A Gallavotti-Cohen-Evans-Morriss Like Symmetry for a Class of Markov Jump Processes

We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochastic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.     

Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.     

Structure and Randomness of Continuous-Time,Discrete-Event Processes

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (\(\epsilon \)-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.     

Rank-Driven Markov Processes

We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak–Sneppen model of evolution, in which the system represents an evolutionary ‘fitness landscape’ and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large-N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ _N on {1,2,…,N} ^K . Our main results are that, under appropriate conditions on κ _N , the system exhibits threshold behavior at s ^∗∈[0,1], where s ^∗ is a function of κ _N , and the marginal distribution of a randomly selected element converges to U[s ^∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the ‘mean-field’ or ‘random neighbor’ Bak–Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster–Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.     

The Viterbi Algorithm for Models of Hidden Markov Processes with the Unknown Moment of Appearance of Parameter Jump

The methods of the theory of optimal nonlinear filtering of the Markov processes is used to develop the Viterbi algorithm for obtaining optimal estimates of a sequence of hidden states in the model of discrete-value Markov processes generalized to the case of jump-like changing parameters with an unknown time of the jump appearance. The results of numerical simulation of the algorithm performance are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 358–366, April 2005.     

A Variational Principle for Markov Processes

In this note, we first present a result concerning a variational principle for general Markov processes. Then we apply it to spin particle systems to obtain a full form of a variational principle characterizing the stationary Markov laws of the systems. A related extreme decomposition for any stationary distribution of such Markov systems is also given.     

Self-Duality of Markov Processes and Intertwining Functions

We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two representations of a certain Lie algebra is the self-duality function of a (Markov) operator. In concrete terms, the two representations are associated to two operators in interwining relation. The self-dual operator, which arise from an appropriate symmetric linear combination of them, is the generator of a Markov process. The theorem is applied to a series of examples, including Markov processes with a discrete state space (e.g. interacting particle systems) and Markov processes with continuous state space (e.g. diffusion processes). In the examples we use explicit representations of Lie algebras that are unitarily equivalent. As a consequence, in the discrete setting self-duality functions are given by orthogonal polynomials whereas in the continuous context they are Bessel functions.     

Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ ^d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry relation with involution map different from time-reversal.     

Entropy of Hidden Markov Processes via Cycle Expansion

Hidden Markov Processes (HMP) is one of the basic tools of the modern probabilistic modeling. The characterization of their entropy remains however an open problem. Here the entropy of HMP is calculated via the cycle expansion of the zeta-function, a method adopted from the theory of dynamical systems. For a class of HMP this method produces exact results both for the entropy and the moment-generating function. The latter allows to estimate, via the Chernoff bound, the probabilities of large deviations for the HMP. More generally, the method offers a representation of the moment-generating function and of the entropy via convergent series.     

Inference,Prediction, & Entropy-Rate Estimation of Continuous-Time,Discrete-Event Processes

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network’s universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.     

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.     

一类受Poisson干扰的Markov过程应跳性逼近

对于随机微分方程约束下受Poison干扰的Markov过程,给出了一种具有应跳性的轨道逼近方法:将每条轨道分解为若干连续阶段,在每个阶段中建立了相应的常微分方程,并采用Runge-Kuta方法求解。该方法已用于研究Langevin方程和Dufing-VanderPol振子。     

Nonlinear Markov Semigroups and Interacting Lévy Type Processes

Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space R ^d (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.     

Characterizing the Evolution of Porosity during Controlled Drug Release

Nuclear magnetic resonance (NMR) techniques have been successfully used to characterize the evolving pore structure of partially soluble pharmaceutical pellets as they absorb water and release soluble components. The restricted diffusivity of water trapped within pellets, which have been immersed in water for differing times, has been measured by pulsed field gradient NMR. These measurements have been used to calculate the surface-to-volume ratio and tortuosity of the pore structure. A one-shot Carr–Purcell–Meiboom–Gill sequence has been used to measure the spin–spin (T ₂) relaxation time of water trapped within the pellets. These data have been regularized and then analyzed by the Brownstein–Tarr model to provide a pore size distribution for the pellets as a function of increasing immersion time. It has been found that pore structure changes significantly as water enters the pellet matrix. Two pellet formulations (herein referred to as placebo and drug-loaded) were studied and showed the same trends of a decreasing surface-to-volume ratio and tortuosity with increasing immersion time. At an immersion time of 10 min, both of these parameters decreased to approximately 70% of their values compared to an immersion time of 2 min. The placebo material tested consistently had both a higher tortuosity and surface-to-volume ratio than the drug-loaded material. At an immersion time of 2 min, the tortuosity for the placebo and drug-loaded materials were about 18 and about 10, respectively, and surface-to-volume ratios of about 6 μm⁻¹ and about 5 μm⁻¹, respectively. The materials tested also show changes in their pore size distribution with immersion time. In both formulations the mean and modal pore sizes increase with immersion time. The placebo material maintains an approximately similar mean and modal pore size, about 2 μm over the timescales studied, suggesting a more symmetric pore size distribution. In the drug-loaded pellets the mean pore size is much higher than the modal pore size, their values being 6.5 and 2.1 μm after 10 min immersion time, respectively. Authors' address: Michael D. Mantle, Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK     

移动式间隔蓄热器的蓄放热特性分析

通过FLUENT软件对不同布置方式的蓄热器进行数值模拟,结果表明,采用间隔式蓄热器会使蓄热器的材料温度更高,前中期蓄放热速率更快;但存在很明显的区域不均匀的现象:具体表现为中心区域要较其他区域反应速率更快,温升明显更高.从模拟结果来看,此种布置方法虽然一定程度上节省了余热资源,但由于区域反应的不平衡,致使总反应时间滞后...     

Two-Stage Technique of Controlling the Heat Release Distribution

Physics of Atomic Nuclei - A two-stage method is proposed for controlling the regulators in the fuel burnup process during a single operating period. At the first stage, the coefficient of the heat...     

Computer Controlled AAS Scanning Method to Study Flame Atomization Processes

By slightly changing the optical and burner systems of the conventional atomic absorption spectrometer, a computer controlled scanning method has been developed, which enables us to get a picture of absorbance distribution over the entire cross section of the analytical flames quickly, reproducibly and in high resolution. The plotting of different distribution functions obtainable by computerized data processing and the conclusions drawn from them are illustrated with some examples of flame atomization of cobalt and magnesium salts. The newly discovered method, by its reliability and little demand on time, allows the extension of the general applicability of AAS in revealing analytical interference effects and in the study of flame-chemical processes.