distributed subgradient methods for convex optimization over random networks we consider the problem of cooperatively minimizing the sum of convex functions where the functions represent local objective functions of the agents we assume that each agent has information about his local function and communicate with the other agents over a time varying network topology for this problem we propose a distributed subgradient method that uses averaging algorithms for locally sharing information among the agents in contrast to previous works on multi agent optimization that make worst case assumptions about the connectivity of the agents such as bounded communication intervals between nodes we assume that links fail according to a given stochastic process under the assumption that the link failures are independent and identically distributed over time possibly correlated across links we provide almost sure convergence results for our subgradient algorithm

a unified convergence analysis of block successive minimization methods for nonsmooth optimization the block coordinate descent bcd method is widely used for minimizing a continuous function f of several block variables at each iteration of this method a single block of variables is optimized while the remaining variables are held fixed to ensure the convergence of the bcd method the subproblem of each block variable needs to be solved to its unique global optimal unfortunately this requirement is often too restrictive for many practical scenarios in this paper we study an alternative inexact bcd approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f the main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods especially for the cases where the objective functions are either nondifferentiable or nonconvex our results unify and extend the existing convergence results

chaotic properties of dilute two and three dimensional random lorentz gases equilibrium systems we compute the lyapunov spectrum and the kolmogorov sinai entropy for a moving particle placed in a dilute random array of hard disk or hard sphere scatterers i e the dilute lorentz gas model this is carried out in two ways first we use simple kinetic theory arguments to compute the lyapunov spectrum for both two and three dimensional systems in order to provide a method that can easily be generalized to nonuniform systems we then use a method based upon extensions of the lorentz boltzmann lb equation to include variables that characterize the chaotic behavior of the system the extended lb equations depend upon the number of dimensions and on whether one is computing positive or negative lyapunov exponents in the latter case the extended lb equation is closely related to an anti lorentz boltzmann equation where the collision operator has the opposite sign to the ordinary lb equation finally we compare our results with computer simulations of dellago and posch phys rev e 52 2401 1995 phys rev lett 78 211 1997 and find very good agreement

a direct formulation for sparse pca using semidefinite programming given a covariance matrix we consider the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination this problem arises in the decomposition of a covariance matrix into sparse factors or sparse principal component analysis pca and has wide applications ranging from biology to finance we use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix where cardinality is constrained and derive a semidefinite programming based relaxation for our problem we also discuss nesterov s smooth minimization technique applied to the semidefinite program arising in the semidefinite relaxation of the sparse pca problem the method has complexity o n 4 sqrt log n epsilon where n is the size of the underlying covariance matrix and epsilon is the desired absolute accuracy on the optimal value of the problem

distributed non convex first order optimization and information processing lower complexity bounds and rate optimal algorithms we consider a class of popular distributed non convex optimization problems in which agents connected by a network mathcal g collectively optimize a sum of smooth possibly non convex local objective functions we address the following question if the agents can only access the gradients of local functions what are the fastest rates that any distributed algorithms can achieve and how to achieve those rates first we show that there exist difficult problem instances such that it takes a class of distributed first order methods at least mathcal o 1 sqrt xi mathcal g times bar l epsilon communication rounds to achieve certain epsilon solution where xi mathcal g denotes the spectral gap of the graph laplacian matrix and bar l is some lipschitz constant second we propose near optimal methods whose rates match the developed lower rate bound up to a ploylog factor the key in the algorithm design is to properly embed the classical polynomial filtering techniques into modern first order algorithms to the best of our knowledge this is the first time that lower rate bounds and optimal methods have been developed for distributed non convex optimization problems

existence and asymptotic behaviour for a discrete hyperbolic system in a real hilbert space we investigate the existence uniqueness and asymptotic behaviour of the strong and weak solutions to a nonlinear infinite hyperbolic system subject to a boundary condition and initial data

kolmogorov sinai entropy for dilute gases in equilibrium we consider the density expansion of the kolmogorov sinai ks entropy per particle for a dilute gas in equilibrium and use methods from the kinetic theory of gases to compute the leading term for an equilibrium system the ks entropy hks is the sum of all of the positive lyapunov exponents characterizing the chaotic behavior of the gas we compute hks n where n is the number of particles in the gas this quantity has a density expansion of the form hks n5an 2ln n 1b1o n where n is the single particle collision frequency and nis the reduced number density of the gas the theoretical values for the coefficients a and b are compared with the results of computer simulations with excellent agreement for a and less than satisfactory agreement for b possible reasons for this difference in b are discussed s1063 651x 97 06911 0

quasistationary distributions for one dimensional diffusions with killing we extend some results on the convergence of one dimensional diffusions killed at the boundary conditioned on extended survival to the case of general killing on the interior we show under fairly general conditions that a diffusion conditioned on long survival either runs off to infinity almost surely or almost surely converges to a quasistationary distribution given by the lowest eigenfunction of the generator in the absence of internal killing only a sufficiently strong inward drift can keep the process close to the origin to allow convergence in distribution an alternative that arises when general killing is allowed is that the conditioned process is held near the origin by a high rate of killing near oo we also extend to the case of general killing the standard result on convergence to a quasistationary distribution of a diffusion on a compact interval

exponential convergence to quasi stationary distribution and q process for general almost surely absorbed markov processes we obtain necessary and sufficient conditions for exponential convergence to a unique quasi stationary distribution in the total variation norm these conditions also ensure the existence and exponential ergodicity of the q process the process conditioned to never be absorbed we apply these results to one dimensional birth and death processes with catastrophes multi dimensional birth and death processes infinite dimensional population models with brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain

iteration complexity of first order augmented lagrangian methods for convex programming this paper considers a special class of convex programming cp problems whose feasible regions consist of a simple compact convex set intersected with an affine manifold we present first order methods for this class of problems based on an inexact version of the classical augmented lagrangian al approach where the subproblems are approximately solved by means of nesterov s optimal method we then establish a bound on the total number of nesterov s optimal iterations i e the inner iterations performed throughout the entire inexact al method to obtain a near primal dual optimal solution we also present variants with possibly better iteration complexity bounds than the original inexact al method which consist of applying the original approach directly to a perturbed problem obtained by adding a strongly convex component to the objective function of the cp problem

existence of quasi stationary distributions a renewal dynamical approach we consider markov processes on the positive integers for which the origin is an absorbing state quasi stationary distributions qsd s are described as fixed points of a transformation phi in the space of probability measures under the assumption that the absorption time at the origin r of the process starting from state x goes to infinity in probability as x rightarrow infty we show that the existence of a operatorname qsd is equivalent to e xe lambda r infty for some positive lambda and x we also prove that a subsequence of phi n delta x converges to a minimal operatorname qsd for a birth and death process we prove that phi n delta x converges along the full sequence to the minimal operatorname qsd the method is based on the study of the renewal process with interarrival times distributed as the absorption time of the markov process with a given initial measure mu the key tool is the fact that the residual time in that renewal process has as stationary distribution the distribution of the absorption time of phi mu

open billiards invariant and conditionally invariant probabilities on cantor sets billiards are the simplest models for understanding the statistical theory of the dynamics of a gas in a closed compartment we analyze the dynamics of a class of billiards the open billiard on the plane in terms of invariant and conditionally invariant probabilities the dynamical system has a horseshoe structure the stable and unstable manifolds are analytically described the natural probability mu is invariant and has support in a cantor set this probability is the conditional limit of a conditional probability mu f that has a density with respect to the lebesgue measure a formula relating entropy lyapunov exponent and hausdorff dimension of a natural probability mu for the system is presented the natural probability mu is a gibbs state of a potential psi cohomologous to the potential associated to the positive lyapunov exponent see formula 0 1 and we show that for a dense set of such billiards the potential tb is not lattice as the system has a horseshoe structure

on the enhancement of diffusion by chaos escape rates and stochastic instability we consider stochastic perturbations of expanding maps of the interval where the noise can project the trajectory outside the interval we estimate the escape rate as a function of the amplitude of the noise and compare it with the purely diffusive case this is done under a technical hypothesis which corresponds to stability of the absolutely continuous invariant measure against small perturbations of the map we also discuss in detail a case of instability and show how stability can be recovered by considering another invariant measure

on the boltzmann equation for the lorentz gas we consider the boltzmann grad limit for the lorentz or wind tree model we prove that if is a fixed configuration of scatterer centers belonging to a set of full measure with respect to the poisson distribution with parameter 0 then the evolution of an initial a c particle density tends in the boltzmann grad limit to the solution of the boltzmann equation for the model as an intermediate step we prove that the process of the free path lengths and impact parameters induced by the lebesgue measure on a small region tends to a limiting independent process

on the dirichlet problem for asymmetric zero range process on increasing domains in order to obtain hitting time estimates for the asymmetric zero range process azrp on d in dimensions d 3 we characterize the principal eigenvalue of the generator of the azrp with dirichlet boundary on special domains we obtain a donsker varadhan variational representation and show that the corresponding eigenfunction is unique in a natural class of functions

local convergence of exact and inexact augmented lagrangian methods under the second order sufficient optimality condition we establish local convergence and rate of convergence of the classical augmented lagrangian algorithm under the sole assumption that the dual starting point is close to a multiplier satisfying the second order sufficient optimality condition in particular no constraint qualifications of any kind are needed previous literature on the subject required in addition the linear independence constraint qualification and either the strict complementarity assumption or a stronger version of the second order sufficient condition that said the classical results allow the initial multiplier estimate to be far from the optimal one at the expense of proportionally increasing the threshold value for the penalty parameters although our primary goal is to avoid constraint qualifications if the stronger assumptions are introduced then starting points far from the optimal multiplier are allowed within our analysis as well using only the second order sufficient optimality condition for penalty parameters large

perturbed proximal primal dual algorithm for nonconvex nonsmooth optimization in this paper we propose a perturbed proximal primal dual algorithm pprox pda for an important class of linearly constrained optimization problems whose objective is the sum of smooth possibly nonconvex and convex possibly nonsmooth functions this family of problems can be used to model many statistical and engineering applications such as high dimensional subspace estimation and the distributed machine learning the proposed method is of the uzawa type in which a primal gradient descent step is performed followed by an approximate dual gradient ascent step one distinctive feature of the proposed algorithm is that the primal and dual steps are both perturbed appropriately using past iterates so that a number of asymptotic convergence and rate of convergence results to first order stationary solutions can be obtained finally we conduct extensive numerical experiments to validate the effectiveness of the proposed algorithm

parallel algorithms for constrained tensor factorization via alternating direction method of multipliers tensor factorization has proven useful in a wide range of applications from sensor array processing to communications speech and audio signal processing and machine learning with few recent exceptions all tensor factorization algorithms were originally developed for centralized in memory computation on a single machine and the few that break away from this mold do not easily incorporate practically important constraints such as non negativity a new constrained tensor factorization framework is proposed in this paper building upon the alternating direction method of multipliers admom it is shown that this simplifies computations bypassing the need to solve constrained optimization problems in each iteration and it naturally leads to distributed algorithms suitable for parallel implementation this opens the door for many emerging big data enabled applications the methodology is exemplified using non negativity as a baseline constraint but the proposed framework can incorporate many other types of constraints numerical experiments are encouraging indicating that admom based non negative tensor factorization ntf has high potential as an alternative to state of the art approaches

existence and uniqueness for a nonlinear discrete hyperbolic system the existence uniqueness and asymptotic behaviour of the solutions to a nonlinear discrete hyperbolic system subject to some extreme conditions and initial data are investigated in a real hilbert space

statistical properties of lorentz gas with periodic configuration of scatterers in our previous paper markov partitions for some classes of dispersed billiards were constructed using these partitions we estimate the decay of velocity auto correlation function and prove the central limit theorem of probability theory and donsker s invariance principle for lorentz gas with periodic configuration of scatterers

global convergence of splitting methods for nonconvex composite optimization we consider the problem of minimizing the sum of a smooth function h with a bounded hessian and a nonsmooth function we assume that the latter function is a composition of a proper closed function p and a surjective linear map mathcal m with the proximal mappings of tau p tau 0 simple to compute this problem is nonconvex in general and encompasses many important applications in engineering and machine learning in this paper we examined two types of splitting methods for solving this nonconvex optimization problem the alternating direction method of multipliers and the proximal gradient algorithm for the direct adaptation of the alternating direction method of multipliers we show that if the penalty parameter is chosen sufficiently large and the sequence generated has a cluster point then it gives a stationary point of the nonconvex problem we also establish convergence of the whole sequence under an additional assumption that the functions h and p are semialgebraic further

escape rates and physically relevant measures for billiards with small holes we study the billiard map corresponding to a periodic lorentz gas in 2 dimensions in the presence of small holes in the table we allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers for a large class of smooth initial distributions we establish the existence of a common escape rate and normalized limiting distribution this limiting distribution is conditionally invariant and is the natural analogue of the srb measure of a closed system finally we prove that as the size of the hole tends to zero the limiting distribution converges to the smooth invariant measure of the billiard map

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

infinite horizon lorentz tubes and gases recurrence and ergodic properties we construct classes of two dimensional aperiodic lorentz systems that have infinite horizon and are chaotic in the sense that they are poincare recurrent uniformly hyperbolic ergodic and the first return map to any scatterer is k mixing in the case of the lorentz tubes i e lorentz gases in a strip we define general measured families of systems emph ensembles for which the above properties occur with probability 1 in the case of the lorentz gases in the plane we define families endowed with a natural metric within which the set of all chaotic dynamical systems is uncountable and dense

quasi stationary distributions for stochastic processes with an absorbing state we study the long time behaviour of stochastic models with an absorbing state conditioned on survival for a large class of processes in which saturation prevents unlimited growth statistical properties of the surviving sample attain time independent limiting values we may then define a quasi stationary probability distribution as one in which the ratios pn t pm t for any pair of non absorbing states n and m are time independent this is not a true stationary distribution since the overall normalization decays as probability flows irreversibly to the absorbing state we construct quasi stationary solutions for the contact process on a complete graph the malthus verhulst process

existence for a nonlinear hyperbolic system 1 3 here l c and ix are some positive constants problems of this type occur in theory of the electrical transmission lines the equation of telegraphy and hydraulics the equation of water hammer existence uniqueness and asymptotic behaviour for such problems have been studied by many authors we mention in this context l 4 and refer the reader to 5 for further references and significant results in 6 the first author has proved existence and uniqueness of solutions for general boundary value conditions of local type the attempt made in 7 to solve problems of the form l lt 1 3 failed since the abstract existence scheme developed there does not cover global boundary value conditions of the form 1 3 the main result of this paper theorem 1 below gives existence and uniqueness of a strong solution to system 1 1 t 1 3 under the following assumptions h each of the real valued functions u 4 x u and u b x u is continuous and mono tone increasing on

quasi stationary distributions for discrete state models this paper contains a survey of results related to quasi stationary distributions which arise in the setting of stochastic dynamical systems that eventually evanesce and which may be useful in describing the long term behaviour of such systems before evanescence we are concerned mainly with continuous time markov chains over a finite or countably infinite state space since these processes most often arise in applications but will make reference to results for other processes where appropriate next to giving an historical account of the subject we review the most important results on the existence and identification of quasi stationary distributions for general markov chains and give special attention to birth death processes and related models the question of under what circumstances a quasi stationary distribution given its existence is indeed a good descriptor of the long term behaviour of a system before evanescence is addressed as well we conclude with a discussion of computational aspects with more details given in a web appendix accompanying this paper

quasi stationary measures for conservative dynamics in the infinite lattice we study quasi stationary measures for conservative particle systems in the in finite lattice existence of quasi stationary measures is established for a fairly general class of reversible systems for the special cases of a system of independent random walks and the symmetric simple exclusion process it is shown that qualitative features of quasi stationary measures change drastically with dimension

escape rates and singular limiting distributions for intermittent maps with holes we study the escape dynamics in the presence of a hole of a standard family of intermittent maps of the unit interval with neutral fixed point at the origin and finite absolutely continuous invariant measure provided that the hole is a cylinder that does not contain any neighborhood of the origin the surviving volume is shown to decay at polynomial speed with time the associated polynomial escape rate depends on the density of the initial distribution more precisely on its behavior in the vicinity of the origin moreover the associated normalized push forward measures are proved to converge to the point mass supported at the origin in sharp contrast to systems with exponential escape rate finally a similar result is obtained for more general systems with subexponential escape rates namely that the cesaro limit of normalized push forward measures is generally singular invariant and supported on the asymptotic survivor set

convergence analysis of alternating direction method of multipliers for a family of nonconvex problems the alternating direction method of multipliers admm is widely used to solve large scale linearly constrained optimization problems convex or nonconvex in many engineering fields however there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex in this paper we analyze the convergence of the admm for solving certain nonconvex consensus and sharing problems we show that the classical admm converges to the set of stationary solutions provided that the penalty parameter in the augmented lagrangian is chosen to be sufficiently large for the sharing problems we show that the admm is convergent regardless of the number of variable blocks our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many admm variants involving proximal update rules and various flexible block selection rules

on the existence of a quasistationary measure for a markov chain we consider a markov chain on a locally compact metric space with an absorbing set necessary and sufficient conditions are provided for the existence of a quasistationary probability distribution

nonlinear differential problems with first or second order differences in hilbert spaces abstract in a real hilbert space we investigate the existence uniqueness and asymptotic properties of the generalized solutions of some nonlinear differential systems with first or second order differences subject to extreme conditions and initial data some generalizations of minty s theorem for the characterization of maximal monotone operators are also presented

coding with side information for rate constrained consensus average consensus algorithms are protocols to compute the average value of all sensor measurements via near neighbors communications they offer a natural tradeoff between the number of messages exchanged among terminals and the accuracy in the computation most of the models adopted for the message exchange in the literature however neither include explicit rate constraints nor explore the rate distortion tradeoff associated with the algorithm the contribution of our work is in examining the impact of such constraints and in finding strategies to minimize the communication cost in terms of rate the main motivation behind the proposed coding strategies is the observation that consensus algorithms offer the perfect example of a network communication problem where there is an increasing correlation between the data exchanged as the algorithm iterates henceforth it is possible to utilize previously exchanged data and current side information to significantly reduce the demands of quantization bit rate for a certain precision we analyze the case of a network where the links are assumed to be reliable at a constant bit rate we explore the conditions on the quantization noise which lead to a consensus value whose mean squared distance from the initial average is bounded in the case of infinite length vector coding with gaussian states we show that our proposed schemes achieve bounded convergence with vanishing rates as the iteration index tends to infinity

an augmented lagrangian based algorithm for distributed nonconvex optimization this paper is about distributed derivative based algorithms for solving optimization problems with a separable potentially nonconvex objective function and coupled affine constraints a parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented lagrangian algorithms the method negotiates shared dual variables that may be interpreted as prices a concept employed in dual decomposition methods and the alternating direction method of multipliers admm here each agent solves its own small scale nonlinear programming problem and communicates with other agents by solving coupled quadratic programming problems these coupled quadratic programming problems have equality constraints for which parallelizable methods are available the use of techniques associated with standard sequential quadratic programming methods gives a method with superlinear or quadratic convergence rate under suitable conditions this is in contrast to existing decomposition

extra an exact first order algorithm for decentralized consensus optimization recently there has been growing interest in solving consensus optimization problems in a multiagent network in this paper we develop a decentralized algorithm for the consensus optimization problem mathrm minimize x in mathbb r p bar f x frac 1 n sum i 1 n f i x which is defined over a connected network of n agents where each function f i is held privately by agent i and encodes the agent s data and objective all the agents shall collaboratively find the minimizer while each agent can only communicate with its neighbors such a computation scheme avoids a data fusion center or long distance communication and offers better load balance to the network this paper proposes a novel decentralized exact first order algorithm abbreviated as extra to solve the consensus optimization problem exact means that it can converge to the exact solution extra uses a fixed large step size which can be determined independently of the network size or topology the local variable of every a

on the linear convergence of the alternating direction method of multipliers we analyze the convergence rate of the alternating direction method of multipliers admm for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints previous analysis of the admm typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks moreover there has been no rate of convergence analysis for the admm without strong convexity in the objective function in this paper we establish the global r linear convergence of the admm for minimizing the sum of any number of convex separable functions assuming that a certain error bound condition holds true and the dual stepsize is sufficiently small such an error bound condition is satisfied for example when the feasible set is a compact polyhedron and the objective function consists of a smooth strictly convex function composed with a linear mapping and a nonsmooth ell 1 l1 regularizer this result implies the linear convergence of the admm for contemporary applications such as lasso without assuming strong convexity of the objective function

proximity without consensus in online multiagent optimization we consider stochastic optimization problems in multiagent settings where a network of agents aims to learn parameters that are optimal in terms of a global convex objective while giving preference to locally observed streaming information to do so we depart from the canonical decentralized optimization framework where agreement constraints are enforced and instead formulate a problem where each agent minimizes a global convex objective while enforcing network proximity constraints this formulation includes online consensus optimization as a special case but allows for the more general hypothesis that there is data heterogeneity across the network to solve this problem we propose using a stochastic saddle point algorithm inspired by arrow and hurwicz this method yields a decentralized algorithm for processing observations sequentially received at each node of the network using lagrange multipliers to penalize the discrepancy between them only neighboring nodes exchange model information we establish that under a constant step size regime the time average suboptimality and constraint violation are contained in a neighborhood whose radius vanishes with increasing number of iterations as a consequence we prove that the time average primal vectors converge to the optimal objective while satisfying the network proximity constraints we apply this method to the problem of sequentially estimating a correlated random field in a sensor network as well as an online source localization problem both of which demonstrate the empirical validity of the aforementioned convergence results

decomposition by partial linearization parallel optimization of multi agent systems we propose a novel decomposition framework for the distributed optimization of general nonconvex sum utility functions arising naturally in the system design of wireless multi user interfering systems our main contributions are i the development of the first class of inexact jacobi best response algorithms with provable convergence where all the users simultaneously and iteratively solve a suitably convexified version of the original sum utility optimization problem ii the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based instead on heuristics and iii a framework that can be easily particularized to well known applications giving rise to very efficient practical jacobi or gauss seidel algorithms that outperform existing ad hoc methods proposed for very specific problems interestingly our framework contains as special cases well known gradient algorithms for nonconvex sum utility problems and many block coordinate descent schemes for convex functions

some estimates for 2 dimensional infinite and bounded dilute random lorentz gases we present a mostly rigorous approach to unbounded and bounded open dilute random lorentz gases relying on previous rigorous results on the dilute boltzmann grad limit we compute the asymptotics of the lyapunov exponent in the unbounded case for the bounded open case in a circular region we give here an incomplete rigorous analysis which gives the asymptotics for large radius of the escape rate and of the rescaled quasi invariant q i or quasi stationary measure we finally give a complete proof on existence and asymptotic properties of the q i measure in a one dimensional caricature

ratio limits and limiting conditional distributions for discrete time birth death processes we consider discrete time birth death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually in particular we establish conditions for the convergence of these distributions to a proper distribution as n the problem turns out to be closely related to that of finding conditions for the existence of limits of ratios of n step transition probabilities as n orthogonal polynomials feature in the spectral representation for the n step transition probabilities of a birth death process and consequently play a key role in the analysis

consensus in ad hoc wsns with noisy links part i distributed estimation of deterministic signals we deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks wsns we cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation different from existing alternatives our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages thus allowing for decentralized computation even of nonlinear estimators including maximum likelihood estimators mle in nonlinear and non gaussian data models we prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal furthermore our decentralized algorithms exhibit resilience in the presence of receiver and or quantization noise in particular we introduce a decentralized scheme for least squares and best linear unbiased estimation blue and establish its convergence in the presence of communication noise our algorithms also exhibit potential for higher convergence rate with respect to existing schemes corroborating simulations demonstrate the merits of the novel distributed estimation algorithms