queueing process with excluded volume effect we introduce an extension of the m m 1 queueing process with a spatial structure and excluded volume effect the rule of particle hopping is the same as for the totally asymmetric simple exclusion process tasep a stationary state solution is constructed in a slightly arranged matrix product form of the open tasep we obtain the critical line that separates the parameter space depending on whether the model has the stationary state we calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state we also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the m m 1 queueing process and the open tasep

scaling of avalanche queues in directed dissipative sandpiles using numerical simulations and analytical methods we study a two dimensional directed sandpile automaton with nonconservative random defects concentration c and varying driving rate r the automaton is driven only at the top row and driving rate is measured by the number of added particles per time step of avalanche evolution the probability distribution of duration of elementary avalanches at zero driving rate is exactly given by p 1 t c t ensuremath 3 2 mathrm exp t mathrm ln 1 ensuremath c for driving rates in the interval 0lrl 1 the avalanches are queuing one after another increasing the periods of noninterrupted activity of the automaton recognizing the probability p 1 as a distribution of service time of jobs arriving at a server with frequency r the model represents an example of the class e 1 gi ensuremath infty 1 server queue in the queue theory we study scaling properties of the busy period and dissipated energy of sequences of noninterrupted activity in the limit stackrel ensuremath rightarrow c 0 and varying linear system size l ensuremath ll 1 c we find that at driving rates rl l ensuremath 1 2 the distributions of duration and energy of the avalanche queues are characterized by a multifractal scaling and we determine the corresponding spectral functions for l ensuremath gg 1 c increasing the driving rate somewhat compensates for the energy losses at defects above the line r ensuremath sim sqrt c the scaling exponents of the distributions in this region of phase diagram vary approximately linearly with the driving rate using properties of recurrent states and the probability theory we determine analytically the exact upper bound of the probability distribution of busy periods in the case of conservative dynamics c 0 the probability of a continuous flow increases as f ensuremath infty ensuremath sim r 2 for small driving rates

nonequilibrium phase transition in a non integrable zero range process the present work is an endeavour to determine analytically features of the stationary measure of a non integrable zero range process and to investigate the possible existence of phase transitions for such a nonequilibrium model the rates defining the model do not satisfy the constraints necessary for the stationary measure to be a product measure even in the absence of a drive detailed balance with respect to this measure is violated analytical and numerical investigations on the complete graph demonstrate the existence of a first order phase transition between a fluid phase and a condensed phase where a single site has macroscopic occupation the transition is sudden from an imbalanced fluid where both species have densities larger than the critical density to a critical neutral fluid and an imbalanced condensate

spacetime texture representation and recognition based on a spatiotemporal orientation analysis this paper is concerned with the representation and recognition of the observed dynamics i e excluding purely spatial appearance cues of spacetime texture based on a spatiotemporal orientation analysis the term spacetime texture is taken to refer to patterns in visual spacetime x y t that primarily are characterized by the aggregate dynamic properties of elements or local measurements accumulated over a region of spatiotemporal support rather than in terms of the dynamics of individual constituents examples include image sequences of natural processes that exhibit stochastic dynamics e g fire water and windblown vegetation as well as images of simpler dynamics when analyzed in terms of aggregate region properties e g uniform motion of elements in imagery such as pedestrians and vehicular traffic spacetime texture representation and recognition is important as it provides an early means of capturing the structure of an ensuing image stream in a meaningful fashion toward such ends a novel approach to spacetime texture representation and an associated recognition method are described based on distributions histograms of spacetime orientation structure empirical evaluation on both standard and original image data sets shows the promise of the approach including significant improvement over alternative state of the art approaches in recognizing the same pattern from different viewpoints

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

motion estimation using the correlation transform the zero mean normalized cross correlation is shown to improve the accuracy of optical flow but its analytical form is quite complicated for the variational framework this paper addresses this issue and presents a new direct approach to this matching measure our approach uses the correlation transform to define very discriminative descriptors that are pre computed and that have to be matched in the target frame it is equivalent to the computation of the optical flow for the correlation transforms of the images the smoothness energy is non local and uses a robust penalty in order to preserve motion discontinuities the model is associated with a fast and parallelizable minimization procedure based on the projected proximal point algorithm the experiments confirm the strength of this model and implicitly demonstrate the correctness of our solution the results demonstrate that the involved data term is very robust with respect to changes in illumination especially where large illumination exists

phase transition in tumor growth i avascular development abstract we propose a mechanism for avascular tumor growth based on a simple chemical network this model presents a logistic behavior and shows a second order phase transition we prove the fractal origin of the empirical logistics and gompertz constant and its relation to mitosis and apoptosis rate finally the thermodynamics framework developed demonstrates the entropy production rate as a lyapunov function during avascular tumor growth

active tracking strategy for monocular depth inference over multiple frames the extraction of depth information from a sequence of images is investigated an algorithm that exploits the constraint imposed by active motion of the camera is described within this framework in order to facilitate measurement of the navigation parameters a constrained egomotion strategy was adopted in which the position of the fixation point is stabilized during the navigation in an anthropomorphic fashion this constraint reduces the dimensionality of the parameter space without increasing the complexity of the equations a further distinctive point is the use of two sampling rates the faster related to the computation of the instantaneous optical flow is fast enough to allow the local operator to sense the passing edge or in other words to allow the tracking of moving contour points while the slower used to perform the triangulation procedure necessary to derive depth is slow enough to provide a sufficiently large baseline for triangulation experimental results on real image sequences are presented

oriented structure of the occlusion distortion is it reliable in the energy spectrum of an occlusion sequence the distortion term has the same orientation as the velocity of the occluding signal other works claimed that this oriented structure can be used to distinguish the occluding velocity from the occluded one we argue that the orientation structure of the distortion cannot always work as a reliable feature due to the rapidly decreasing energy contribution this already weak orientation structure is further blurred by a superposition of distinct distortion components we also indicate that the superposition principle of shizawa and mase 1991 for multiple motion estimation needs to be adjusted

structure of the condensed phase in the inclusion process we establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum occupation number we make use of size biased sampling to study the structure of the condensed phase which can extend over more than one lattice site and exhibit an interesting hierarchical structure characterized by the poisson dirichlet distribution while this approach is established in other areas including population genetics or random permutations we show that it also provides a powerful tool to analyse homogeneous condensation in stochastic particle systems with stationary product distributions we discuss the main mechanisms beyond inclusion processes that lead to the interesting structure of the condensed phase and the connection to other generic particle systems our results are exact and we present monte carlo simulation data and recursive numerics for partition functions to illustrate the main points

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

dynamical analysis of the exclusive queueing process recently the stationary state of a parallel update totally asymmetric simple exclusion process with varying system length which can be regarded as a queueing process with excluded volume effect exclusive queueing process was obtained c arita and d yanagisawa j stat phys 141 829 2010 in this paper we analyze the dynamical properties of the number of particles n t and the position of the last particle the system length l t using an analytical method generating function technique as well as a phenomenological description based on domain wall dynamics and monte carlo simulations the system exhibits two phases corresponding to linear convergence or divergence of n t and l t these phases can both further be subdivided into high density and maximal current subphases the predictions of the domain wall theory are found to be in very good agreement quantitively with results from monte carlo simulations in the convergent phase on the other hand in the divergent phase only the prediction for n t agrees with simulations

asymmetric inclusion process we introduce and explore the asymmetric inclusion process asip an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process asep in both processes random events cause particles to propagate unidirectionally along a one dimensional lattice of n sites in the asep particles are subject to exclusion interactions whereas in the asip particles are subject to inclusion interactions that coalesce them into inseparable clusters we study the dynamics of the asip derive evolution equations for the mean and probability generating function pgf of the sites occupancy vector obtain explicit results for the above mean at steady state and describe an iterative scheme for the computation of the pgf at steady state we further obtain explicit results for the load distribution in steady state with the load being the total number of particles present in all lattice sites finally we address the problem of load optimization and solve it under various criteria the asip model establishes bridges between statistical physics and queueing theory as it represents a tandem array of queueing systems with unlimited batch service and a tandem array of growth collapse processes

asymmetric exclusion process and extremal statistics of random sequences a mapping is established between sequence alignment one of the most commonly used tools of computational biology at a certain choice of scoring parameters and the asymmetric exclusion process one of the few exactly solvable models of nonequilibrium physics the statistical significance of sequence alignments is characterized through studying the total hopping current of the discrete time and space version of the asymmetric exclusion process

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

matching two perspective views a computational approach to image matching is described it uses multiple attributes associated with each image point to yield a generally overdetermined system of constraints taking into account possible structural discontinuities and occlusions in the algorithm implemented intensity edgeness and cornerness attributes are used in conjunction with the constraints arising from intraregional smoothness field continuity and discontinuity and occlusions to compute dense displacement fields and occlusion maps along the pixel grids the intensity edgeness and cornerness are invariant under rigid motion in the image plane in order to cope with large disparities a multiresolution multigrid structure is employed coarser level edgeness and cornerness measures are obtained by blurring the finer level measures the algorithm has been tested on real world scenes with depth discontinuities and occlusions a special case of two view matching is stereo matching where the motion between two images is known the algorithm can be easily specialized to perform stereo matching using the epipolar constraint

stochastic queueing theory approach to human dynamics recently numerous studies have shown that human dynamics cannot be described accurately by exponential laws for instance barabasi nature london 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

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

occupancy correlations in the asymmetric simple inclusion process the asymmetric simple inclusion process asip a lattice gas model for unidirectional transport with irreversible aggregation has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch service counterpart of the tandem jackson network to date the analytical tractability of the model has been limited while the average particle density in the model is easy to compute very little is known about the joint occupancy distribution to partially bridge this gap we study occupancy correlations in the asip we take an analytical approach to this problem and derive an exact formula for the covariance matrix of the steady state occupancy vector we verify the validity of this formula numerically in small asip systems where monte carlo simulations can provide reliable estimates for correlations in reasonable time and further use it to draw a comprehensive picture of spatial occupancy correlations in asip systems of arbitrary size

discontinuous condensation transition and nonequivalence of ensembles in a zero range process we study a zero range process where the jump rates do not only depend on the local particle configuration but also on the size of the system rigorous results on the equivalence of ensembles are presented characterizing the occurrence of a condensation transition in contrast to previous results the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases this leads to a richer phase diagram including nonequivalence of ensembles in certain phase regions the paper is motivated by results from granular clustering where these features have been observed experimentally

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

zero range processes with multiple condensates statics and dynamics the steady state distributions and dynamical behaviour of zero range processes with hopping rates which are non monotonic functions of the site occupation are studied we consider two classes of non monotonic hopping rates the first results in a condensed phase containing a large but subextensive number of mesocondensates each containing a subextensive number of particles the second results in a condensed phase containing a finite number of extensive condensates we study the scaling behaviour of the peak in the distribution function corresponding to the condensates in both cases in studying the dynamics of the condensate we identify two timescales one for creation the other for evaporation of condensates at a given site the scaling behaviour of these timescales is studied within the arrhenius law approach and by numerical simulations

optical flow with an intensity weighted smoothing matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images for such images global gradient based methods may be more appropriate some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity weighted method of estimating dense displacement fields is presented which attempts to avoid some of the problems of the standard methods the only derivative required is the intensity gradient and the method includes procedures for automatic parameter evaluation the algorithm is expected to perform better than conventional algorithms on images without strong texture as is demonstrated on the test set of images

dynamics of the breakdown of granular clusters recently van der meer et al studied the breakdown of a granular cluster phys rev lett 88 174302 2002 we reexamine this problem using an urn model which takes into account fluctuations and finite size effects general arguments are given for the absence of a continuous transition when the number of urns compartments is greater than two monte carlo simulations show that the lifetime of a cluster ensuremath tau diverges at the limits of stability as ensuremath tau ensuremath sim n 1 3 where n is the number of balls after the breakdown depending on the dynamical rules of our urn model either normal or anomalous diffusion of the cluster takes place

on the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction gradient based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field the author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey level image intensity function based on three simple assumptions about the smoothness constraint 1 it must be expressed in a form that is independent of the choice of cartesian coordinate system in the image 2 it must be positive definite and 3 it must not couple different component of the optical flow it is shown that there are essentially only four such constraints any smoothness constraint satisfying 1 2 or 3 must be a linear combination of these four possibly multiplied by certain quantities invariant under a change in the cartesian coordinate system beginning with the three assumptions mentioned above the author mathematically demonstrates that all best known smoothness constraints appearing in the literature are special cases of this general form and in particular that the weight matrix introduced by h h nagel is essentially modulo invariant quantities the only physically plausible such constraint

zero range model of traffic flow a multicluster model of traffic flow is studied in which the motion of cars is described by a stochastic master equation assuming that the escape rate from a cluster depends only on the cluster size the dynamics of the model is directly mapped to the mathematically well studied zero range process knowledge of the asymptotic behavior of the transition rates for large clusters allows us to apply an established criterion for phase separation in one dimensional driven systems the distribution over cluster sizes in our zero range model is given by a one step master equation in one dimension it provides an approximate mean field dynamics which however leads to the exact stationary state based on this equation we have calculated the critical density at which phase separation takes place we have shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in within this approach we have estimated the critical cluster size and the mean nucleation time for a condensate in a large system the metastablity in the zero range process is reflected in a metastable branch of the fundamental flux density diagram of traffic flow our work thus provides a possible analytical description of traffic jam formation as well as important insight into condensation in the zero range process

phase transitions in tumor growth v what can be expected from cancer glycolytic oscillations abstract experimental evidence confirms the existence of glycolytic oscillations in cancer which allows it to self organize in time and space far from thermodynamic equilibrium and provides it with high robustness complexity and adaptability a kinetic model is proposed for hela tumor cells grown in hypoxia conditions it shows oscillations in a wide range of parameters two control parameters glucose and inorganic phosphate concentration were varied to explore the phase space showing also the presence of limit cycles and bifurcations the complexity of the system was evaluated by focusing on stationary state stability and lempel ziv complexity moreover the calculated entropy production rate was demonstrated behaving as a lyapunov function

limit laws for the asymmetric inclusion process the asymmetric inclusion process asip is a unidirectional lattice gas flow model which was recently introduced as an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process an iterative algorithm that allows the computation of the probability generating function pgf of the asip s steady state exists but practical considerations limit its applicability to small asip lattices large lattices on the other hand have been studied primarily via monte carlo simulations and were shown to display a wide spectrum of intriguing statistical phenomena in this paper we bypass the need for direct computation of the pgf and explore the asip s asymptotic statistical behavior we consider three different limiting regimes heavy traffic regime large system regime and balanced system regime in each of these regimes we obtain analytically and in closed form stochastic limit laws for five key asip observables traversal time overall load busy period first occupied site and draining time the results obtained yield a detailed limit laws perspective of the asip numerical simulations demonstrate the applicability of these laws as useful approximations

occupation probabilities and fluctuations in the asymmetric simple inclusion process the asymmetric simple inclusion process asip a lattice gas model of unidirectional transport and aggregation was recently proposed as an inclusion counterpart of the asymmetric simple exclusion process in this paper we present an exact closed form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites our results are expressed in terms of the entries of catalan s trapezoids number arrays which generalize catalan s numbers and catalan s triangle we further prove that the asip is asymptotically governed by the following i an inverse square root law of occupation ii a square root law of fluctuation and iii a rayleigh law for the distribution of interexit times the universality of these results is discussed

the structure of multiplicative motions in natural imagery a theoretical investigation of the frequency structure of multiplicative image motion signals is presented e g as associated with translucency phenomena previous work has claimed that the multiplicative composition of visual signals generally results in the annihilation of oriented structure in the spectral domain as a result research has focused on multiplicative signals in highly specialized scenarios where highly structured spectral signatures are prevalent or introduced a nonlinearity to transform the multiplicative image signal to an additive one in contrast in this paper it is shown that oriented structure is present in multiplicative cases when natural domain constraints are taken into account this analysis suggests that the various instances of naturally occurring multiple motion structures can be treated in a unified manner as an example application of the developed theory a multiple motion estimator previously proposed for translation additive transparency and occlusion is adapted to multiplicative image motions this estimator is shown to yield superior performance over the alternative practice of introducing a nonlinear preprocessing step

estimation of multiple time varying motions using time frequency representations and moving objects segmentation we extend existing spatiotemporal approaches to handle time varying motions estimation of multiple objects it is shown that multiple time varying motions estimation is equivalent to the instantaneous frequency estimation of superpoliteness fm sinusoids therefore we apply established signal processing tools such as time frequency representations to show that for each time instant the energy is concentrated along planes in the 3 d space spatial frequencies instantaneous frequency using fuzzy c planes we estimate indirectly the instantaneous velocities furthermore adapting existing approaches to our problem we attain the identification of the moving objects the experimental results verify the effectiveness of our methodology

probabilistic detection and tracking of motion boundaries we propose a bayesian framework for representing and recognizing local image motion in terms of two basic models translational motion and motion boundaries motion boundaries are represented using a non linear generative model that explicitly encodes the orientation of the boundary the velocities on either side the motion of the occluding edge over time and the appearance disappearance of pixels at the boundary we represent the posterior probability distribution over the model parameters given the image data using discrete samples this distribution is propagated over time using a particle filtering algorithm to efficiently represent such a high dimensional space we initialize samples using the responses of a low level motion discontinuity detector the formulation and computational model provide a general probabilistic framework for motion estimation with multiple non linear models

exact dynamical state of the exclusive queueing process with deterministic hopping the exclusive queueing process eqp has recently been introduced as a model for the dynamics of queues that takes into account the spatial structure of the queue it can be interpreted as a totally asymmetric exclusion process of varying length here we investigate the case of deterministic bulk hopping p 1 that turns out to be one of the rare cases where exact nontrivial results for the dynamical properties can be obtained using a time dependent matrix product form we calculate several dynamical properties e g the density profile of the system

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

design and use of linear models for image motion analysis linear parameterized models of optical flow particularly affine models have become widespread in image motion analysis the linear model coefficients are straightforward to estimate and they provide reliable estimates of the optical flow of smooth surfaces here we explore the use of parameterized motion models that represent much more varied and complex motions our goals are threefold to construct linear bases for complex motion phenomenas to estimate the coefficients of these linear modelss and to recognize or classify image motions from the estimated coefficients we consider two broad classes of motions i generic motion features such as motion discontinuities and moving barss and ii non rigid object specific motions such as the motion of human mouths for motion features we construct a basis of steerable flow fields that approximate the motion features for object specific motions we construct basis flow fields from example motions using principal component analysis in both cases the model coefficients can be estimated directly from spatiotemporal image derivatives with a robust multi resolution scheme finally we show how these model coefficients can be use to detect and recognize specific motions such as occlusion boundaries and facial expressions

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

dynamics of the condensate in zero range processes for stochastic processes leading to condensation the condensate once it is formed performs an ergodic stationary state motion over the system we analyse this motion and especially its characteristic time for zero range processes the characteristic time is found to grow with the system size much faster than the diffusive time scale but not exponentially fast this holds both in the mean field geometry and on finite dimensional lattices in the generic situation where the critical mass distribution follows a power law the characteristic time grows as a power of the system size

analytic study of clustering in shaken granular material using zero range processes abstract we show that models used to describe granular clustering due to vertical shaking belong to the class of zero range processes this correspondence allows us to derive analytically in the large particle number limit in a very easy and straightforward manner a number of properties of the models like particle distribution functions phase diagram and characteristic time of clusterization

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

thermodynamic limit for the invariant measures in supercritical zero range processes we prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles it is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system we show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density this improves the result of groskinsky schutz and spohn where convergence is obtained for the finite dimensional marginals we obtain as corollaries limit theorems for the order statistics of the components and for the fluctuations of the bulk

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

condensation for a fixed number of independent random variables a family of m independent identically distributed random variables indexed by a chemical potential 0 represents piles of particles as increases to the mean number of particles per site converges to a maximal density c the distribution of particles conditioned on the total number of particles equal to n does not depend on canonical ensemble for fixed m as n goes to infinity the canonical ensemble measure behave as follows removing the site with the maximal number of particles the distribution of particles in the remaining sites converges to the grand canonical measure with density c the remaining particles concentrate condensate on a single site

time needed to board an airplane a power law and the structure behind it a simple model for the boarding of an airplane is studied passengers have reserved seats but enter the airplane in arbitrary order queues are formed along the aisle as some passengers have to wait to reach the seats for which they have reservation we label a passenger by the number of his or her reserved seat in most cases the boarding process is much slower than for the optimal situation where passenger and seat orders are identical we study this dynamical system by calculating the average boarding time when all permutations of n passengers are given equal weight to first order the boarding time for a given permutation ordering of the passengers is given by the number s of sequences of monotonically increasing values in the permutation we show that the distribution of s is symmetric on 1 n which leads to an average boarding time n 1 2 we have found an exact expression for s and have shown that the full distribution of s approaches a normal distribution as n increases however there are significant corrections to the first order results due to certain correlations between passenger ordering and the substrate seat ordering this occurs for some cases in which the sequence of the seats is partially mirrored in the passenger ordering these cases with correlations have a boarding time that is lower than predicted by the first order results the large number of cases with reduced boarding times have been classified we also give some indicative results on the geometry of the correlations with sorting into geometry groups with increasing n both the number of correlation types and the number of cases belonging to each type increase rapidly using enumeration we find that as a result of these correlations the average boarding time behaves like n with 0 69 as compared with 1 0 for the first order approximation

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

applications of little s law to stochastic models of gene expression the intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells to explain this variability different sources of messenger rna mrna fluctuations poisson and telegraph processes have been proposed in stochastic models of gene expression both poisson and telegraph scenario models explain experimental observations of noise in protein levels in terms of bursts of protein expression correspondingly there is considerable interest in establishing relations between burst and steady state protein distributions for general stochastic models of gene expression in this work we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory by applying a general theorem from queueing theory little s law we derive exact relations which connect burst and steady state distribution means for models with arbitrary waiting time distributions for arrival and degradation of mrnas and proteins the derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression to illustrate this we consider a model for regulation of protein expression bursts by small rnas for a broad range of parameters we derive analytical expressions validated by stochastic simulations for the mean protein levels as the levels of regulatory small rnas are varied the results obtained show that the degree of transcriptional bursting can in principle be determined from changes in mean steady state protein levels for general stochastic models of gene expression

phase transitions in tumor growth iv relationship between metabolic rate and fractal dimension of human tumor cells abstract by the use of thermodynamics formalism of irreversible processes complex systems theory and systems biology it is derived a relationship between the production of entropy per unit time the fractal dimension and the tumor growth rate for human tumors cells the thermodynamics framework developed demonstrates that the dissipation function is a landau potential and also the lyapunov function of the dynamical behavior of tumor growth which indicate the directional character stability and robustness of the phenomenon the entropy production rate may be used as a quantitative index of the metastatic potential of tumors the current theoretical framework will hopefully provide a better understanding of cancer and contribute to improvements in cancer treatment

bridging genetic networks and queueing theory one of the main challenges facing biology today is the understanding of the joint action of genes proteins and rna molecules interwoven in intricate interdependencies commonly known as genetic networks to this end several mathematical approaches have been introduced to date in addition to developing the analytical tools required for this task anew one can utilize knowledge found in existing disciplines specializing in the representation and analysis of systems featuring similar aspects we suggest queueing theory as a possible source of such knowledge this discipline which focuses on the study of workloads forming in a variety of scenarios offers an assortment of tools allowing for the derivation of the statistical properties of the inspected systems we argue that a proper adaptation of modeling techniques and analytical methods used in queueing theory can contribute to the study of genetic regulatory networks this is demonstrated by presenting a queueing inspired model of a genetic network of arbitrary size and structure for which the probability distribution function is derived this model is further applied to the description of the lac operon regulation mechanism in addition we discuss the possible benefits stemming for queueing theory from the interdisciplinary dialogue with molecular biology in particular the incorporation of various dynamical behaviours into queueing networks

condensation in stochastic particle systems with stationary product measures we study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities we review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit this leads to strengthened results on weak convergence for subcritical systems and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions extending previous results which focused on attractive and finite systems we use relative entropy techniques which provide simple proofs making use of general versions of local limit theorems for independent random variables

michaelis menten reaction scheme as a unified approach towards the optimal restart problem we study the effect of restart and retry on the mean completion time of a generic process the need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of michaelis and menten stopping a process in its midst only to start it all over again may prolong leave unchanged or even shorten the time taken for its completion here we are interested in the optimal restart problem i e in finding a restart rate which brings the mean completion time of a process to a minimum we derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest we then continue to discover regimes at which solutions to the problem take on universal details independent forms which further give rise to optimal scaling laws the formalism we develop and the results obtained can be utilized when optimizing stochastic search processes and randomized computer algorithms an immediate connection with kinetic proofreading is also noted and discussed

traffic of molecular motors through tube like compartments the traffic of molecular motors through open tube like compartments is studied using lattice models these models exhibit boundary induced phase transitions related to those of the asymmetric simple exclusion process asep in one dimension the location of the transition lines depends on the boundary conditions at the two ends of the tubes three types of boundary conditions are studied a periodic boundary conditions which correspond to a closed torus like tube b fixed motor densities at the two tube ends where radial equilibrium holds locally and c diffusive motor injection at one end and diffusive motor extraction at the other end in addition to the phase diagrams we also determine the profiles for the bound and unbound motor densities using mean field approximations and monte carlo simulations our theoretical predictions are accessible to experiments

urn model of separation of sand we introduce an urn model that describes spatial separation of sand in this dynamical model in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken the steady state equation for an order parameter a critical line and the tricritical point on the phase diagram are found exactly the master equation and the first passage problem for the model are solved numerically and the results are used to locate first order transitions exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability in certain cases characteristic time diverges as n z where n is the number of balls and z frac 1 2 critical line frac 2 3 tricritical point or frac 1 3 limits of stability