate that ongoing Red Queen dynamics is unlikely. In fact, they collapse rapidly when two critical pieces of realism are acknowledged: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants. Conclusion Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations. PMID:24252104
Perišić, Ognjen; Lu, Hui
2014-01-01
The potential of mean force (PMF) calculation in single molecule manipulation experiments performed via the steered molecular dynamics (SMD) technique is a computationally very demanding task because the analyzed system has to be perturbed very slowly to be kept close to equilibrium. Faster perturbations, far from equilibrium, increase dissipation and move the average work away from the underlying free energy profile, and thus introduce a bias into the PMF estimate. The Jarzynski equality offers a way to overcome the bias problem by being able to produce an exact estimate of the free energy difference, regardless of the perturbation regime. However, with a limited number of samples and high dissipation the Jarzynski equality also introduces a bias. In our previous work, based on the Brownian motion formalism, we introduced three stochastic perturbation protocols aimed at improving the PMF calculation with the Jarzynski equality in single molecule manipulation experiments and analogous computer simulations. This paper describes the PMF reconstruction results based on full-atom molecular dynamics simulations, obtained with those three protocols. We also want to show that the protocols are applicable with the second-order cumulant expansion formula. Our protocols offer a very noticeable improvement over the simple constant velocity pulling. They are able to produce an acceptable estimate of PMF with a significantly reduced bias, even with very fast perturbation regimes. Therefore, the protocols can be adopted as practical and efficient tools for the analysis of mechanical properties of biological molecules. PMID:25232859
NASA Astrophysics Data System (ADS)
Pandey, Ras B.
1998-03-01
A stochastic cellular automata (SCA) approach is introduced to study the growth and decay of cellular population in an immune response model relevant to HIV. Four cell types are considered: macrophages (M), helper cells (H), cytotoxic cells (C), and viral infected cells (V). Mobility of the cells is introduced and viral mutation is considered probabilistically. In absence of mutation, the population of the host cells, helper (N_H) and cytotxic (N_C) cells in particular, dominates over the viral population (N_V), i.e., N_H, NC > N_V, the immune system wins over the viral infection. Variation of cellular population with time exhibits oscillations. The amplitude of oscillations in variation of N_H, NC and NV with time decreases at high mobility even at low viral mutation; the rate of viral growth is nonmonotonic with NV > N_H, NC in the long time regime. The viral population is much higher than that of the host cells at higher mutation rate, a possible cause of AIDS.
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.
Logic signals driven stochastic resonance in bistable dynamics subjected to 1/f noise floor
NASA Astrophysics Data System (ADS)
Zhang, L.; Song, A. G.; He, J.
2011-03-01
In the presence of 1/ f β noise, we investigate the logical stochastic resonance (LSR) in an asymmetric bistable model driven by various cycling combinations of two logic inputs. The probability of correct logic outputs is calculated according to true table of logic relationships. Two major results are presented. Firstly, it is shown that the LSR effect can be obtained by changing noise strength. Over entire range of noise variance, white noise can be considered to be better than 1/ f noise or 1/ f 2 noise to obtain clean logic operation. At a smaller noise level, 1/ f noise can realize higher output probability than white noise or 1/ f 2 noise. In the sense, 1/ f noise can be considered to be better than white noise or 1/ f 2. On the other hand, the correct probability can evolves nonmonotonically as noise exponent β increases, and a kind of SR-like effect can be obtained as a result of β. At certain intermediate noise variance, the output probability is able to attain its minimum at β = 1. It is also shown that actually some finite β sometime can be better than β = 0 at small range of noise variance. The study might provide some potential complement to LSR effect in the presence of 1/ f β noise.
Critical dynamics in the evolution of stochastic strategies for the iterated prisoner's dilemma.
Iliopoulos, Dimitris; Hintze, Arend; Adami, Christoph
2010-10-07
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.
Enhanced stochasticity of domain wall motion in magnetic racetracks due to dynamic pinning.
Jiang, Xin; Thomas, Luc; Moriya, Rai; Hayashi, Masamitsu; Bergman, Bastiaan; Rettner, Charles; Parkin, Stuart S P
2010-06-15
Understanding the details of domain wall (DW) motion along magnetic racetracks has drawn considerable interest in the past few years for their applications in non-volatile memory devices. The propagation of the DW is dictated by the interplay between its driving force, either field or current, and the complex energy landscape of the racetrack. In this study, we use spin-valve nanowires to study field-driven DW motion in real time. By varying the strength of the driving magnetic field, the propagation mode of the DW can be changed from a simple translational mode to a more complex precessional mode. Interestingly, the DW motion becomes much more stochastic at the onset of this propagation mode. We show that this unexpected result is a consequence of an unsustainable gain in Zeeman energy of the DW, as it is driven faster by the magnetic field. As a result, the DW periodically releases energy and thereby becomes more susceptible to pinning by local imperfections in the racetrack.
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.
Kamppeter, T.; Mertens, F.G.; Moro, E.; Sanchez, A.; Bishop, A.R.
1998-09-01
We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a highly non-trivial result as multiplicative and additive noises usually modify the dynamics in very different ways. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.
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.
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.
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
2015-04-01
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.
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 modeling for dynamics of HIV-1 infection using cellular automata: A review.
Precharattana, Monamorn
2016-02-01
Recently, the description of immune response by discrete models has emerged to play an important role to study the problems in the area of human immunodeficiency virus type 1 (HIV-1) infection, leading to AIDS. As infection of target immune cells by HIV-1 mainly takes place in the lymphoid tissue, cellular automata (CA) models thus represent a significant step in understanding when the infected population is dispersed. Motivated by these, the studies of the dynamics of HIV-1 infection using CA in memory have been presented to recognize how CA have been developed for HIV-1 dynamics, which issues have been studied already and which issues still are objectives in future studies.
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)
Pandian, Arun; Swisher, Nora C.; Abarzhi, S. I.
2017-01-01
Rayleigh-Taylor (RT) mixing occurs in a variety of natural and man-made phenomena in fluids, plasmas and materials, from celestial event to atoms. In many circumstances, RT flows are driven by variable acceleration, whereas majority of existing studies have considered only sustained acceleration. In this work we perform detailed analytical and numerical study of RT mixing with a power-law time-dependent acceleration. A set of deterministic nonlinear non-homogeneous ordinary differential equations and nonlinear stochastic differential equations with multiplicative noise are derived on the basis of momentum model. For a broad range of parameters, self-similar asymptotic solutions are found analytically, and their statistical properties are studied numerically. We identify two sub-regimes of RT mixing dynamics depending on the acceleration exponent—the acceleration-driven mixing and dissipation-driven mixing. Transition between the sub-regimes is studied, and it is found that each sub-regime has its own characteristic dimensionless invariant quantity.
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)
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)
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.
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.
Luo, Chao; Wang, Xingyuan
2013-01-01
A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme. PMID:23785502
Mendonça, Philipe RF; Vargas-Caballero, Mariana; Erdélyi, Ferenc; Szabó, Gábor; Paulsen, Ole; Robinson, Hugh PC
2016-01-01
Most cortical neurons fire regularly when excited by a constant stimulus. In contrast, irregular-spiking (IS) interneurons are remarkable for the intrinsic variability of their spike timing, which can synchronize amongst IS cells via specific gap junctions. Here, we have studied the biophysical mechanisms of this irregular spiking in mice, and how IS cells fire in the context of synchronous network oscillations. Using patch-clamp recordings, artificial dynamic conductance injection, pharmacological analysis and computational modeling, we show that spike time irregularity is generated by a nonlinear dynamical interaction of voltage-dependent sodium and fast-inactivating potassium channels just below spike threshold, amplifying channel noise. This active irregularity may help IS cells synchronize with each other at gamma range frequencies, while resisting synchronization to lower input frequencies. DOI: http://dx.doi.org/10.7554/eLife.16475.001 PMID:27536875
Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model.
Funk, Sebastian; Camacho, Anton; Kucharski, Adam J; Eggo, Rosalind M; Edmunds, W John
2016-12-16
Real-time forecasts of infectious diseases can help public health planning, especially during outbreaks. If forecasts are generated from mechanistic models, they can be further used to target resources or to compare the impact of possible interventions. However, paremeterising such models is often difficult in real time, when information on behavioural changes, interventions and routes of transmission are not readily available. Here, we present a semi-mechanistic model of infectious disease dynamics that was used in real time during the 2013-2016 West African Ebola epidemic, and show fits to a Ebola Forecasting Challenge conducted in late 2015 with simulated data mimicking the true epidemic. We assess the performance of the model in different situations and identify strengths and shortcomings of our approach. Models such as the one presented here which combine the power of mechanistic models with the flexibility to include uncertainty about the precise outbreak dynamics may be an important tool in combating future outbreaks.
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.
Prototype extraction in material attractor neural networks with stochastic dynamic learning
NASA Astrophysics Data System (ADS)
Fusi, Stefano
1995-04-01
Dynamic learning of random stimuli can be described as a random walk among the stable synaptic values. It is shown that prototype extraction can take place in material attractor neural networks when the stimuli are correlated and hierarchically organized. The network learns a set of attractors representing the prototypes in a completely unsupervised fashion and is able to modify its attractors when the input statistics change. Learning and forgetting rates are computed.
NASA Astrophysics Data System (ADS)
Lu, Z.; Porporato, A. M.
2012-12-01
seasonally dry areas, which are widely distributed in the world, are usually facing an intensive disparity between the lack of natural resource and the great demand of social development. In dry seasons of such areas, the distribution/allocation of water resource is an extremely critical and sensitive issue, and conflicts often occur due to lack of appropriate water allocation scheme. Among the many uses of water, the need of agricultural irrigation water is highly elastic, but this factor has not yet been made full use to free up water from agriculture use. The primary goal of this work is to design an optimal distribution scheme of water resource for dry seasons to maximize benefits from precious water resources, considering the high elasticity of agriculture water demand due to the dynamic of soil moisture affected by the uncertainty of precipitation and other factors like canopy interception. A dynamic programming model will be used to figure out an appropriate allocation of water resources among agricultural irrigation and other purposes like drinking water, industry, and hydropower, etc. In this dynamic programming model, we analytically quantify the dynamic of soil moisture in the agricultural fields by describing the interception with marked Poisson process and describing the rainfall depth with exponential distribution. Then, we figure out a water-saving irrigation scheme, which regulates the timetable and volumes of water in irrigation, in order to minimize irrigation water requirement under the premise of necessary crop yield (as a constraint condition). And then, in turn, we provide a scheme of water resource distribution/allocation among agriculture and other purposes, taking aim at maximizing benefits from precious water resources, or in other words, make best use of limited water resource.
Alonso, Daniel; Vega, Ines de
2010-06-15
Open quantum systems are often encountered in many different physical situations. From quantum optics to statistical mechanics, they are fundamental in the understanding of a great variety of different phenomena. Some of the most common examples are the relaxation to equilibrium, the existence of nonequilibrium stationary states, and the dynamics of atoms in interaction with electromagnetic fields. A crucial step in the analysis is to consider the quantum open system and its environment as the two mutually interacting components of a larger isolated system. Thereafter, the so-called Markov approximation is often considered, which consists on assuming that the time scales associated to the dynamics of the quantum open system are larger than those of the environment. It is the interplay of the different time scales associated with the system and the environment what determines the validity of the different approximations made. In this paper we will discuss the dynamics of a open quantum system in contact with a reservoir when the Markov approximation is not valid, and we have to include some non-Markovian or memory effects.
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.
Cooperative unmanned aerial vehicle (UAV) search in dynamic environments using stochastic methods
NASA Astrophysics Data System (ADS)
Flint, Matthew D.
Within this dissertation, the problem of the control of the decentralized path planning decision processes of multiple cooperating autonomous aerial vehicles engaged in search of an uncertain environment is considered. The environment is modeled in a probabilistic fashion, such that both a priori and dynamic information about it can be incorporated. The components of the environment include both target information and threat information. Using the information about the environment, a computationally feasible decision process is formulated that can decide; in a near optimal fashion, which path a searching vehicle should take, using a dynamic programming algorithm with a limited look ahead horizon, with the possibility to extend the horizon using Approximate Dynamic Programming. A planning vehicle trust take into account the effects of its (local) actions on meeting global goals. This is accomplished using a passive and predictive cooperation scheme among the vehicles. Lastly, a flexible simulator has been developed, using sound simulation analysis methods, to simulate a UAV search team, which can be used to create statistically valid results demonstrating the effectiveness of the model and solution methods.
NASA Astrophysics Data System (ADS)
Bedard-Hearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.
2005-12-01
The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence—the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state—and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrödinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of
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.
Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas
NASA Astrophysics Data System (ADS)
Amaral, Marco A.; Wardil, Lucas; Perc, Matjaž; da Silva, Jafferson K. L.
2016-09-01
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a win-stay-lose-shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average neighbor. Here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale-free networks. By using the master equation and Monte Carlo simulations, we find that cooperators coexist with defectors in the whole phase diagram, even at high temptations to defect. We study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second-order neighbors, rather than by means of network reciprocity that dominates in imitation-based models. For the square lattice the master equation can be solved analytically in the large temperature limit of the Fermi function, while for other cases the resulting differential equations must be solved numerically. Either way, we find good qualitative agreement with the Monte Carlo simulation results. Our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology, including the number of neighbors that are considered for payoff determination on lattices, which further corroborates the local character of the microscopic dynamics. Unlike large-scale spatial patterns that typically emerge due to network reciprocity, here local checkerboard-like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network.
Lelievre, Tony . E-mail: lelievre@cermics.enpc.fr; Rousset, Mathias . E-mail: rousset@cermics.enpc.fr; Stoltz, Gabriel . E-mail: stoltz@cermics.enpc.fr
2007-03-20
The computation of free energy differences through an exponential weighting of out-of-equilibrium paths (known as the Jarzynski equality [C. Jarzynski, Equilibrium free energy differences from nonequilibrium measurements: a master equation approach, Phys. Rev. E 56 (5) (1997) 5018-5035, C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78 (14) (1997) 2690-2693]) is often used for transitions between states described by an external parameter in the Hamiltonian. An extension to transitions between states defined by different values of some reaction coordinate is presented here, using a projected Brownian dynamics. In contrast with other approaches (see e.g. [S. Park, F. Khalili-Araghi, E. Tajkhorshid, K. Schulten, Free energy calculation from steered molecular dynamics simulations using Jarzynski's equality, J. Chem. Phys. 119 (6) (2003) 3559-3566]), a projection is used rather than a constraining potential to let the constraints associated with the reaction coordinate evolve. It is shown how to use the Lagrange multipliers associated with these constraints to compute the work associated with a given trajectory. Appropriate discretizations are proposed. Some numerical results demonstrate the applicability of the method for the computation of free energy difference profiles.
NASA Astrophysics Data System (ADS)
Liu, Jie; Sun, Xingsheng; Li, Kun; Jiang, Chao; Han, Xu
2015-11-01
Aiming at structures containing random parameters with multi-peak probability density functions (PDFs) or great variable coefficients, an analytical method of probability density function discretization and approximation (PDFDA) is proposed for dynamic load identification. Dynamic loads are expressed as the functions of time and random parameters in time domain and the forward model is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions. The PDF of each random parameter is discretized into several subintervals and in each subinterval the original PDF curve is approximated via uniform distribution PDF with equal probability value. Then the joint distribution model is built and hence the equivalent deterministic equations are solved to identify unknown loads. Inverse analysis is operated separately at each variable in the joint distribution model through regularization because of noise-contaminated measured responses. In order to assess the accuracy of identified results, PDF curves and statistical properties of loads are achieved based on the specially assumed distributions of identified loads. Numerical simulations demonstrate the efficiency and superiority of the presented method.
Extinction transition in stochastic population dynamics in a random, convective environment
NASA Astrophysics Data System (ADS)
Juhász, Róbert
2013-10-01
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random reproduction rates are systematically greater in one direction than in the opposite one. The spatial disorder turns out to be a relevant perturbation but, according to results of Monte Carlo simulations, the behavior of the model at the extinction transition is different from the (infinite-randomness) critical behavior of the disordered symmetric contact process. Depending on the strength a of the asymmetry, the critical population drifts either with a finite velocity or with an asymptotically vanishing velocity as x(t) ∼ tμ(a), where μ(a) < 1. Dynamical quantities are non-self-averaging at the extinction transition; the survival probability, for instance, shows multiscaling, i.e. it is characterized by a broad spectrum of effective exponents. For a sufficiently weak asymmetry, a Griffiths phase appears below the extinction transition, where the survival probability decays as a non-universal power of the time while, above the transition, another extended phase emerges, where the front of the population advances anomalously with a diffusion exponent continuously varying with the control parameter.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Stability of small molecular clusters modelled with stochastic and deterministic dynamics
NASA Astrophysics Data System (ADS)
Natarajan, Sukina
This investigation concerns the transition pathway of the condensation phase transition. Under certain conditions condensation is initiated by nucleation events, which are driven by fluctuations or instabilities in the vapour phase. This involves the spontaneous formation of groups of particles, which we refer to as clusters. The clusters have a highly unstable nature and exist momentarily, before breaking up. This makes them difficult to study experimentally and model mathematically, in comparison to larger more stable systems. The aim of this study is to explore the stability of these tiny molecular clusters that exist momentarily within their environment, in terms of the time taken for the cluster to lose particles (decay). To do this we employ a microscopic cluster model of n-nonane molecules in which the cluster is treated in isolation from the vapour particles that would normally surround it. The interactions between cluster particles are modelled using empirical potentials. The cluster's dynamics is modelled using deterministic molecular dynamics simulations. The simulations generate a time evolved trajectory of all the positions, velocities and forces of all the atoms in the cluster. The process of cluster decay in n-nonane clusters is modelled using a Langevin interpretation of the decay mechanism. This treatment views cluster decay as a process of single particle escape from a confining potential of mean force, driven by a particle's interactions with the surrounding cluster particles. The motion of a cluster particle is modelled using a Langevin equation, which is parameterised using the MD generated data in order to extract the decay related parameters. The decay parameters are used to evaluate an Arrhenius type equation for the kinetic decay rate. This is used to calculate the mean timescale of cluster decay for n-nonane clusters, which we refer to as the mean cluster lifetime. We compare the dynamically generated lifetimes calculated from the model to
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.
NASA Astrophysics Data System (ADS)
Wang, Guochao; Wang, Jun
2017-01-01
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.
Eigenvalue density of linear stochastic dynamical systems: A random matrix approach
NASA Astrophysics Data System (ADS)
Adhikari, S.; Pastur, L.; Lytova, A.; Du Bois, J.
2012-02-01
Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko-Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.
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. E 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 f(C)>f(D) (where f(C/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 f(C)>f(D) 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. E 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.
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.
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 R(2) = 0 .99396.
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
Frederiksen, M; Daunt, F; Harris, M P; Wanless, S
2008-09-01
1. Most scenarios for future climate change predict increased variability and thus increased frequency of extreme weather events. To predict impacts of climate change on wild populations, we need to understand whether this translates into increased variability in demographic parameters, which would lead to reduced population growth rates even without a change in mean parameter values. This requires robust estimates of temporal process variance, for example in survival, and identification of weather covariates linked to interannual variability. 2. The European shag Phalacrocorax aristotelis (L.) shows unusually large variability in population size, and large-scale mortality events have been linked to winter gales. We estimated first-year, second-year and adult survival based on 43 years of ringing and dead recovery data from the Isle of May, Scotland, using recent methods to quantify temporal process variance and identify aspects of winter weather linked to survival. 3. Survival was highly variable for all age groups, and for second-year and adult birds process variance declined strongly when the most extreme year was excluded. Survival in these age groups was low in winters with strong onshore winds and high rainfall. Variation in first-year survival was not related to winter weather, and process variance, although high, was less affected by extreme years. A stochastic population model showed that increasing process variance in survival would lead to reduced population growth rate and increasing probability of extinction. 4. As in other cormorants, shag plumage is only partially waterproof, presumably an adaptation to highly efficient underwater foraging. We speculate that this adaptation may make individuals vulnerable to rough winter weather, leading to boom-and-bust dynamics, where rapid population growth under favourable conditions allows recovery from periodic large-scale weather-related mortality. 5. Given that extreme weather events are predicted to become
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)
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.
Avitable, Daniele; Wedgwood, Kyle C A
2017-02-01
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times.
Ertaş, Mehmet; Deviren, Bayram; Keskin, Mustafa
2012-11-01
Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.
NASA Astrophysics Data System (ADS)
Pulkkinen, A.; Klimas, A.; Vassiliadis, D.; Uritsky, V.
2005-12-01
Understanding the evolution of bursts of activity in the magnetosphere-ionosphere system has been one of the central challenges in space physics since, and even prior to the introduction of the term "substorm". An extensive amount of work has been put to the characterization of the average near-space plasma environment behavior during substorms and several more or less deterministic models have been introduced to explain the observations. However, although most of substorms seem to have some common characteristics (otherwise any classification would be completely meaningless), like intensification of auroral electric currents, dipolarization of the magnetotail and injections of plasma sheet charged particles, each substorm has its distinct features in terms of strong fluctuations around the average "typical" behavior. This highly complex nature of individual substorms suggests that stochastic processes may play a role, even a central one in the evolution of substorms. In this work, we develop a simple stochastic model for the AE-index variations to investigate the role of random fluctuations in the substorm phenomenon. We show that by the introduction of a stochastic component, we are able to capture some fundamental features of the AE-index variations. More specifically, complex variations associated with individual bursts are a central part of the model. It will be demonstrated that by analyzing the structure of the constructed stochastic model some presently open questions about substorm-related bursts of the AE-index can be addressed quantitatively. First and foremost, it will be shown that the stochastic fluctuations are a fundamental part of the AE-index evolution and cannot be neglected even when the average properties of the index are of interest.
Stochastic simulation of transport phenomena
Wedgewood, L.E.; Geurts, K.R.
1995-10-01
In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.
NASA Astrophysics Data System (ADS)
Toledo-Marín, J. Quetzalcóatl; Naumis, Gerardo G.
2017-03-01
The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers' transition theory, which arises in a very natural manner to calculate transition rates between wells. Then the corresponding stochastic master equation is analytically solved to find the population of metastable states. A relation between the cooling rate, the characteristic relaxation time, and the population of metastable states is found from the solution of such equation. From this, a relationship between the relaxation times and the frequency of oscillation at the metastable states, i.e., the short time dynamics, is obtained. Since the model is able to capture either a glass transition or a crystallization depending on the cooling rate, this gives a conceptual framework in which to discuss some aspects of rigidity theory, for example.
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.
NASA Astrophysics Data System (ADS)
Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R.
2016-12-01
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of observables to describe their non-equilibrium steady states. Here we consider stochastic motion of a (k - 1) -dimensional object, which sweeps out a k-dimensional trajectory, and gives rise to a higher k-dimensional current. By employing the low-temperature (low-noise) limit, we reduce the problem to a discrete Markov chain model on a CW complex, a topological construction which generalizes the notion of a graph. This reduction allows the mean fluxes and currents of the process to be expressed in terms of solutions to the discrete Supersymmetric Fokker-Planck (SFP) equation. Taking the adiabatic limit, we show that generic driving leads to rational quantization of the generated higher dimensional current. The latter is achieved by implementing the recently developed tools, coined the higher-dimensional Kirchhoff tree and co-tree theorems. This extends the study of motion of extended objects in the continuous setting performed in the prequel (Catanzaro et al.) to this manuscript.
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.
Stochastic Models of Polymer Systems
2016-01-01
algorithms for big data applications . (2) We studied stochastic dynamics of polymer systems in the mean field limit. (3) We studied noisy Hegselmann-Krause...DISTRIBUTION AVAILIBILITY STATEMENT 6. AUTHORS 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES 15. SUBJECT TERMS b. ABSTRACT 2. REPORT TYPE 17. LIMITATION...Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the
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.
Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto
2016-12-01
It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low
NASA Astrophysics Data System (ADS)
Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto
2016-12-01
It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low
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
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
Zou, Lei; Wang, Zidong; Gao, Huijun; Liu, Xiaohui
2016-02-19
This paper is concerned with the state estimation problem for a class of nonlinear dynamical networks with time-varying delays subject to the round-robin protocol. The communication between the state estimator and the nodes of the dynamical networks is implemented through a shared constrained network, in which only one node is allowed to send data at each time instant. The round-robin protocol is utilized to orchestrate the transmission order of nodes. By using a switch-based approach, the dynamics of the estimation error is modeled by a periodic parameter-switching system with time-varying delays. The purpose of the problem addressed is to design an estimator, such that the estimation error is exponentially ultimately bounded with a certain asymptotic upper bound in mean square subject to the process noise and exogenous disturbance. Furthermore, such a bound is subsequently minimized by the designed estimator parameters. A novel Lyapunov-like functional is employed to deal with the dynamics analysis issue of the estimation error. Sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square by applying the stochastic analysis approach. Then, the desired estimator gains are characterized by solving a convex problem. Finally, a numerical example is given to illustrate the effectiveness of the estimator design scheme.
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)
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.
Statistical validation of stochastic models
Hunter, N.F.; Barney, P.; Paez, T.L.; Ferregut, C.; Perez, L.
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Vezzoli, R; De Michele, C; Pavlopoulos, H; Scholes, R J
2008-05-01
In drylands the soil water availability is a key factor ruling the architecture of the ecosystem. The soil water reflects the exchanges of water among soil, vegetation, and atmosphere. Here, a dryland ecosystem is investigated through the analysis of the local interactions between soil water and vegetation forced by rainfall having seasonal and stochastic occurrence. The evolution of dryland ecosystems is represented by a system of two differential equations, having two steady states, one vegetated and the other unvegetated. The rainfall forcing is described by a diffusion process with monthly parameters. In each of the two possible steady states, the probability density functions of soil water and vegetation are derived analytically in terms of the rainfall distribution. The results show how the seasonality of rainfall influences the oscillation of the ecosystem between its vegetated steady state during the wet season and its unvegetated steady state during the dry season.
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…
Baudracco, J; Lopez-Villalobos, N; Holmes, C W; Comeron, E A; Macdonald, K A; Barry, T N
2013-05-01
A whole-farm, stochastic and dynamic simulation model was developed to predict biophysical and economic performance of grazing dairy systems. Several whole-farm models simulate grazing dairy systems, but most of them work at a herd level. This model, named e-Dairy, differs from the few models that work at an animal level, because it allows stochastic behaviour of the genetic merit of individual cows for several traits, namely, yields of milk, fat and protein, live weight (LW) and body condition score (BCS) within a whole-farm model. This model accounts for genetic differences between cows, is sensitive to genotype × environment interactions at an animal level and allows pasture growth, milk and supplements price to behave stochastically. The model includes an energy-based animal module that predicts intake at grazing, mammary gland functioning and body lipid change. This whole-farm model simulates a 365-day period for individual cows within a herd, with cow parameters randomly generated on the basis of the mean parameter values, defined as input and variance and co-variances from experimental data sets. The main inputs of e-Dairy are farm area, use of land, type of pasture, type of crops, monthly pasture growth rate, supplements offered, nutritional quality of feeds, herd description including herd size, age structure, calving pattern, BCS and LW at calving, probabilities of pregnancy, average genetic merit and economic values for items of income and costs. The model allows to set management policies to define: dry-off cows (ceasing of lactation), target pre- and post-grazing herbage mass and feed supplementation. The main outputs are herbage dry matter intake, annual pasture utilisation, milk yield, changes in BCS and LW, economic farm profit and return on assets. The model showed satisfactory accuracy of prediction when validated against two data sets from farmlet system experiments. Relative prediction errors were <10% for all variables, and concordance
NASA Astrophysics Data System (ADS)
Ross, D. K.; Moreau, William
1995-08-01
We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics ( sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h µυ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(ω), must be proportional to 1/ω 2. The proportionality constant is determined by the Planck condition that the energy density consist ofħω/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh(ω) =√16πc 2Lp/ω2. As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R iojo(Oτ-δτ/2)R kolo(O,τ+δτ/2)) of the measureable geodesic deviation tensor field,R iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order inaδτ/c provided that the temperature and acceleration satisfy the relationkT=ħa/2πc.
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.
Xu, Yifang; Collins, Leslie M
2005-06-01
This work investigates dynamic range and intensity discrimination for electrical pulse-train stimuli that are modulated by noise using a stochastic auditory nerve model. Based on a hypothesized monotonic relationship between loudness and the number of spikes elicited by a stimulus, theoretical prediction of the uncomfortable level has previously been determined by comparing spike counts to a fixed threshold, Nucl. However, no specific rule for determining Nucl has been suggested. Our work determines the uncomfortable level based on the excitation pattern of the neural response in a normal ear. The number of fibers corresponding to the portion of the basilar membrane driven by a stimulus at an uncomfortable level in a normal ear is related to Nucl at an uncomfortable level of the electrical stimulus. Intensity discrimination limens are predicted using signal detection theory via the probability mass function of the neural response and via experimental simulations. The results show that the uncomfortable level for pulse-train stimuli increases slightly as noise level increases. Combining this with our previous threshold predictions, we hypothesize that the dynamic range for noise-modulated pulse-train stimuli should increase with additive noise. However, since our predictions indicate that intensity discrimination under noise degrades, overall intensity coding performance may not improve significantly.
Eksin, Ceyhun; Shamma, Jeff S.; Weitz, Joshua S.
2017-01-01
Individuals change their behavior during an epidemic in response to whether they and/or those they interact with are healthy or sick. Healthy individuals may utilize protective measures to avoid contracting a disease. Sick individuals may utilize preemptive measures to avoid spreading a disease. Yet, in practice both protective and preemptive changes in behavior come with costs. This paper proposes a stochastic network disease game model that captures the self-interests of individuals during the spread of a susceptible-infected-susceptible disease. In this model, individuals strategically modify their behavior based on current disease conditions. These reactions influence disease spread. We show that there is a critical level of concern, i.e., empathy, by the sick individuals above which disease is eradicated rapidly. Furthermore, we find that risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals. Empathy is more effective than risk-aversion because when infectious individuals change behavior, they reduce all of their potential infections, whereas when healthy individuals change behavior, they reduce only a small portion of potential infections. This imbalance in the role played by the response of the infected versus the susceptible individuals on disease eradication affords critical policy insights. PMID:28290504
NASA Astrophysics Data System (ADS)
Sharma, Rati; Cherayil, Binny J.
2013-10-01
Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p,r,t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p,r,t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t → ∞. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.
Analysis of bilinear stochastic systems. [involving multiplicative noise processes
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Marcus, S. I.; Martin, D. N.
1974-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
NASA Astrophysics Data System (ADS)
Zhao, Nan
2017-01-01
The origin of winter Northern Hemispheric low-frequency variability (hereafter, LFV) is regarded to be related to the coupled earth-atmosphere system characterized by the interaction of the jet stream with mid-latitude mountain ranges. On the other hand, observed LFV usually appears as transitions among multiple planetary-scale flow regimes of Northern Hemisphere like NAO + , AO +, AO - and NAO - . Moreover, the interaction between synoptic-scale eddies and the planetary-scale disturbance is also inevitable in the origin of LFV. These raise a question regarding how to incorporate all these aspects into just one framework to demonstrate (1) a planetary-scale dynamics of interaction of the jet stream with mid-latitude mountain ranges can really produce LFV, (2) such a dynamics can be responsible for the existence of above multiple flow regimes, and (3) the role of interaction with eddy is also clarified. For this purpose, a hierarchy of low-order stochastic dynamical models of the coupled earth-atmosphere system derived empirically from different timescale ranges of indices of Arctic Oscillation (AO), North Atlantic Oscillation (NAO), Pacific/North American (PNA), and length of day (LOD) and related probability density function (PDF) analysis are employed in this study. The results seem to suggest that the origin of LFV cannot be understood completely within the planetary-scale dynamics of the interaction of the jet stream with mid-latitude mountain ranges, because (1) the existence of multiple flow regimes such as NAO+, AO+, AO- and NAO- resulted from processes with timescales much longer than LFV itself, which may have underlying dynamics other than topography-jet stream interaction, and (2) we find LFV seems not necessarily to come directly from the planetary-scale dynamics of the interaction of the jet stream with mid-latitude mountain, although it can produce similar oscillatory behavior. The feedback/forcing of synoptic-scale eddies on the planetary
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit
NASA Astrophysics Data System (ADS)
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
NASA Astrophysics Data System (ADS)
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
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.
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.
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 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.
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.
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.
Oroji, Amin; Omar, Mohd; Yarahmadian, Shantia
2016-10-21
In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to the cell cycle, each cell belongs to one of three subpopulations G, S, or M, representing gap, synthesis and mitosis subpopulations. Cells in the M subpopulation are highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant. Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately, the small changes in cell death rate in each subpopulation during treatment are considered. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 breast cancer cell line. Consequently, the proposed model is able to predict tumor lifespan based on the number of initial carcinoma cells. The results show the effectiveness of the radiation under the condition of stability, which describes the decreasing trend of the tumor cells population.
Frank, Andreas O; Freudenberger, J Christoph; Shaytan, Alexey K; Kessler, Horst; Luy, Burkhard
2015-03-01
Residual dipolar couplings are highly useful NMR parameters for calculating and refining molecular structures, dynamics, and interactions. For some applications, however, it is inevitable that the preferred orientation of a molecule in an alignment medium is calculated a priori. Several methods have been developed to predict molecular orientations and residual dipolar couplings. Being beneficial for macromolecules and selected small-molecule applications, such approaches lack sufficient accuracy for a large number of organic compounds for which the fine structure and eventually the flexibility of all involved molecules have to be considered or are limited to specific, well-studied liquid crystals. We introduce a simplified model for detailed all-atom molecular dynamics calculations with a polymer strand lined up along the principal axis as a new approach to simulate the preferred orientation of small to medium-sized solutes in polymer-based, gel-type alignment media. As is shown by a first example of strychnine in a polystyrene/CDCl3 gel, the simulations potentially enable the accurate prediction of residual dipolar couplings taking into account structural details and dynamic averaging effects of both the polymer and the solute.
Strasser, Michael; Theis, Fabian J; Marr, Carsten
2012-01-04
A toggle switch consists of two genes that mutually repress each other. This regulatory motif is active during cell differentiation and is thought to act as a memory device, being able to choose and maintain cell fate decisions. Commonly, this switch has been modeled in a deterministic framework where transcription and translation are lumped together. In this description, bistability occurs for transcription factor cooperativity, whereas autoactivation leads to a tristable system with an additional undecided state. In this contribution, we study the stability and dynamics of a two-stage gene expression switch within a probabilistic framework inspired by the properties of the Pu/Gata toggle switch in myeloid progenitor cells. We focus on low mRNA numbers, high protein abundance, and monomeric transcription-factor binding. Contrary to the expectation from a deterministic description, this switch shows complex multiattractor dynamics without autoactivation and cooperativity. Most importantly, the four attractors of the system, which only emerge in a probabilistic two-stage description, can be identified with committed and primed states in cell differentiation. To begin, we study the dynamics of the system and infer the mechanisms that move the system between attractors using both the quasipotential and the probability flux of the system. Next, we show that the residence times of the system in one of the committed attractors are geometrically distributed. We derive an analytical expression for the parameter of the geometric distribution, therefore completely describing the statistics of the switching process and elucidate the influence of the system parameters on the residence time. Moreover, we find that the mean residence time increases linearly with the mean protein level. This scaling also holds for a one-stage scenario and for autoactivation. Finally, we study the implications of this distribution for the stability of a switch and discuss the influence of the
Non-Markov effects in intersecting sprays
NASA Astrophysics Data System (ADS)
Panchagnula, Mahesh; Kumaran, Dhivyaraja; Deevi, Sri Vallabha; Tangirala, Arun
2016-11-01
Sprays have been assumed to follow a Markov process. In this study, we revisit that assumption relying on experimental data from intersecting and non-intersecting sprays. A phase Doppler Particle Analyzer (PDPA) is used to measure particle diameter and velocity at various axial locations in the intersection region of two sprays. Measurements of single sprays, with one nozzle turned off alternatively are also obtained at the same locations. This data, treated as an unstructured time series is classified into three bins each for diameter (small, medium, large) and velocity (slow, medium, fast). Conditional probability analysis on this binned data showed a higher static correlation between droplet velocities, while diameter correlation is significantly alleviated (reduced) in intersecting sprays, compared to single sprays. Further analysis using serial correlation measures: auto-correlation function (ACF) and partial auto-correlation function (PACF) shows that the lagged correlations in droplet velocity are enhanced while those in the droplet diameter are significantly debilitated in intersecting sprays. We show that sprays are not necessarily Markov processes and that memory persists, even though curtailed to fewer lags in case of size, and enhanced in case of droplet velocity.
NASA Astrophysics Data System (ADS)
Robbins, Brian; Field, Rich; Grigoriu, Mircea; Jamison, Ryan; Mesh, Mikhail; Casper, Katya; Dechant, Lawrence
2016-11-01
During reentry, a hypersonic vehicle undergoes a period in which the flow about the vehicle transitions from laminar to turbulent flow. During this transitional phase, the flow is characterized by intermittent formations of localized turbulent behavior. These localized regions of turbulence are born at the onset of transition and grow as they move to the aft end of the flight vehicle. Throughout laminar-turbulent transition, the moving turbulent spots cause pressure fluctuations on the outer surface of the vehicle, which leads to the random vibration of the structure and its internal components. In light of this, it is of great interest to study the dynamical response of a flight vehicle undergoing transitional flow so that aircraft can be better designed to prevent structural failure. In this talk, we present a statistical model that calculates the birth, evolution, and pressure field of turbulent spots over a generic slender cone structure. We then illustrate that the model appropriately quantifies intermittency behavior and pressure loading by comparing the intermittency and root-mean-square pressure fluctuations produced by the model with theory and experiment. Finally, we present results pertaining to the structural response of a housing panel on the slender cone. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
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.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
NASA Astrophysics Data System (ADS)
Ribeiro, Andre S.
2007-06-01
Genetic toggle switches (TSs) are one of the best studied small gene regulatory networks (GRNs), due to their simplicity and relevant role. They have been interpreted as decision circuits in cell differentiation, a process long hypothesized to be bistable [1], or as cellular memory units [2]. In these contexts, they must be reliable. Once a “decision” is made, the system must remain stable. One way to gain stability is by duplicating the genes of a TS and coupling the two TSs. Using a recent modeling strategy of GRNs, driven by a delayed stochastic simulation algorithm (delayed SSA) that allows modeling transcription and translation as multidelayed reactions, we analyze the stability of systems of coupled TSs. For this, we introduce the coupling strength (C) , a parameter to characterize the GRN structure, against which we compare the GRN stability (S) . We first show that time delays in transcription, associated to the promoter region release, ensure bistability of a TS, given no cooperative binding or self-activation reactions. Next, we couple two TSs and measure their toggling frequencies as C varies. Three dynamical regimes are observed: (i) for weak coupling, high frequency synchronized oscillations, (ii) for average coupling, low frequency synchronized oscillations, and (iii) for strong coupling the system becomes stable after a transient, in one of two steady states. The system stability, S , goes through a first order phase transition as C increases, in the average coupling regime. After, we study the effects of spatial separation in two compartments on the dynamics of two coupled TSs, where spatial separation is modeled as normally distributed random time delayed reactions. The phase transition of S , as C increases, occurs for lower values of C than when the two TSs are in the same compartment. Finally, we couple weakly and homogeneously several TSs within a single compartment and observe that as the number of coupled TSs increases, the system goes
Stochastic synchronization in finite size spiking networks.
Doiron, Brent; Rinzel, John; Reyes, Alex
2006-09-01
We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.
Complexity and synchronization in stochastic chaotic systems
NASA Astrophysics Data System (ADS)
Dang, Thai Son; 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.
Stochastic Forcing for Ocean Uncertainty Prediction
2013-09-30
shallow water waves governed by Korteweg-de Vries ( KdV ) dynamics with stochastic forcing. Uncertain Boundary Conditions and DO Equations : A...schemes to time-integrate shallow water surface waves governed by KdV equations with external stochastic forcing. We find that the DO scheme is...free- surface primitive equation model and Error Subspace Statistical Estimation (ESSE). The variability in the pdfs are illustrated and discussed
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Stochastic Modeling Of Biochemical Reactions
2006-11-01
chemical reactions. Often for these reactions, the dynamics of the first M-order statistical moments of the species populations do not form a closed...results a stochastic model for gene expression is investigated. We show that in gene expression mechanisms , in which a protein inhibits its own...chemical reactions [7, 8, 4, 9, 10]. Since one is often interested in only the first and second order statistical moments for the number of molecules of
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.
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
Brownian motors and stochastic resonance.
Mateos, José L; Alatriste, Fernando R
2011-12-01
We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
Stochastic symmetries of Wick type stochastic ordinary differential equations
NASA Astrophysics Data System (ADS)
Ünal, Gazanfer
2015-04-01
We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space (S)-1N. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in (S)-1N are obtained. A stochastic version of canonical variables is also introduced.
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.
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 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.
Multiple fields in stochastic inflation
Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-06-24
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-δN formalism.
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 perturbation of the two-body problem
NASA Astrophysics Data System (ADS)
Cresson, J.; Pierret, F.; Puig, B.
2013-11-01
We study the impact of a stochastic perturbation on the classical two-body problem in particular concerning the preservation of first integrals and the Hamiltonian structure. Numerical simulations are performed which illustrate the dynamical behavior 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.
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.
Kaniyamattam, K; Elzo, M A; Cole, J B; De Vries, A
2016-10-01
The objective of this study was to develop a daily stochastic dynamic dairy simulation model that included multitrait genetics and to evaluate the effects of reduced genetic models and various reproduction and selection strategies on the genetic, technical, and financial performance of a dairy herd. The 12 correlated genetic traits included in the 2014 lifetime net merit (NM$) index were modeled for each animal. For each animal, a true breeding value (TBV) for each trait was calculated as the average of the sire's and dam's TBV, plus a fraction of the inbreeding and Mendelian sampling variability. Similarly, an environmental component for each trait was calculated and was partitioned into a permanent and a daily (temporary) effect. The combined TBV and environmental effects were converted into the phenotypic performance of each animal. Hence, genetics and phenotypic performances were associated. Estimated breeding values (EBV) were also simulated. Genetic trends for each trait for the service sire were based on expected trends in US Holsteins. Surplus heifers were culled based on various ranking criteria to maintain a herd size of 1,000 milking cows. In the first 8 scenarios, culling of surplus heifers was either random or based on the EBV of NM$. Four different genetic models, depending on the presence or absence of genetic trends or genetic and environmental correlations, or both, were evaluated to measure the effect of excluding multitrait genetics on animal performance. In the last 5 scenarios, the full genetic model was used and culling of surplus heifers was either random or based on the EBV of NM$ or the EBV of milk. Sexed semen use and reliability of the EBV were also varied. Each scenario was simulated for 15yr into the future. Results showed that genetic models without all 12 genetic trends and genetic and environmental correlations provided biased estimates of the genetic, technical, and financial performance of the dairy herd. Average TBV of NM$ of all
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.
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.
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.
Turbulence, Spontaneous Stochasticity and Climate
NASA Astrophysics Data System (ADS)
Eyink, Gregory
Turbulence is well-recognized as important in the physics of climate. Turbulent mixing plays a crucial role in the global ocean circulation. Turbulence also provides a natural source of variability, which bedevils our ability to predict climate. I shall review here a recently discovered turbulence phenomenon, called ``spontaneous stochasticity'', which makes classical dynamical systems as intrinsically random as quantum mechanics. Turbulent dissipation and mixing of scalars (passive or active) is now understood to require Lagrangian spontaneous stochasticity, which can be expressed by an exact ``fluctuation-dissipation relation'' for scalar turbulence (joint work with Theo Drivas). Path-integral methods such as developed for quantum mechanics become necessary to the description. There can also be Eulerian spontaneous stochasticity of the flow fields themselves, which is intimately related to the work of Kraichnan and Leith on unpredictability of turbulent flows. This leads to problems similar to those encountered in quantum field theory. To quantify uncertainty in forecasts (or hindcasts), we can borrow from quantum field-theory the concept of ``effective actions'', which characterize climate averages by a variational principle and variances by functional derivatives. I discuss some work with Tom Haine (JHU) and Santha Akella (NASA-Goddard) to make this a practical predictive tool. More ambitious application of the effective action is possible using Rayleigh-Ritz schemes.