a stochastic model of the production of multiple proteins in cells the production processes of several classes of proteins in prokaryotic cells is investigated a markov process is introduced to study how the limited common resources of the cell like ribosomes are used understanding the impact of this limitation on the production process is a key issue we focus on the allocation of ribosomes in the case of the production of multiple classes of proteins asymptotic results are obtained under a scaling procedure and a realistic biological assumption on the limited number of ribosomes available in the cell it is shown that in the limit the number of nonallocated ribosomes at equilibrium converges in distribution to a poisson distribution whose parameter satisfies a fixed point equation it is also shown that the production process of different types of proteins can be seen as independent production processes but with modified parameters

asymptotic expansions for large closed queueing networks with multiple job classes a closed bcmp queuing network consisting of r job classes chains k 1 single server fixed rate nodes and m sub j class j jobs j 1 2 r is considered asymptotic expansions are constructed for the partition function under assumptions 1 k 1 2 m sub j 1 for each j and 3 k m sub j o 1 analytic expressions for performance measures such as the mean queue length are also given the approach employs the ray method and the method of matched asymptotic expansions numerical comparisons illustrate the accuracy of the approximations

different methods to estimate the einstein markov coherence length in turbulence we study the markov property of experimental velocity data of different homogeneous isotropic turbulent flows in particular we examine the stochastic cascade process of nested velocity increments r u x r u x as a function of scale r for different nesting structures it was found in previous work that for a certain nesting structure the stochastic process of r has the markov property for step sizes larger than the so called einstein markov coherence length l em which is of the order of magnitude of the taylor microscale phys lett a 359 335 2006 we now show that if a reasonable definition of the effective step size of the process is applied this result holds independently of the nesting structure furthermore we analyze the stochastic process of the velocity u as a function of the spatial position x although this process does not have the exact markov property a characteristic length scale l u x l em can be identified on the basis of a statistical test for the markov property using a method based on the matrix of transition probabilities we examine the significance of the non markovian character of the velocity u x for the statistical properties of turbulence

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

current fluctuations of the one dimensional symmetric simple exclusion process with step initial condition for the symmetric simple exclusion process on an infinite line we calculate exactly the fluctuations of the integrated current qt during time t through the origin when in the initial condition the sites are occupied with density a on the negative axis and with density b on the positive axis all the cumulants of qt grow like sqrt t in the range where q t sim sqrt t the decay exp qt3 t of the distribution of qt is non gaussian our results are obtained using the bethe ansatz and several identities derived recently by tracy and widom for exclusion processes on the infinite line

asymptotic expansions for closed markovian networks with state dependent service rates a method is presented for calculating the partition function and from it performance measures for closed markovian stochastic networks with queuing centers in which the service or processing rate depends on the center s state or load the analysis on which this method is based is new and a major extension of our earlier work on load independent queuing networks the method gives asymptotic expansions for the partition function in powers of 1 n where n is a parameter that reflects the size of the network the expansions are particularly useful for large networks with many classes each class having many customers the end result is a decomposition by which expansion coefficients are obtained exactly by linear combinations of partition function values of small network constructs called pseudonetworks effectively computable bounds are given for errors arising from the use of a finite number of expansion terms this method is important because load dependence is at once an essential element of sophisticated network models of computers computer communications and switching teletraffic and manufacturing systems and the cause of very intensive computations in conventional techniques with this method very large load dependent networks can be analyzed whereas previously only small networks were computationally tractable

asymptotic analysis for a closed processor sharing system with switching times normal usage in a closed processor sharing system with cpu switching times the probability distribution of the waiting time w p varepsilon t mathbb p w t varepsilon geqq 0 where varepsi

asymptotic expansions of the sojourn time distribution functions of jobs in closed product form queuing networks striking progress has been made recently in obtaining expressions for the sojourn time distribution function stdf of a job at a c server first come first serve fcfs center in a closed product form queuing network these results have more recently been extended and expressions have been obtained for the joint distribution function df of the sojourn times of a job at a sequence of single server fcfs centers lying on an overtake free path however these formulas present considerable computational problems in the case of large closed queuing networks in this paper asymptotic techniques developed by mitra and mckenna for the calculation of the partition function of large product form closed queuing networks are applied to the sojourn time problem asymptotic expansions are obtained for the stdf of a job at c server fcfs center in closed product form queuing networks similar expansions are obtained for the joint df of the sojourn times of a job at a sequence of single server fcfs centers lying on an overtake free path in addition integral expressions are obtained for the stdf of a job at a single server fcps center in a closed product form queuing network in which all the centers are load independent these integral expressions also yield useful asymptotic expansions finally integral expressions are also obtained for the joint df of the sojourn times of a job at the centers of an overtake free path in such a network

statistical properties of a turbulent cascade abstract statistical properties of a turbulent cascade are evaluated by considering the joint probability distribution p 1 l1 2 l2 for two velocity increments 1 2 of different length scales l1 l2 we present experimental evidence that the conditional probability distribution p 2 l2 1 l1 obeys a chapman kolmogorov equation we evaluate the kramers moyal coefficient and show evidence that higher order coefficients vanish except for the drift and diffusion coefficient as a result the joint probability distributions obeys a fokker planck equation we calculate drift and diffusion coefficients and discuss their relationship to universal behaviour in the scaling region and to intermittency of the turbulent cascade

closed queueing networks under congestion nonbottleneck independence and bottleneck convergence we analyze the behavior of closed multiclass product form queueing networks when the number of customers grows to infinity and remains proportionate on each route or class first we focus on the stationary behavior and prove the conjecture that the stationary distribution at nonbottleneck queues converges weakly to the stationary distribution of an ergodic open product form queueing network which is geometric this open network is obtained by replacing bottleneck queues with per route poissonian sources whose rates are uniquely determined by the solution of a strictly concave optimization problem we strengthen such results by also proving convergence of the first moment of the queue lengths of nonbottleneck stations then we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid or customers on each route eventually concentrates on the bottleneck queues only and that the long term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network

symmetric exclusion process with a localized source we investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source the average total number of particles entering an initially empty system grows with time as t in one dimension t ln t in two dimensions and linearly in higher dimensions in one and two dimensions the leading asymptotic behaviors for the average total number of particles are independent of the intensity of the source we also discuss fluctuations of the total number of particles and determine the asymptotic growth of the variance in one dimension

current fluctuations in one dimensional diffusive systems with a step initial density profile we show how to apply the macroscopic fluctuation theory mft of bertini de sole gabrielli jona lasinio and landim to study the current fluctuations of diffusive systems with a step initial condition we argue that one has to distinguish between two ways of averaging the annealed and the quenched cases depending on whether we let the initial condition fluctuate or not although the initial condition is not a steady state the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem we show how the equations of the mft can be solved in the case of non interacting particles the symmetry of these equations can be used to deduce the distribution of the current for several other models from its knowledge derrida and gerschenfeld in j stat phys 136 1 15 2009 for the symmetric simple exclusion process in the range where the integrated current q t sim sqrt t we show that the non gaussian decay exp q t 3 t of the distribution of q t is generic

improved estimation of fokker planck equations through optimization an improved method for the description of hierarchical complex systems by means of a fokker planck equation is presented in particular the limited memory broyden fletcher goldfarb shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the fokker planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the fokker planck equation the optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine

a boundary property of semimartingale reflecting brownian motions we consider a class of reflecting brownian motions on the non negative orthant inr k in the interior of the orthant such a process behaves like brownian motion with a constant covariance matrix and drift vector at each of the k 1 dimensional faces that form the boundary of the orthant the process reflects instantaneously in a direction that is constant over the face we give a necessary condition for the process to have a certain semimartingale decomposition and then show that the boundary processes appearing in this decomposition do not charge the set of times that the process is at the intersection of two or more faces this boundary property plays an essential role in the derivation performed in a separate work of an analytical characterization of the stationary distributions of such semimartingale reflecting brownian motions

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

asymptotic expansion for large closed queuing networks in this paper a new asymptotic method is developed for analyzing closed bcmp queuing networks with a single class chain consisting of a large number of customers a single infinite server queue and a large number of single server queues with fixed state independent service rates asymptotic approximations are computed for the normalization constant partition function starting directly from a recursion relation of buzen the approach of the authors employs the ray method of geometrical optics and the method of matched asymptotic expansions the method is applicable when the servers have nearly equal relative utilizations or can be divided into classes with nearly equal relative utilizations numerical comparisons are given that illustrate the accuracy of the asymptotic approximations

increment definitions for scale dependent analysis of stochastic data the question how to nest the increments on di erent scales r r isinvestigated here we show that in some cases spurious correlations between scales can be introducedby the common left justi ed de nition the consequences for a markov process are discussed thesespurious correlations can be avoided by an appropriate nesting of increments we demonstrate thise ect for di erent data sets and show how it can be detected and quanti ed the problem allowsto propose a unique method to distinguish between experimental data generated by a noiselike or alangevin like random walk process respectively

on the distribution of multidimensional reflected brownian motion let z z t t 0 be a reflected brownian motion on the k dimensional nonnegative orthant with the direction of reflection constant over each boundary surface such processes arise in heavy traffic theory for k station networks of queues this paper continues our study of the diffusion process z with attention restricted to the case k 2 for simplicity most of the results extend directly to higher dimensions our notation and style of argument are designed to suggest appropriate generalizations for arbitrary k wherever possible the backward equation for the transition density function with boundary and initial conditions the corresponding forward equation and the equation for the steady state distribution are all derived informally also presented are various calculations relating to steady state distributions including a moment formula and the derivation of a condition involving the drifts and directions of reflection that we conjecture to be necessary and sufficient for existence

exact results for kinetics of catalytic reactions the kinetics of an irreversible catalytic reaction on substrate of arbitrary dimension is examined in the limit of infinitesimal reaction rate reaction controlled limit we solve the dimer dimer surface reaction model or voter model exactly in arbitrary dimension d the density of reactive interfaces is found to exhibit a power law decay for d 2 and a slow logarithmic decay in two dimensions we discuss the relevance of these results for the monomer monomer surface reaction model

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

fluctuations of current in nonstationary diffusive lattice gases we employ the macroscopic fluctuation theory to study fluctuations of integrated current in one dimensional lattice gases with a steplike initial density profile we analytically determine the variance of the current fluctuations for a class of diffusive processes with a density independent diffusion coefficient our calculations rely on a perturbation theory around the noiseless hydrodynamic solution we consider both quenched and annealed types of averaging the initial condition is allowed to fluctuate in the latter situation the general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the kipnis marchioro presutti model kipnis marchioro and presutti j stat phys 27 65 1982 we also probe large deviations of the current for the symmetric exclusion process this is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm