violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

computationally feasible bounds for partially observed markov decision processes a partially observed markov decision process pomdp is a sequential decision problem where information concerning parameters of interest is incomplete and possible actions include sampling surveying or otherwise collecting additional information such problems can theoretically be solved as dynamic programs but the relevant state space is infinite which inhibits algorithmic solution this paper explains how to approximate the state space by a finite grid of points and use that grid to construct upper and lower value function bounds generate approximate nonstationary and stationary policies and bound the value loss relative to optimal for using these policies in the decision problem a numerical example illustrates the methodology

integral bilinear forms coxeter transformations and coxeter polynomials of finite posets abstract linear algebra technique in the study of linear representations of finite posets is developed in the paper a concept of a quadratic wandering on a class of posets i is introduced and finite posets i are studied by means of the four integral bilinear forms b i b i b i b i z i z i z 1 1 the associated coxeter transformations and the coxeter polynomials in connection with bilinear forms of dynkin diagrams extended dynkin diagrams and irreducible root systems are also studied bilinear equivalences between some of the forms are established and equivalences with the bilinear forms of dynkin diagrams and extended dynkin diagrams are discussed a homological interpretation of the bilinear forms 1 1 is given and z bilinear equivalences between them are discussed by applying well known results of bongartz loupias and zavadskij shkabara we give several characterisations of posets i with the euler form q i x b i x x weakly positive resp with the reduced euler form q i x b i x x weakly positive and posets i with the tits form q i x b i x x weakly positive

numeric and mesh algorithms for the coxeter spectral study of positive edge bipartite graphs and their isotropy groups we develop algorithmic techniques for the coxeter spectral analysis of the class ubigr n of connected loop free positive edge bipartite graphs d with n 2 vertices i e signed graphs in particular we present numerical and graphical algorithms allowing us a computer search in the study of such graphs d by means of their gram matrix email protected d the complex spectrum specc email protected c of the coxeter matrix cox d email protected email protected email protected d t r and the geometry of weyl orbits in the set mor d d of matrix morsifications email protected m n z of a simply laced dynkin diagram email protected a n d n e 6 e 7 e 8 associated with d and mesh root systems of type email protected our algorithms construct the coxeter gram polynomials cox d t z t and mesh geometries of root orbits of small connected loop free positive edge bipartite graphs d we apply them to the study of the following coxeter spectral analysis problem does email protected email protected hold i e the email protected email protected d arez congruent for any pair of connected positive loop free edge bipartite graphs d d inubigr nsuch thatspecc d specc d the problem if any square integer matrix email protected m n z is z congruent with its transpose a t r is also discussed we present a solution for graphs in ubigr n with email protected 6

partially observable markov decision processes incorporating epistemic uncertainties abstract the use of markov decision processes for inspection maintenance and rehabilitation of civil engineering structures relies on the use of several transition matrices related to the stochastic degradation process maintenance actions and imperfect inspections point estimators for these matrices are usually used and they are evaluated using statistical inference methods and or expert evaluation methods thus considerable epistemic uncertainty often veils the true values of these matrices our contribution through this paper is threefold first we present a methodology for incorporating epistemic uncertainties in dynamic programming algorithms used to solve finite horizon markov decision processes which may be partially observable second we propose a methodology based on the use of dirichlet distributions which answers in our sense much of the controversy found in the literature about estimating markov transition matrices third we show how the complexity resulting from the use of monte carlo simulations for the transition matrices can be greatly overcome in the framework of dynamic programming the proposed model is applied to concrete bridge under degradation in order to provide the optimal strategy for inspection and maintenance the influence of epistemic uncertainties on the optimal solution is underlined through sensitivity analysis regarding the input data

periodicity in bilinear lattices and the coxeter formalism abstract we introduce and study in detail so called circulant coxeter periodic elements and circulant families in a bilinear lattice k as well as their dual versions called anti circulant we show that they form a natural environment for a systematic explanation of certain cyclotomic factors of the coxeter polynomial k of k and in consequence of coxeter polynomials of algebras of finite global dimension we discuss the properties of quadratic forms induced by circulant and anti circulant families moreover we interpret the results in the language of representation theory of algebras and point out applications facts concerning tubular families in auslander reiten quivers and quadratic forms of algebras abstract considerations in bilinear lattices are illustrated with a collection of non trivial examples arising from module and derived categories the results show that techniques of linear algebra and number theory provide efficient tools for explaining various representation theoretic facts

on algorithmic coxeter spectral analysis of positive posets abstract following a general framework of coxeter spectral analysis of signed graphs and finite posets i introduced by simson siam j discrete math 27 827 854 2013 we present efficient numerical algorithms for the coxeter spectral study of finite posets i 1 n i that are positive in the sense that the symmetric gram matrix g i 1 2 c i c i t r m n q is positive definite where c i m n z is the incidence matrix of i encoding the relation i in the framework of scientific computing we present a complete coxeter spectral classification of finite positive posets i of size n i 20 it extends one of the main results obtained in gasiorek et al eur j comb 48 127 142 2015 for posets of size n 10 we also show that the connectivity of such posets i is determined by the complex coxeter spectrum specc i c equivalently by the coxeter polynomial cox i t z t od i one of the main results of the paper is a new technique to compute in a polynomial time a z invertible matrix b i m n z such that b i t r c i b i g d i where g d i m n z is a non symmetric gram matrix of a simply laced dynkin diagram d i a n d n e 6 e 7 e 8 associated with a finite positive poset i

optimal control of hidden markov models with binary observations a hidden markov model hmm consisting of a controlled markov chain and a binary output is considered the binary output reports the occurrence of a certain state versus any other state in the markov chain the transition matrix of the markov chain depends on a control vector which is to be chosen to minimize a discounted infinite horizon cost function the information provided for decision making is the entire history of the binary output which presents an incomplete knowledge of the markov chain and as a consequence leads to a stochastic control problem with partial observations the solution to such a problem is a control policy consisting of two components an estimator to derive the posterior probability distribution of the markov chain from the observation set and a nonlinear control law to map this estimate into the control vector this paper introduces a nonlinear state space representation for the estimator develops analytical expressions for the control law and presents numerical methods for efficient computation of the optimal control application of these results to optimal management of a class of inventory systems is discussed and the performance of optimal control for this application is examined by numerical simulations

random close packing in a granular model we introduce a two dimensional lattice model of granular matter using a combination of proof and simulation we demonstrate an order disorder phase transition in the model to which we associate the granular phenomenon of random close packing we use peierls contours to prove that the model is sensitive to boundary conditions at high density and markov chain monte carlo simulation to show it is insensitive at low density

geometrical families of mechanically stable granular packings we enumerate and classify nearly all of the possible mechanically stable ms packings of bidipserse mixtures of frictionless disks in small sheared systems we find that ms packings form continuous geometrical families where each family is defined by its particular network of particle contacts we also monitor the dynamics of ms packings along geometrical families by applying quasistatic simple shear strain at zero pressure for small numbers of particles nl16 we find that the dynamics is deterministic and highly contracting that is if the system is initialized in a ms packing at a given shear strain it will quickly lock into a periodic orbit at subsequent shear strain and therefore sample only a very small fraction of the possible ms packings in steady state in studies with ng16 we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space we argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of ms packing geometrical families visited in steady state this work is part of our long term research program to develop a master equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems

local theory of the statistics of sphere packings abstract we describe a theory for the statistics of random packings of spheres in terms of the distributions of local voronoi cells in the packing several sum rules are shown to apply to the voronoi cells generated from a packing of spheres the theory is implemented numerically by applying these sum rules to randomly generated cells and we compare predictions for the packing fraction and the distribution of cell shapes in sphere packings with known results

on model order estimation for partially observed markov chains abstract model order estimation for the partially observed markov chain pomc also called the hidden markov model is addressed model order is defined as the number of independent model parameters simulation is used to investigate the small sample performance of a number of model order criteria as applied to pomc models with low state dimension and binary observations consistency of these criteria in the context of pomc models with discrete state and observation space is also investigated a criterion due to akaike is shown not to be consistent simulation results indicate that akaike s criterion can provide more accurate estimation in the small sample case

stochastic switching for partially observable dynamics and optimal asset allocation abstractin industrial applications optimal control problems frequently appear in the context of decision making under incomplete information in such framework decisions must be adapted dynamically to account for possible regime changes of the underlying dynamics using stochastic filtering theory markovian evolution can be modelled in terms of latent variables which naturally leads to high dimensional state space making practical solutions to these control problems notoriously challenging in our approach we utilise a specific structure of this problem class to present a solution in terms of simple reliable and fast algorithms the algorithms presented in this paper have already been implemented in an r package

entropy maximization in the force network ensemble for granular solids a long standing issue in the area of granular media is the tail of the force distribution in particular whether this is exponential gaussian or even some other form here we resolve the issue for the case of the force network ensemble in two dimensions we demonstrate that conservation of the total area of a reciprocal tiling a direct consequence of local force balance is crucial for predicting the local stress distribution maximizing entropy while conserving the tiling area and total pressure leads to a distribution of local pressures with a generically gaussian tail that is in excellent agreement with numerics both with and without friction and for two different contact networks

inflation algorithm for loop free non negative edge bipartite graphs of corank at least two we continue the study of finite connected loop free edge bipartite graphs with m 3m 3 vertices a class of signed graphs we started in simson 2013 48 and m g siorek et al 2016 19 by means of the non symmetric gram matrix g mm z of its symmetric gram matrix g 12 g g tr mm 12z and the gram quadratic form q zm zq zm z in particular we study connected non negative edge bipartite graphs with n r 3n r 3 vertices of corank r 2r 2 in the sense that the symmetric gram matrix g mn r z g mn r z of is positive semi definite of rank n 1n 1 the edge bipartite graphs of corank r 2r 2 are studied up to the weak gram zz congruence z z where z z means that g btr g bg btr g b for some b mn r z b mn r z such that det b 1det b 1 our main result of the paper asserts that given a connected edge bipartite graph with n r 3n r 3 vertices of corank r 2r 2 there exists a suitably chosen sequence t of the inflation operators of the form tab such that the composite operator t reduces to a connected bigraph d n r such that zd n r and d n r is one of the canonical r vertex extensions a n r n 1n 1 d n r n 4n 4 e 6 r e 7 r and e 8 r with n rn r vertices of the simply laced dynkin diagrams an dn e6 e7 e8an dn e6 e7 e8 with n 1n 1 vertices the algorithm constructs also a matrix b mn r z b mn r z with det b 1det b 1 defining the weak gram zz congruence zd n r that is satisfying the equation gd n r btr g b

granular contact force density of states and entropy in a modified edwards ensemble a method has been found to analyze edwards granular contact force probability functional for a special case as a result the granular contact force probability density functions are obtained from first principles for this case the results are in excellent agreement with the experimental and simulation data the derivation assumes edwards flat measure a density of states dos that is uniform within the metastable regions of phase space the enabling assumption supported by physical arguments and empirical evidence is that correlating information is not significantly recursive through loops in the packing maximizing a state counting entropy results in a transport equation that can be solved numerically for the present this has been done using the mean structure approximation projecting the dos across all angular coordinates to more clearly identify its predominant nonuniformities these features are 1 the grain factor psi related to grain stability and strong correlation between the contact forces on the same grain and 2 the structure factor upsilon related to newton s third law and strong correlation between neighboring grains

multivariate bayesian process control for a finite production run abstract most industrial products and processes are characterized by several typically correlated measurable variables which jointly describe the product or process quality various control charts such as hotelling s t2 ewma and cusum charts have been developed for multivariate quality control where the values of the chart parameters namely the sample size sampling interval and the control limits are determined to satisfy given economic and or statistical requirements it is well known that this traditional non bayesian approach to a control chart design is not optimal but very few results regarding the form of the optimal bayesian control policy have appeared in the literature all limited to a univariate chart design in this paper we consider a multivariate bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent normally distributed vectors of random variables the problem is formulated in the pomdp partially observable markov decision process framework and the objective is to determine a control policy minimizing the total expected cost it is proved that under standard operating and cost assumptions the control limit policy is optimal cost comparisons with the benchmark chi squared chart and the mewma chart show that the bayesian chart is highly cost effective the savings are larger for smaller values of the critical mahalanobis distance between the in control and out of control process mean

congruences of a square matrix and its transpose abstract it is known that any square matrix a over any field is congruent to its transpose at stas for some nonsingular s moreover s can be chosen such that s2 i that is s can be chosen to be involutory we show that a and at are congruent over any field f of characteristic not two with involution a a the involution can be the identity a t s t as for some nonsingular s moreover s can be chosen such that s s i that is s can be chosen to be coninvolutory the short and simple proof is based on sergeichuk s canonical form for congruence math ussr izvestiya 31 3 1988 481 it follows that any matrix a over f can be represented as a eb in which e is coninvolutory and b is symmetric

control limits for two state partially observable markov decision processes abstract a production process can be in either a good or a bad state the true state is unknown and can only be inferred from observations if the state is good during one period it may deteriorate and become bad during the next period two actions are available continue or replace for a fixed cost the objective is to maximize the expected discounted value of the total future profits we prove that dominance in expectation the expected profit is larger in the good state than in the bad state suffices for the optimal policy to be of a control limit clt type continue if and only if the good state probability exceeds the clt this condition is weaker than stochastic dominance which has been prevailing we also show that the expected profit function is convex strictly increasing

entropy of particle packings an illustration on a toy model a toy model of particle packing is presented which consists in arranging hexagons on a triangular lattice according to local stability rules the number of stable packings is analytically computed and found to grow exponentially with the size of the lattice which illustrates the concept of packing entropy first proposed by edwards and collaborators the analysis is carried out for both the monodispersed case and the more interesting i e more disordered bidispersed case

ensemble theory for force networks in hyperstatic granular matter an ensemble approach for force networks in static granular packings is developed the framework is based on the separation of packing and force scales together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle in this paper we will give a general formulation of this force network ensemble and derive the general expression for the force distribution psfd for small regular packings these probability densities are obtained in closed form while for larger packings we present a systematic numerical analysis since technically the problem can be written as a noninvertible matrix problem where the matrix is determined by the contact geometry we study what happens if we perturb the packing matrix or replace it by a random matrix the resulting psfd s differ significantly from those of normal packings which touches upon the deep question of how network statistics is related to the underlying network structure overall the ensemble formulation opens up a different perspective on force networks that is analytically accessible and which may find applications beyond granular matter

computation of isotopisms of algebras over finite fields by means of graph invariants in this paper we define a pair of faithful functors that map isomorphic and isotopic finite dimensional algebras over finite fields to isomorphic graphs these functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic in order to illustrate their efficiency we determine explicitly the classification of two and three dimensional partial quasigroup rings

optimal stopping under partial observation near value iteration we propose a new approximate value iteration method namely near value iteration nvi to solve continuous state optimal stopping problems under partial observation which in general cannot be solved analytically and also pose a great challenge to numerical solutions nvi is motivated by the expression of the value function as the supremum over an uncountable set of linear functions in the belief state after a smart manipulation of the operations in the updating equation for the value function we reduce the set to only two functions at every time step so as to achieve significant computational savings nvi yields a value function approximation bounded by the tightest lower and upper bounds that can be achieved by existing algorithms in the same class so the nvi approximation is closer to the true value function than at least one of these bounds we demonstrate the effectiveness of our approach on an example of pricing american options under stochastic volatility

nonparametric adaptive control of discrete time partially observable stochastic systems abstract we consider discrete time partially observable stochastic control systems x t 1 f x t u t v t t 0 1 y t g u t 1 x t w t t 1 2 y 0 g 0 x 0 w 0 where x t u t and y t are respectively the state control and observation at time t and the state and observation disturbance processes v t and w t are sequences of i i d random elements with distributions and respectively we study the non parametric adaptive control problem of maximizing the infinite horizon discounted reward criterion when and are unknown and determine conditions for several adaptive policies to be asymptotically optimal and for almost surely uniform approximations of the optimal reward function our approach combines convergence results for empirical processes and recent results on parameter adaptive stochastic control problems

edwards measure and the steady state regime of a model with kinetic constraints under tapping we study the tapping dynamics of a one dimensional ising model with symmetric kinetic constraints we define and test a variant of the edwards hypothesis that one may build a thermodynamics for the steady state by using a flat measure over the metastable states with several macroscopic quantities fixed various types of tapping are compared and the accuracy of this measure becomes quickly excellent when the number of quantities fixed on average increases independent of the way the system is excited we attribute the validity of the naive flat measure at weak tapping to the spatial separation of density defects

higher order corrections to the effective potential close to the jamming transition in the perceptron model in view of the results achieved in a previously related work a altieri s franz and g parisi j stat mech 2016 093301 10 1088 1742 5468 2016 09 093301 regarding a plefka like expansion of the free energy up to the second order in the perceptron model we improve the computation here focusing on the role of third order corrections the perceptron model is a simple example of constraint satisfaction problem falling in the same universality class as hard spheres near jamming and hence allowing us to get exact results in high dimensions for more complex settings our method enables to define an effective potential or thouless anderson palmer free energy namely a coarse grained functional which depends on the generalized forces and the effective gaps between particles the analysis of the third order corrections to the effective potential reveals that albeit irrelevant in a mean field framework in the thermodynamic limit they might instead play a fundamental role in considering finite size effects we also study the typical behavior of generalized forces and we show that two kinds of corrections can occur the first contribution arises since the system is analyzed at a finite distance from jamming while the second one is due to finite size corrections we nevertheless show that third order corrections in the perturbative expansion vanish in the jamming limit both for the potential and the generalized forces in agreement with the isostaticity argument proposed by wyart and coworkers finally we analyze the relevant scaling solutions emerging close to the jamming line which define a crossover regime connecting the control parameters of the model to an effective temperature

symbolic computation of strong gram congruences for cox regular positive edge bipartite graphs with loops abstract the paper can be viewed as a second part of the author s paper simson 2018 43 our main aim is to construct symbolic algorithms for the coxeter spectral classification of a class of signed graphs called edge bipartite graphs with n 2 vertices we started in simson 2013 37 and bocian et al 2014 6 more precisely we construct algorithms for the classification up to the strong gram z congruence z of all finite connected cox regular edge bipartite graphs with at least one loop bigraphs for short that are positive in the sense that the associated symmetric gram matrix g 1 2 g g t r m n 1 2 z is positive definite where g m n z is the non symmetric gram matrix of defined in section 1 and z means that there is a z invertible matrix b m n z such that g b t r g b we recall from 43 that every such a bigraph with a loop is strongly gram z congruent with a bigraph d that is one of the positive cox regular bigraphs b n n 2 c n n 3 f 4 m 4 g 2 presented in section 1 here by applying the geometry of mesh root system technique we construct symbolic algorithms that compute the correspondence d and the set gl n z d of all z invertible matrices b m n z defining the strong gram z congruence z d for any connected positive bigraph with n 2 vertices and at least one loop

optimal transmission rate control policies in a wireless link under partial state information we consider the problem of phy layer transmission rate control for maximum throughput on a wireless link over a finite time horizon for each link state there exists a most advantageous transmission rate for the controller the controller needs to rely on incomplete link state information in the form of positive acknowledgements acks and negative acknowledgements nacks for transmitted packets we cast the problem as a partially observed markov decision processes pomdp we focus on the special case of time invariant or slowly time varying link quality with two states and two control options in that case the optimal control problem is a state estimation one and the optimal strategy is of threshold structure where the thresholds are certain values of the belief of being in one of the two states the policy admits a simple interpretation increase rate when the number of successive acks exceeds a threshold and decrease rate when the number of successive nacks exceeds a threshold

theory of powders starting from the observations that powders have a large number of particles and reproducible properties we show how statistical mechanics applies to powders the volume of the powder plays the role of the energy in conventional statistical mechanics with the hypothesis that all states of a specified volume are equally probable we introduce a variable x the compactivity which is analogous to the temperature in thermodynamics some simple models are considered which demonstrate how the problems involved can be tackled using the concept of compactivity there is an increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic nor in equilibrium but which still fulfil a remaining tenet of statistical physics which is that systems can be completely defined by a very small number of parameters and can be constructed in a reproducible way powders fall into this category if a powder consists for example of uniform cubes of salt and is poured into a container falling at low density uniformly from a great height one expects a salt powder of a certain density repeating the preparation reproduces the same density a treatment such as shaking the powder by a definite routine produces a new density and the identical routine applied to another sample of the initial powder will result in the same final density clearly a maxwell demon could arrange the little cubes of nacl to make a material of different properties to that of our experiment but if such demonics are ignored and we restrict ourselves to extensive operations such as stirring shaking compressing all actions which do not act on grains individually then well defined states of the powder result in this paper we will set up a framework for describing the state of the powder basing our development on anologies with statistical mechanics some attempts have been made to apply information theory ideas directly to powders

self organized criticality within fractional lorenz scheme abstract the theory of a flux steady state related to avalanche formation is presented for the simplest model of a sand pile within the framework of the lorenz approach the stationary values of sand velocity and sand pile slope are derived as functions of a control parameter driven sand pile slope the additive noise of above values are introduced for building a phase diagram where the noise intensities determine both avalanche and non avalanche domains as well as mixed one corresponding to the soc regime the last domain is crucial to affect of the noise intensity of the vertical component of sand velocity and especially sand pile slope to address to a self similar behavior a fractional feedback is used as an efficient ingredient of the modified lorenz system in the spirit of edwards paradigm an effective thermodynamics is introduced to determine a distribution over an avalanche ensemble with negative temperature steady state behavior of the moving grains number as well as non extensive values of entropy and energy is studied in detail the power law distribution over the avalanche size is described within a fractional lorenz scheme where the energy noise plays a crucial role this distribution is shown to be a solution of both fractional and nonlinear fokker planck equation as a result we obtain new relations between the exponent of the size distribution fractal dimension of phase space characteristic exponent of multiplicative noise number of governing equations dynamical exponents and non extensivity parameter

schurian sp representation finite right peak pi rings and their indecomposable socle projective modules such that soc r is an essential right ideal in r and it is isomorphic to a direct sum of finitely many copies of p called a right peak of r here f f are local rings f f is a division ring imj is an fi fj bimodule and the multiplication in r is given by fi f bimodule maps cii imj im jm satisfying the natural associativity conditions we denote by p p p the right indecomposable row ideals of r

p critical integral quadratic forms and positive unit forms an algorithmic approach abstract we introduce the class of p critical integral unit forms q z n z containing the critical forms in the sense of ovsienko 13 several characterisations of p critical forms are given in particular it is proved that q is p critical if and only if there is a uniquely determined extended dynkin diagram a n d n e 6 e 7 e 8 and a special group isomorphism t z n z n such that q t is the quadratic form q z n z n 0 of the diagram a correspondence between positive forms p z n 1 z with a sincere root and p critical forms q z n z is described and efficient linear algebra algorithms for computing p critical unit forms and positive forms are constructed

asymptotic dynamics of self driven vehicles in a closed boundary we study the asymptotic dynamics of self driven vehicles in a loop using a car following model with the consideration of volume exclusions in particular we derive the dynamical steady states for the single cluster case and obtain the corresponding fundamental diagrams exhibiting two branches representative of entering and leaving the jam respectively by simulations we find that the speed average over all vehicles eventually reaches the same value regardless of final clustering states the autocorrelation functions for overall speed average and single vehicle speed are studied each revealing a unique time scale we also discuss the role of noises in vehicular accelerations based on our observations we give trial definitions about the degree of chaoticity for general self driven many body systems

is a local description of stable 2d random packing possible local models of stable 2d random packing by williams 1985 and by uhler and schilling 1985 are discussed in terms of car parking and equilibrium fluid 1d distributions a numerical simulation of a simple 2d model is also presented whose results are different from the previous two it is concluded that those simple minded approaches to the problem of random 2d packing are questionable and accurate answers to the problem will have to come from more realistic models

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

on edwards theory of powders abstract we briefly review a statistical mechanics approach for the description of granular materials following the original ideas developed by edwards we show that edwards assumptions works very well for a class of lattice models and we discuss some recent analytic results obtained in such a framework on their phase diagram jamming transition and mixing segregation properties

state of the art a survey of partially observable markov decision processes theory models and algorithms this paper surveys models and algorithms dealing with partially observable markov decision processes a partially observable markov decision process pomdp is a generalization of a markov decision process which permits uncertainty regarding the state of a markov process and allows for state information acquisition a general framework for finite state and action pomdp s is presented next there is a brief discussion of the development of pomdp s and their relationship with other decision processes a wide range of models in such areas as quality control machine maintenance internal auditing learning and optimal stopping are discussed within the pomdp framework lastly algorithms for computing optimal solutions to pomdp s are presented

convergence of reinforcement learning algorithms and acceleration of learning the techniques of reinforcement learning have been gaining increasing popularity recently however the question of their convergence rate is still open we consider the problem of choosing the learning steps ensuremath alpha n and their relation with discount ensuremath gamma and exploration degree ensuremath epsilon appropriate choices of these parameters may drastically influence the convergence rate of the techniques from analytical examples we conjecture optimal values of ensuremath alpha n and then use numerical examples to verify our conjectures

fundamental problems in statistical physics of jammed packings abstract for packed i e jammed hard and rough objects kinetic energy is a minor and ignorable quantity as is elastic strain hence in the static case the stress equations need supplementing by missing equations depending solely on configurations a different pathway of analysis is the calculation of the probability distribution of interparticle forces this paper presents the mini review of recently obtained results in this field and poses a number of fundamental problems which are yet to be solved

a gram classification of non negative corank two loop free edge bipartite graphs we continue the coxeter spectral study of finite connected loop free edge bipartite graphs with m 2 3 vertices a class of signed graphs started in simson 2013 49 by means of the non symmetric gram matrix g mm 2 z of its symmetric gram matrix g 12 g g tr mm 2 12z the gram quadratic form q zm 2 z and the coxeter spectrum specc c i e the complex spectrum of the coxeter matrix cox g g tr gl m 2 z in the present paper we study non negative edge bipartite graphs of corank two in the sense that the symmetric gram matrix g mm 2 z of is positive semi definite of rank m 1 one of our aims is to get a complete classification of all connected corank two loop free edge bipartite graphs with m 2 3 vertices up to the weak gram z congruence z where z means that g btr g b for some b mm 2 z such that det b 1 by one vertex extensions of the simply laced euclidean diagrams a m m 1 d m m 4 e 6 e 7 e 8 we construct a family of connected loop free corank two diagrams a m 2 d m 2 e 6 2 e 7 2 e 8 2 called simply extended euclidean diagrams such that they classify all connected corank two loop free edge bipartite graphs with m 2 3 vertices up to the weak gram z congruence z a structure of connected corank two loop free edge bipartite graphs is described it is shown that every such contains a connected positive edge bipartite subgraph that is z congruent with a simply laced dynkin diagram dyn called the dynkin type of such that is a two point extension u w of along two roots u w of the positive definite gram form q zm z this yields a combinatorial algorithm u w u w allowing us to construct all connected corank two loop free edge bipartite graphs with m 2 3 vertices and d dyn from the triples u w where is positive of the dynkin type d and u w are roots of the positive definite gram form q zm z

stochastic control theory and operational research abstract the paper gives an overview of stochastic optimal control theory and its applications to operational research stochastic control theory deals with the intertemporal optimization of dynamic systems under uncertainty after a short review of deterministic optimal control theory and the theory of stochastic dynamic systems a general stochastic optimal control problem is formulated both in discrete and continuous time among the method for solving such problems particularly stochastic dynamic programming and the stochastic maximum principle are introduced examples from the areas of finance advertising production inventory models and information policy illustrate the applicability of stochastic control theory to operational research problems moreover its actual and potential impact on or is discussed from a methodological point of view

definition of temperature in dense granular media in this paper we report the measurement of a pseudotemperature for compacting granular media on the basis of the fluctuation dissipation relations in the aging dynamics of a model system from the violation of the fluctuation dissipation theorem emerges an effective temperature a dynamical temperature t dyn whose value depends on the particle density we compare the results for t dyn at several densities with the values of edwards compactivity at the corresponding densities s f edwards in granular matter an interdisciplinary approach edited by a mehta springer verlag new york 1994 and references therein it turns out that the dynamical temperature and edwards compactivity coincide on a large range of densities opening in this way the door to experimental checks as well as theoretical constructions

perturbative theory of the packing of mixtures and of non spherical particles abstract we present a simple theory for the packing of irregular particles and mixtures considered as a perturbation of a packing of monodisperse spheres using the perturbation theory we extract the different geometrical effects which effect the packing density and discuss why packings of irregular particles are generally less dense than packings of monodisperse spheres whereas packings of mixtures of particles of different sizes are generally denser than monodisperse sphere packings

edwards measures for powders and glasses can one construct a thermodynamics for compact slowly moving powders and grains a few years ago edwards proposed a possible step in this direction raising the fascinating perspective that such systems have a statistical mechanics of their own different from that of maxwell boltzmann and gibbs allowing us to have some information while still ignoring dynamic details recent developments in the theory of glasses have come to confirm these ideas within mean field in order to go beyond we explicitly generate edwards measure in a 3d model comparison of the results with the irreversible compaction data shows very good agreement the present framework immediately suggests new experimental checks

complexity of finite horizon markov decision process problems controlled stochastic systems occur in science engineering manufacturing social sciences and many other cntexts if the systems is modeled as a markov decision process mdp and will run ad infinitum the optimal control policy can be computed in polynomial time using linear programming the problems considered here assume that the time that the process will run is finite and based on the size of the input there are mny factors that compound the complexity of computing the optimal policy for instance there are many factors that compound the complexity of this computation for instance if the controller does not have complete information about the state of the system or if the system is represented in some very succint manner the optimal policy is provably not computable in time polynomial in the size of the input we analyze the computational complexity of evaluating policies and of determining whether a sufficiently good policy exists for a mdp based on a number of confounding factors including the observability of the system state the succinctness of the representation the type of policy even the number of actions relative to the number of states in almost every case we show that the decision problem is complete for some known complexity class some of these results are familiar from work by papadimitriou and tsitsiklis and others but some such as our pl completeness proofs are surprising we include proofs of completeness for natural problems in the as yet little studied classes np pp

void probabilities and cauchy schwarz divergence for generalized labeled multi bernoulli models the generalized labeled multi bernoulli glmb is a family of tractable models that alleviates the limitations of the poisson family in dynamic bayesian inference of point processes in this paper we derive closed form expressions for the void probability functional and the cauchy schwarz divergence for glmbs the proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a glmb while the proposed analytic cauchy schwarz divergence provides a tractable measure of similarity between glmbs we demonstrate the use of both results on a partially observed markov decision process for glmbs with cauchy schwarz divergence based reward and void probability constraint

transmission of stress in granular materials as a problem of statistical mechanics abstract we consider the problem of stress transmission in granular materials we formulate the simplest statically determinate problem of stress transmission through a static granular material this is the case when grains are rigid and have an average coordination number of z d 1 under this condition the system of newton s equations of interparticle force and torque balance is complete this means that there exists a complete set of equations for the macroscopic stress tensor ij r i e the d where d is the dimension of the problem equations of force balance j ij r g i r have to be supported by d d 1 2 equations these equations have their origin in newton s laws of interparticle force and torque balance and incorporate tensorial geometrical characteristics of the packing we conjecture that in order to have a coherent and self consistent continuum theory of stress transmission in static granular media it is necessary to link the averaging procedure to the concept of compactivity we emphasize that although real granular materials have many features ignored within the proposed framework it is essential for making progress to derive equations of stress transmission for the simplest model as opposed to guessing and postulating

a multiperiod newsvendor problem with partially observed demand we consider a newsvendor problem with partially observed markovian demand demand is observed if it is less than the inventory otherwise only the event that it is larger than or equal to the inventory is observed these observations are used to update the demand distribution from one period to the next the state of the resulting dynamic programming equation is the current demand distribution which is generally infinite dimensional we use unnormalized probabilities to convert the nonlinear state transition equation to a linear one this helps in proving the existence of an optimal feedback ordering policy so as to learn more about the demand the optimal order is set to exceed the myopic optimal order the optimal cost decreases as the demand distribution decreases in the hazard rate order in a special case with finitely many demand values we characterize a near optimal solution by establishing that the value function is piecewise linear

some monotonicity results for partially observed markov decision processes this paper provides sufficient conditions for the optimal value in a discrete time finite partially observed markov decision process to be monotone on the space of state probability vectors ordered by likelihood ratios the paper also presents sufficient conditions for the optimal policy to be monotone in a simple machine replacement problem and in the general case for the optimal policy to be bounded from below by an easily calculated monotone function

a two state partially observable markov decision process with three actions abstract a process can be in either a stable or an unstable state interchangeably the true state is unobservable and can only be inferred from observations three actions are available continue with the process con repair the process for a certain fee bring the process to the stable state rep and obtain the state of the process for a cost ins the objective is to maximize the expected discounted value of the total future profits we formulate the problem as a discrete time partially observable markov decision process pomdp we show that the expected profit function is convex and strictly increasing and that the optimal policy has either one or two control limits also we show that dominance in expectation the expected revenue is larger in the stable state than in the unstable state suffices for a control limit structure

a model for the packing of irregularly shaped grains in this paper we will attempt to address the problem of the packing properties of granular materials composed of irregularly shaped grains using configurational statistical mechanics in particular we will develop a model for a system of irregular grains based upon perturbing a packing of mono or poly disperse spheres in the mono disperse case we will show that the system packs less densely than a packing of perfect spheres except when local correlations between configurations of grains are taken into account the opposite is found to be true for a perturbation expansion based upon poly disperse spheres finally we will show that for a bi disperse packing of spheres phase segregation occurs for any size ratio and discuss whether this is to be expected

protocol independent granular temperature supported by numerical simulations a possible approach to the statistical description of granular assemblies starts from edwards s assumption that all blocked states occupying the same volume are equally probable edwards and oakeshott physica a 157 1080 1989 we performed computer simulations using two dimensional polygonal particles excited periodically according to two different protocols excitation by pulses of negative gravity and excitation by rotating gravity the first protocol exhibits a nonmonotonous dependency of the mean volume fraction on the pulse strength the overlapping histogram method is used in order to test whether the volume distribution is described by a boltzmann like distribution and to calculate the inverse compactivity as well as the logarithm of the partition sum we find that the mean volume is a unique function of the measured granular temperature independently of the protocol and of the branch in g and that all determined quantities are in agreement with edwards s theory

applications of the statistical mechanics of inherent states to granular media abstract we review the results of a statistical mechanics approach to granular materials and its extension to non thermal systems in their inherent states we introduce a tapping dynamics based on a dynamics used for real granular matter which allows to visit the space of the inherent states it is assumed that under stationarity or quasi stationarity the distribution among the inherent states satisfies the principle of maximum entropy this leads to a distribution characterised by a configurational temperature related to edwards compactivity the prediction from such an approach are checked on a standard hamiltonian lattice model and in the present unifying framework it is possible to explain a variety of properties of granular materials ranging from their logarithmic compaction to typical memory phenomena

one peak posets with positive quadratic tits form their mesh translation quivers of roots and programming in maple and python by applying linear algebra and computer algebra tools we study finite posets with positive quadratic tits form our study is motivated by applications of matrix representations of posets in representation theory where a matrix representation of a partially ordered set t p1 pn with a partial order means a block matrix m m1 m2 mn over a field k of size d d1 dn determined up to all elementary row transformations elementary column transformations within each of the substrips m1 m2 mn and additions of linear combinations of columns of mi to columns of mj if pi pj drozd 10 proves that t has only a finite number of direct sum indecomposable representations if and only if its quadratic tits form q x1 xn x x12 xn2 x 2 pi pjxixj x x1 xn is weakly positive i e q a1 an a 0 for all non zero vectors a1 an a with integral non negative coefficients in this case there exists an indecomposable representation m of size d d1 dn if and only if d1 dn d is a root of q i e q d1 dn d 1 bondarenko and stepochkina 8 give a list of posets t with positive tits form consisting of four infinite series and 108 posets up to duality in the paper we construct this list in an alternative way by applying computational algorithms implemented in maple and python moreover given any poset t of the list we show that a the coxeter polynomial coxi t of the poset i t obtained from t by adding a unique maximal element called a peak is a coxeter polynomial f i t of a simply laced dynkin diagram i an dn e6 e7 e8 and b the set of orbits of the set rq of integral roots of q admits a mesh translation quiver structure rq of a cylinder shape where is the coxeter transformation of i t in the sense of drozd 10

nonequilibrium identities and response theory for dissipative particles we derive some nonequilibrium identities such as the integral fluctuation theorem and the jarzynski equality starting from a nonequilibrium state for dissipative classical systems thanks to the existence of the integral fluctuation theorem we can naturally introduce an entropy like quantity for dissipative classical systems in far from equilibrium states we also derive the generalized green kubo formula as a nonlinear response theory for a steady dynamics around a nonequilibrium state we numerically verify the validity of the derived formulas for sheared frictionless granular particles

systems of subspaces of a unitary space abstract for a finite poset p p 1 p t we study systems u 1 u t u of subspaces of a unitary space u such that u i u j if p i p j two systems u 1 u t u and v 1 v t v are said to be isometric if there exists an isometry u v such that u i v i we classify such systems up to isometry if p is a semichain we prove that the problem of their classification is unitarily wild if p is not a semichain a classification problem is called unitarily wild if it contains the problem of classifying linear operators on a unitary space which is hopeless in a certain sense

a nonlinear programming model for partially observable markov decision processes finite horizon case the concept of partially observable markov decision processes was born to handle the problem of lack of information about the state of a markov decision process if the state of the system is unknown to the decision maker then an obvious approach is to gather information that is helpful in selecting an action this problem was already solved using the theory of markov processes we construct a nonlinear programming model for the same problem and develop a solution algorithm that turns out to be a policy iteration algorithm the policies found this way are easier to use than the policies found by the existing method although they have the same optimal objective value

a statistical mechanics approach to the inherent states of granular media abstract we consider a statistical mechanics approach to granular systems by following the original ideas developed by edwards we use the concept of inherent states defined as the stable configurations in the potential energy landscape introduced in the context of glasses under simplifying assumptions the equilibrium inherent states can be characterized by a configurational temperature 1 we link to edwards compactivity and address the problem of its experimental measure we also discuss the possibility to describe the time dependent distribution probability in the inherent states with an appropriate master equation

new kinds of entropy two new entropies are offered in this paper neither belongs to the traditional conservative statistical mechanics the first recognizes that the discovery that there are states of granular or glassy systems which can be restricted by an appropriate experimental pathway implies that an entropy can be defined for them by deriving an appropriate boltzmann equation in which the pathway to the steady state has an increasing entropy until the state characterized by a compactivity x v s is reached the second problem is to consider a state where energy flows in and flows out leaving a steady state e g a steady turbulent flow time dependent correlation functions are well defined and hence a probability of the history of the system is defined there are many ad hocstudies of such systems we ask whether such systems will possess an entropy defined by the usual plogpbut now pis the probability of the entire history of the system and the integral is over all histories

on the undecidability of probabilistic planning and related stochastic optimization problems automated planning the problem of how an agent achieves a goal given a repertoire of actions is one of the foundational and most widely studied problems in the ai literature the original formulation of the problem makes strong assumptions regarding the agent s knowledge and control over the world namely that its information is complete and correct and that the results of its actions are deterministic and known recent research in planning under uncertainty has endeavored te relax these assumptions providing formal and computation models wherein the agent has incomplete or noisy information about the world and has noisy sensors and effectors this research has mainly taken one of two approaches extend the classical planning paradigm to a semantics that admits uncertainty or adopt another framework for approaching the problem most commonly the markov decision process mdp model this paper presents a complexity analysis of planning under uncertainty it begins with the probabilistic classical planning problem showing that problem to be formally undecidable this fundamental result is then applied to a broad class of stochastic optimization problems in brief any problem statement where the agent a operates over an infinite or indefinite time horizon and b has available only probabilistic information about the system s state undecidability is established for policy existence problems for partially observable infinite horizon markov decision processes under discounted and undiscounted total reward models average reward models and state avoidance models the results also apply to corresponding approximation problems with undiscounted objective functions the paper answers a significant open question raised by papadimitriou and tsitsiklis math oper res 12 3 1987 441 450 about the complexity of infinite horizon pomdps

structural characterization and statistical properties of two dimensional granular systems a recently developed method is used for the analysis of structures of planar disordered granular assemblies within this method the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization the second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure our third aim is to quantify the statistics of basic volumes used for the entropic analysis we report the following results 1 quadrons are more useful than grains as basic quasiparticles for the entropic formalism 2 both grain and quadron volume distributions show nontrivial peaks and shoulders these can be understood only in the context of the quadrons in terms of particular conditional distributions 3 increasing friction increases the mean cell size as expected but does not affect the conditional distributions which is explained on a fundamental level we conclude that grain size and shape distributions determine the conditional distributions while their relative weights are dominated by friction and by the pack formation process this separates sharply the different roles that friction and grain shape distributions play 4 the analysis of the quadron volumes shows that gamma distributions which are accepted to describe foamlike structures well are too simplistic for general granular systems 5 a range of quantitative results is obtained for the density of states of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated the structural characteristics of granular systems are compared with numerically generated foamlike dirichlet voronoi constructions

solution procedures for partially observed markov decision processes we present three algorithms to solve the infinite horizon expected discounted total reward partially observed markov decision process pomdp each algorithm integrates a successive approximations algorithm for the pomdp due to a smallwood and e sondik with an appropriately generalized numerical technique that has been shown to reduce cpu time until convergence for the completely observed case the first technique is reward revision the second technique is reward revision integrated with modified policy iteration the third is a standard extrapolation a numerical study indicates the potentially significant computational value of these algorithms

principal component analysis of persistent homology rank functions with case studies of spatial point patterns sphere packing and colloids abstract persistent homology while ostensibly measuring changes in topology captures multiscale geometrical information it is a natural tool for the analysis of point patterns in this paper we explore the statistical power of the persistent homology rank functions for a point pattern x we construct a filtration of spaces by taking the union of balls of radius a centred on points in x x a x x b x a the rank function k x a b r 2 a b r is then defined by k x a b rank h k x a h k x b where is the induced map on homology from the inclusion map on spaces we consider the rank functions as lying in a hilbert space and show that under reasonable conditions the rank functions from multiple simulations or experiments will lie in an affine subspace this enables us to perform functional principal component analysis which we apply to experimental data from colloids at different effective temperatures and to sphere packings with different volume fractions we also investigate the potential of rank functions in providing a test of complete spatial randomness of 2d point patterns using the distances to an empirically computed mean rank function of binomial point patterns in the unit square

tapping thermodynamics of the one dimensional ising model we analyse the steady state regime of a one dimensional ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media the idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure the agreement between the two averages is excellent in all the cases examined showing that a static approach is capable of predicting certain measurable properties of the steady state regime

statistical theory of correlations in random packings of hard particles a random packing of hard particles represents a fundamental model for granular matter despite its importance analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory here we take inspiration from liquid theories for the n particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up a progressive expansion into a shell of particles converges in the large layer limit under a kirkwood like approximation of higher order correlations we apply the formalism to hard disks and predict the density of two dimensional random close packing rcp rcp 0 85 0 01 and random loose packing rlp rlp 0 67 0 01 our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data

equivalence notions and model minimization in markov decision processes many stochastic planning problems can be represented using markov decision processes mdps a difficulty with using these mdp representations is that the common algorithms for solving them run in time polynomial in the size of the state space where this size is extremely large for most real world planning problems of interest recent ai research has addressed this problem by representing the mdp in a factored form factored mdps however are not amenable to traditional solution methods that call for an explicit enumeration of the state space one familiar way to solve mdp problems with very large state spaces is to form a reduced or aggregated mdp with the same properties as the original mdp by combining equivalent states in this paper we discuss applying this approach to solving factored mdp problems we avoid enumerating the state space by describing large blocks of equivalent states in factored form with the block descriptions being inferred directly from the original factored representation the resulting reduced mdp may have exponentially fewer states than the original factored mdp and can then be solved using traditional methods the reduced mdp found depends on the notion of equivalence between states used in the aggregation the notion of equivalence chosen will be fundamental in designing and analyzing algorithms for reducing mdps optimally these algorithms will be able to find the smallest possible reduced mdp for any given input mdp and notion of equivalence i e find the minimal model for the input mdp unfortunately the classic notion of state equivalence from non deterministic finite state machines generalized to mdps does not prove useful we present here a notion of equivalence that is based upon the notion of bisimulation from the literature on concurrent processes our generalization of bisimulation to stochastic processes yields a non trivial notion of state equivalence that guarantees the optimal policy for the reduced model immediately induces a corresponding optimal policy for the original model with this notion of state equivalence we design and analyze an algorithm that minimizes arbitrary factored mdps and compare this method analytically to previous algorithms for solving factored mdps we show that previous approaches implicitly derive equivalence relations that we define here

stationary probability distribution in granular media abstract we discuss recent developments in the formulation of a statistical mechanics approach to non thermal systems such as granular media we review a few important numerical results on the assessment of edwards theory and in particular we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity which can be fully analytically investigated as a consequence we derive the rich phase diagram and predict the features of segregation patterns of the mixture

on the periodicity of coxeter transformations and the non negativity of their euler forms abstract we show that for piecewise hereditary algebras the periodicity of the coxeter transformation implies the non negativity of the euler form contrary to previous assumptions the condition of piecewise heredity cannot be omitted even for triangular algebras as demonstrated by incidence algebras of posets we also give a simple direct proof that certain products of reflections defined for any square matrix a with 2 on its main diagonal and in particular the coxeter transformation corresponding to a generalized cartan matrix can be expressed as a 1 a t where a a are closely associated with the upper and lower triangular parts of a

sunoptimal policies with bounds for parameter adaptive decision processes a parameter adaptive decision process is a sequential decision process where some parameter or parameter set impacting the rewards and or transitions of the process is not known with certainty signals from the performance of the system can be processed by the decision maker as time progresses yielding information regarding which parameter set is operative active learning is an essential feature of these processes and the decision maker must choose actions that simultaneously guide the system in a preferred direction as well as yield information that can be used to better prescribe future actions if the operative parameter set is known with certainty the parameter adaptive problem reduces to a conventional stochastic dynamic program which is presumed solvable previous authors have shown how to use these solutions to generate suboptimal policies with performance bounds for the parameter adaptive problem here it is shown that some desirable characteristics of those bounds are shared by a larger cla