symmetric prismatic tensegrity structures part ii symmetry adapted formulations this paper presents analytical formulations for the symmetry adapted equilibrium force density and geometrical stiffness matrices for prismatic tensegrity structures with dihedral symmetries an analytical expression for the infinitesimal mechanisms is also derived

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

algebraic tensegrity form finding abstract this paper concerns the form finding problem for general and symmetric tensegrity structures with shape constraints a number of different geometries are treated and several fundamental properties of tensegrity structures are identified that simplify the form finding problem the concept of a tensegrity invariance similarity transformation is defined and it is shown that tensegrity equilibrium is preserved under affine node position transformations this result provides the basis for a new tensegrity form finding tool the generality of the problem formulation makes it suitable for the automated generation of the equations and their derivatives state of the art numerical algorithms are applied to solve several example problems examples are given for tensegrity plates shell class symmetric tensegrity structures and structures generated by applying similarity transformation

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

image restoration using the q ising spin glass we investigate static and dynamic properties of gray scale image restoration by making use of the q ising spin glass model whose ladder symmetry allows us to take in account the distance between two spins we thus give an explicit expression of the hamming distance between the original and restored images as a function of the hyperparameters in the mean field limit finally numerical simulations for real world pictures are carried out to prove the efficiency of our model

matrix analysis of statically and kinematically indeterminate frameworks abstract the paper is concerned with the structural mechanics of assemblies of bars and pinjoints particularly where they are simultaneously statically and kinematically indeterminate the physical significance of the four linear algebraic vector subspaces of the equilibrium matrix is examined and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces in particular this algorithm gives full details of any states of self stress and modes of inextensional deformation which an assembly may possess a scheme is devised for the segregation of inextensional modes into rigid body modes up to six of these may be allowed by the foundation constraints and internal mechanisms in some circumstances a state of self stress may impart first order stiffness to an inextensional mode a matrix method for detecting this effect is devised and it is shown that if there is no state of self stress which imparts first order stiffness to a given mode then that mode can undergo rather large distortion which involves either zero change in length of the bars or possibly changes in length of third or higher order in the displacements the significance of negative stiffness as indicated by the matrix method is discussed the paper contains simple examples which illustrate all of the main points of the work

accuracy of the bethe approximation for hyperparameter estimation in probabilistic image processing we investigate the accuracy of statistical mechanical approximations for the estimation of hyperparameters from observable data in probabilistic image processing which is based on bayesian statistics and maximum likelihood estimation hyperparameters in statistical science correspond to interactions or external fields in the statistical mechanics context in this paper hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood a practical algorithm is described for grey level image restoration based on a gaussian graphical model and the bethe approximation the algorithm corresponds to loopy belief propagation in artificial intelligence we examine the accuracy of hyperparameter estimation when we use the bethe approximation it is well known that a practical algorithm for probabilistic image processing can be prescribed analytically when a gaussian graphical model is adopted as a prior probabilistic model in bayes formula we are therefore able to compare in a numerical study results obtained through mean field type approximations with those based on exact calculation

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

physical consideration of an image in image restoration using bayes formula abstract we consider image restoration by bayes formula and investigate the relationship between an image and a prior probability from the following two viewpoints hyperparameter estimation and the accuracy of a restored image the q ising model is adopted as a prior probability in bayes formula not the q ising energy but the potts energy plays an important role in the hyperparameter estimation from the viewpoint of the hyperparameter estimation the relationship between a natural image and a prior probability is characterized through the potts energy and magnetization of an image the potts energy and magnetization of an image are defined by a set of pixels state of an image the closer to the average potts energy and magnetization over a prior probability the potts energy and magnetization of a natural image is the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is for the accuracy of a restored image the image which has a smaller q ising energy is better restored by bayes formula composed of the q ising prior the consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability

the mean field theory in em procedures for markov random fields in many signal processing and pattern recognition applications the hidden data are modeled as markov processes and the main difficulty of using the maximisation em algorithm for these applications is the calculation of the conditional expectations of the hidden markov processes it is shown how the mean field theory from statistical mechanics can be used to calculate the conditional expectations for these problems efficiently the efficacy of the mean field theory approach is demonstrated on parameter estimation for one dimensional mixture data and two dimensional unsupervised stochastic model based image segmentation experimental results indicate that in the 1 d case the mean field theory approach provides results comparable to those obtained by baum s 1987 algorithm which is known to be optimal in the 2 d case where baum s algorithm can no longer be used the mean field theory provides good parameter estimates and image segmentation for both synthetic and real world images

static and dynamic analyses of tensegrity structures part 1 nonlinear equations of motion abstract in order to present basic equations for static and dynamic analyses of a class of truss structures called tensegrity structures large deformation kinematics and kinetics were presented in both eulerian and lagrangian formulations the two sets of equations of motion yield the same values even if different stress and strain measures were employed for their computation the eulerian formulation was implemented in an updated lagrangian finite element code using newton s method with consistently linearized equations of motion by utilizing the linearized lagrangian equations of motion at pre stressed initial configurations harmonic modal analyses of a three bar tensegrity module and a six stage tensegrity beam were conducted in the second part of the paper linearized equations were utilized to investigate the equilibrium configurations of basic tensegrity modules and the stiffness of pre stressed tensegirty structures

hyperparameter estimation in image restoration the hyperparameter in image restoration by the bayes formula is an important quantity this communication shows a physical method for the estimation of the hyperparameter without approximation for artificially generated images by prior probability the hyperparameter is computed accurately for practical images accuracy of the estimated hyperparameter depends on the magnetization and energy of the images we discuss the validity of prior probability for an original image

reshaping of tensegrities using a geometrical variation approach abstract we propose a novel approach for the reshaping of tensegrities and pre stressed pin jointed frameworks both free standing and restrained frameworks are studied first a geometrical variation is introduced and considered as an initial geometrical change to a self equilibrated tensegrity a new nonlinear set of equilibrium equations is then established based on this variation and subsequently linearized using an expansion the linearization provides us with an underdetermined system of linear equations with a rectangular jacobian matrix which is derived in a very simple and compact matrix form the system is finally solved iteratively using a newton raphson method employing a moore penrose pseudo inverse operation to establish a new equilibrium state the method promises to generate very accurate results with a remarkable convergence rate the outstanding features and performance of the proposed method are demonstrated and studied comprehensively through three examples

statistical mechanics of image restoration we develop the statistical mechanics formulation of the image restoration problem pioneered by geman and geman 1984 using bayesian methods we establish the posterior probability distribution for restored images for given data corrupted image and prior assumptions about source and corruption process in the simplest cases studied here the posterior is controlled by a cost function analagous to the configurational energy of an ising model with local fields whose sense is defined by the data through a combination of monte carlo simulation and mean field theory we address three key issues first we explore the sensitivity of the posterior distribution to the choice of prior parameters we find phase transitions separating regions in which the distribution is effective data dominated from regions in which it is ineffective prior dominated second we examine the question of how best to use the posterior distribution to prescribe a single optimal restored image we argue that the mean of the posterior is in general to be preferred over the mode both in principle and in practice finally borrowing from monte carlo techniques for free energy calculations we address the question of prior parameter estimation within the evidence framework of gull 1989 and mackay 1992 our results suggest that parameters identified by this framework provide effective priors leading to optimal restoration only to the extent that the forms of the priors are well matched to the processes they claim to represent

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

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

topology design of tensegrity structures via mixed integer programming this paper presents a numerical method for finding a tensegrity structure based on the ground structure method we first solve a mixed integer programming mip problem which maximizes the number of struts over the self equilibrium condition of axial forces and the discontinuity condition of struts subsequently we solve the minimization problem of the number of cables in order to remove redundant self equilibrium modes which is also formulated as an mip it is regarded to be advantageous that our method does not require any connectivity information of cables and struts to be known in advance while the obtained tensegrity structure is guaranteed to satisfy the discontinuity condition of struts rigorously

a direct approach to design of geometry and forces of tensegrity systems in the process of designing a tensegrity system some constraints are usually introduced for geometry and or forces to ensure uniqueness of the solution because the tensegrity systems are underdetermined in most cases in this paper a new approach is presented to enable designers to specify independent sets of axial forces and nodal coordinates consecutively under the equilibrium conditions and the given constraints to satisfy the distinctly different requirements of architects and structural engineers the proposed method can be used very efficiently for practical applications because only linear algebraic equations are to be solved and no equation of kinematics or material property is needed some numerical examples are given to show not only efficiency of the proposed method but also its ability of searching new configurations

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

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

probabilistic image processing by means of the bethe approximation for the q ising model the framework of bayesian image restoration for multi valued images by means of the q ising model with nearest neighbour interactions is presented hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood a practical algorithm is described for multi valued image restoration based on the bethe approximation the algorithm corresponds to loopy belief propagation in artificial intelligence we conclude that in real world grey level images the q ising model can give us good results

approximations for a frustrated ising model abstract the cluster effective field approximation was proposed as a useful approximation for the study of frustrated ising models in order to examine its usefulness the ising model with frustration on the centred square lattice is studied in the square effective field approximation and the results are compared with those in the pair and in the square approximation and with the exact results the study is made in the framework of the cluster variation method

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

adaptive force density method for form finding problem of tensegrity structures a numerical method is presented for form finding of tensegrity structures eigenvalue analysis and spectral decomposition are carried out iteratively to find the feasible set of force densities that satisfies the requirement on rank deficiency of the equilibrium matrix with respect to the nodal coordinates the equilibrium matrix is shown to correspond to the geometrical stiffness matrix in the conventional finite element formulation a unique and non degenerate configuration of the structure can then be obtained by specifying an independent set of nodal coordinates a simple explanation is given for the required rank deficiency of the equilibrium matrix that leads to a non degenerate structure several numerical examples are presented to illustrate the robustness as well as the strong ability of searching new configurations of the proposed method

an overview and comparison of structural form finding methods for general networks abstract this paper discusses and compares existing form finding methods for discrete networks well known methods such as the force density method dynamic relaxation updated reference strategy and others are discussed by mathematically structuring and presenting them in the same way using the same notation and combining terminology based on this a single computational framework using a sparse branch node data structure is presented it is shown how each method approaches the initial equilibrium problem defines and linearizes the equilibrium equations applied to linear elements and uses particular solving strategies this framework marginalizes any differences related to operating platforms programming language and style offering a better baseline for independent comparison of performance and results as a consequence it is possible to more clearly relate distinguish and compare existing methods allow for hybrid methods and identify new avenues for research

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

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

statistical mechanical approach to image processing the basic frameworks and techniques of the bayesian approach to image restoration are reviewed from the statistical mechanical point of view first a few basic notions in digital image processing are explained to convince the reader that statistical mechanics has a close formal similarity to this problem second the basic formulation of the statistical estimation from the observed degraded image by using the bayes formula is demonstrated the relationship between bayesian statistics and statistical mechanics is also listed particularly it is explained that some correlation inequalities on the nishimori line of the random spin model also play an important role in bayesian image restoration third the framework of bayesian image restoration for binary images by means of the ising model is reviewed some practical algorithms for binary image restoration are given by employing the mean field and the bethe approximations finally bayesian image restoration for a grey level image using the gaussian model is reviewed and the gaussian model is extended to a more practical probabilistic model by introducing the line state to treat the effects of edges the line state is also extended to quantized values

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

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

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

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

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

mean field theory of em algorithm for bayesian grey scale image restoration the em algorithm for the bayesian grey scale image restoration is investigated in the framework of the mean field theory our model system is identical to the infinite range random field ising model the maximum marginal likelihood method is applied to the determination of hyper parameters we calculate both the data averaged mean square error between the original image and its maximizer of posterior marginal estimate and the data averaged marginal likelihood function exactly after evaluating the hyper parameter dependence of the data averaged marginal likelihood function we derive the em algorithm which updates the hyper parameters to obtain the maximum likelihood estimate analytically the time evolutions of the hyper parameters and so called q function are obtained the relation between the speed of convergence of the hyper parameters and the shape of the q function is explained from the viewpoint of dynamics

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

dihedral star tensegrity structures this paper presents conditions for self equilibrium and super stability of dihedral star tensegrity structures based on their dihedral symmetry it is demonstrated that the structures are super stable if and only if they have an odd number of struts and the struts are as close as possible to each other numerical investigations show that their prestress stability is sensitive to the geometry realisation

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

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

statistical mechanics of image restoration and error correcting codes we develop a statistical mechanical formulation for image restoration and error correcting codes these problems are shown to be equivalent to the ising spin glass with ferromagnetic bias under random external fields we prove that the quality of restoration decoding is maximized at a specific set of parameter values determined by the source and channel properties for image restoration in a mean field system a line of optimal performance is shown to exist in the parameter space these results are illustrated by solving exactly the infinite range model the solutions enable us to determine how precisely one should estimate unknown parameters monte carlo simulations are carried out to see how far the conclusions from the infinite range model are applicable to the more realistic two dimensional case in image restoration

on the convergence of kikuchi s natural iteration method in this article we investigate on the convergence of the natural iteration method a numerical procedure widely employed in the statistical mechanics of lattice systems to minimize kikuchi s cluster variational free energies we discuss a sufficient condition for the convergence based on the coefficients of the cluster entropy expansion depending on the lattice geometry we also show that such a condition is satisfied for many lattices usually studied in applications finally we consider a recently proposed class of methods for the minimization of kikuchi functionals showing that the natural iteration method turns out as a particular instance of that class

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