distributed consensus for multi agent systems with delays and noises in transmission channels this paper studies the distributed consensus problem for linear discrete time multi agent systems with delays and noises in transmission channels due to the presence of noises and delays existing techniques such as the lifting technique and the stochastic lyapunov theory are no longer applicable to the analysis of consensus in this paper a novel technique is introduced to overcome the difficulties induced by the delays and noises a consensus protocol with decaying gains satisfying persistence condition is adopted necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non leader follower and leader follower cases under a fixed topology under dynamically switching topologies and randomly switching topologies sufficient conditions for strong consensus and mean square consensus are also obtained numerical examples are given to demonstrate the effectiveness of the proposed protocols

necessary and sufficient conditions for oscillations of partial difference equations with continuous variables abstract this paper is concerned with the delay partial difference equation a 1 y a y a y pa y 0 where p is a real number and are nonnegative real numbers sufficient and necessary conditions for all continuous solutions of this equation to be oscillatory are obtained explicit condition for oscillation in terms of p and is also given

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

distributed average consensus with dithered quantization in this paper we develop algorithms for distributed computation of averages of the node data over networks with bandwidth power constraints or large volumes of data distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted we propose a distributed algorithm in which the nodes utilize probabilistically quantized information i e dithered quantization to communicate with each other the algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely in addition we show that the expected value of the consensus is equal to the average of the original sensor data we derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging pqda moreover we show that the convergence of the pqda is monotonic by studying the evolution of the minimum length interval containing the node values we reveal that the length of this interval is a monotonically nonincreasing function with limit zero we also demonstrate that all the node values in the worst case converge to the final two quantization bins at the same rate as standard unquantized consensus finally we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios

nash social and centralized solutions to consensus problems via mean field control theory the purpose of this paper is to synthesize initial mean consensus behavior of a set of agents from the fundamental optimization principles of i stochastic dynamic games and ii optimal control in the stochastic dynamic game model each agent seeks to minimize its individual quadratic discounted cost function involving the mean of the states of all other agents in this formulation we derive the limiting infinite population mean field equation system and explicitly compute its unique solution the resulting mean field mf control strategies drive each agent to track the overall population s initial state distribution mean and by applying these decentralized strategies any finite population system reaches mean consensus asymptotically as time goes to infinity furthermore these control laws possess an en nash equilibrium property where en goes to zero as the population size n goes to infinity finally the analysis is extended to the case of random mean field couplings in the social cooperative formulation the basic objective is to minimize a social cost as the sum of the individual cost functions containing mean field coupling in this formulation we show that for any individual agent the decentralized mean field social mf social control strategy is the same as the mean field nash mf nash equilibrium strategy hence mf nash controls unashn mf social controls usocn on the other hand the solution to the centralized lqr optimal control formulation yields the standard consensus sc algorithm whenever the graph representing the corresponding topology of the network is completely connected cc hence cent lqr controls ucentn sc cc controls uscn moreover a system with centralized control laws reaches consensus on the initial state distribution mean as time and population size n go to infinity hence asymptotically in time mf nash controls unashn mf social controls usocn cent lqr controls ucent sc cc controls usc finally the analysis is extended to the long time average lta cost functions case

distributed lms estimation over networks with quantised communications this article investigates the problem of distributed least mean square d lms estimation over a network with quantised communication each node in the network has a quantiser consisting of a first order dynamical encoder decoder and can only communicate with its neighbours then a new d lms estimator is proposed by employing a weighted sum of the internal state differences between each node s quantiser and those of its neighbours performance analysis of the proposed quantised d lms algorithm is studied in terms of mean square transient and steady state measurements we show that for gaussian data and sufficiently small step sizes the proposed cooperative d lms with quantisation is mean square stable in all quantisation levels including the 1 bit case and its performance approaches the cooperative d lms without quantisation when the quantisation step size is fairly small furthermore although in unquantised case infinite precision the cooperative d lms always outperforms the non cooperative d lms s

assessing partial association between ordinal variables quantification visualization and hypothesis testing partial association refers to the relationship between variables y1 y2 yk while adjusting for a set of covariates x x1 xp to assess such an association when yk s are recorded on ordinal sca

oscillation of partial difference equations with variable coefficients for the partial difference equations am 1 n am n 1 am n pm nam k n 1 0 and am 1 n am n 1 am n i 1upi m n fi am ki n li 0 we shall obtain sufficient conditions for the oscillation of all solutions

anytime reliable transmission of real valued information through digital noisy channels the problem of reliably transmitting a real valued random vector through a digital noisy channel is relevant for the design of distributed estimation and control techniques over networked systems one important example consists in the remote state estimation under communication constraints in this case an anytime transmission scheme consists of an encoder which maps the real vector into a sequence of channel inputs and a decoder which sequentially updates its estimate of the vector as more and more channel outputs are observed the encoder performs both source and channel coding of the data assuming that no channel feedback is available at the transmitter this paper studies the rates of convergence to zero of the mean squared error two coding strategies are analyzed the first one has exponential convergence rate but is expensive in terms of its encoder decoder computational complexity while the second one has a convenient computational complexity but subexponential convergence rate general bounds are obtained describing the convergence properties of these classes of methods

local versus global association for bivariate ordered responses summary local and global parameters modelling association are examined for contingency tables with both margins ordered responses local association parameters are crossratios of 2 x 2 subtables of adjacent cell probabilities global association parameters are cross ratios of quadrant probabilities the interpretation and various properties of these measures of association are compared and illustrated

on nonparametric measures of dependence for random variables in 1959 a renyi proposed a set of axioms for a measure of dependence for pairs of random variables in the same year a sklar introduced the general notion of a copula this is a function which links an n dimensional distribution function to its one dimensional margins and is itself a continuous distribution function on the unit n cube with uniform margins we show that the copula of a pair of random variables x y is invariant under a s strictly increasing transformations of x and y and that any property of the joint distribution function of x and y which is invariant under such transformations is solely a function of their copula exploiting these facts we use copulas to define several natural nonparametric measures of dependence for pairs of random variables we show that these measures satisfy reasonable modifications of renyi s conditions and compare them to various known measures of dependence e g the correlation coefficient and spearman s rho

distributed averaging with random network graphs and noises we consider a discrete time distributed averaging algorithm over multi agent networks with measurement noises and time varying random graphs each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises the network structure is modeled by a sequence of time varying random digraphs which may be spatially and temporally dependent by stochastic lyapunov method and the combination of algebraic graph theory and martingale convergence theory we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus we prove that all states of the agents converge to a common random variable whose mathematical expectation is the average of initial values in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected an upper bound of the variance of the limit random variable that is the mean square steady state error for stochastic average consensus is given quantitatively related to the weights the algorithm gain and the energy level of the noises

on distributed convex optimization under inequality and equality constraints we consider a general multi agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint a global equality constraint and a global constraint set the objective function is defined by a sum of local objective functions while the global constraint set is produced by the intersection of local constraint sets in particular we study two cases one where the equality constraint is absent and the other where the local constraint sets are identical we devise two distributed primal dual subgradient algorithms based on the characterization of the primal dual optimal solutions as the saddle points of the lagrangian and penalty functions these algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the slater s condition

test of association between two ordinal variables while adjusting for covariates we propose a new set of test statistics to examine the association between two ordinal categorical variables x and y after adjusting for continuous and or categorical covariates z our approach first fits multinomial e g proportional odds models of x and y separately on z for each subject we then compute the conditional distributions of x and y given z if there is no relationship between x and y after adjusting for z then these conditional distributions will be independent and the observed value of x y for a subject is expected to follow the product distribution of these conditional distributions we consider two simple ways of testing the null of conditional independence both of which treat x and y equally in the sense that they do not require specifying an outcome and a predictor variable the first approach adds these product distributions across all subjects to obtain the expected distribution of x y under the null and then contrasts it with the observed unconditional distribution o

stochastic consensus over noisy networks with markovian and arbitrary switches this paper considers stochastic consensus problems over lossy wireless networks we first propose a measurement model with a random link gain additive noise and markovian lossy signal reception which captures uncertain operational conditions of practical networks for consensus seeking we apply stochastic approximation and derive a markovian mode dependent recursive algorithm mean square and almost sure i e probability one convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition subsequently we consider a model with arbitrary random switching and a common stochastic lyapunov function technique is used to prove convergence finally our method is applied to models with heterogeneous quantizers and packet losses and convergence results are proved

multivariate logistic models summary when data composed of several categorical responses together with categorical or continuous predictors are observed the multivariate logistic transform introduced by mccullagh and nelder can be used to define a class of regression models that is in many applications particularly suitable for relating the joint distribution of the responses to predictors in this paper we give a general definition of this class of models and study their properties a computational scheme for performing maximum likelihood estimation for data sets of moderate size is described and a system of model formulae that succinctly define particular models is introduced applications of these models to longitudinal problems are illustrated by numerical examples

a new residual for ordinal outcomes we propose a new residual for regression models of ordinal outcomes defined as e sign y y where y is the observed outcome and y is a random variable from the fitted distribution this new residual is a single value per subject irrespective of the number of categories of the ordinal outcome contains directional information between the observed value and the fitted distribution and does not require the assignment of arbitrary numbers to categories we study its properties describe its connections with other residuals ranks and ridits and demonstrate its use in model diagnostics

convergence and asymptotic agreement in distributed decision problems we consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements possibly at different random times related to the same uncertain random vector each agent has the same objective function and prior probability distribution we assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received possibly at random times by a subset of other agents conditions for asymptotic convergence of each agent s decison sequence and asymptotic agreement of all agents decisions are derived

distributed averaging on digital erasure networks iterative distributed algorithms are studied for computing arithmetic averages over networks of agents connected through memoryless broadcast erasure channels these algorithms do not require the agents to have any knowledge about the global network structure or size almost sure convergence to state agreement is proved and the communication and computational complexities of the algorithms are analyzed both the number of transmissions and the number of computations performed by each agent of the network are shown to grow not faster than poly logarithmically in the desired precision the impact of the graph topology on the algorithms performance is analyzed as well moreover it is shown how in the presence of noiseless communication feedback one can modify the algorithms significantly improving their performance versus complexity trade off

almost certain convergence in double arrays for double arrays of constants ani 1 i k n n 1 and i i d random variables x x i i 1 conditions are given under which the row sums sum limits i 1 k n a ni x i xrightarrow text a text c text 0 both cases k n and k n are treated in general the hypotheses involve a trade off between moment requirements on x and the magnitude of the itani a marcinkiewicz zygmund type strong law is obtained for the special case a ni a i mathord left vphantom a i left sum limits j 1 n a j p right 1 p right kern nulldelimiterspace left sum limits j 1 n a j p right 1 p a i 0 text sum limits text 1 n a j p to infty text 0 p 2

sampled data based average consensus of second order integral multi agent systems switching topologies and communication noises a distributed sampled data based protocol is proposed for the average consensus of second order integral multi agent systems under switching topologies and communication noises under the proposed protocol it is proved that sufficient conditions for ensuring mean square average consensus are the consensus gain satisfies the stochastic approximation type condition and the communication topology graph at each sampling instant is a balanced graph with a spanning tree moreover if the consensus gain takes some particular forms the proposed protocol can solve the almost sure average consensus problem as well compared with the previous work the distinguished features of this paper lie in that 1 a sampled data based stochastic approximation type protocol is proposed for the consensus of second order integral multi agent systems 2 both communication noises and switching topologies are simultaneously considered and 3 average consensus can be reached not only in the mean square sense but also in the almost sure sense c 2013 elsevier ltd all rights reserved

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

a distributed classification estimation algorithm for sensor networks in this paper we address the problem of simultaneous classification and estimation of hidden parameters in a sensor network with communications constraints in particular we consider a network of noisy sensors which measure a common scalar unknown parameter we assume that a fraction of the nodes represent faulty sensors whose measurements are poorly reliable the goal for each node is to simultaneously identify its class faulty or nonfaulty and estimate the common parameter we propose a novel cooperative iterative algorithm which copes with the communication constraints imposed by the network and shows remarkable performance our main result is a rigorous proof of the convergence of the algorithm under a fixed communication graph and a characterization of the limit behavior as the network size goes to infinity in particular we prove that in the limit when the number of sensors goes to infinity the common unknown parameter is estimated with arbitrary small error while the classification error

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

distributed consensus algorithms in sensor networks with imperfect communication link failures and channel noise the paper studies average consensus with random topologies intermittent links and noisy channels consensus with noise in the network links leads to the bias variance dilemma running consensus for long reduces the bias of the final average estimate but increases its variance we present two different compromises to this tradeoff the a nd algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition slowly decaying to zero and the a nc algorithm where the weights are constant but consensus is run for a fixed number of iterations iota then it is restarted and rerun for a total of p runs and at the end averages the final states of the p runs monte carlo averaging we use controlled markov processes and stochastic approximation arguments to prove almost sure convergence of a nd to a finite consensus limit and compute explicitly the mean square error mse variance of the consensus limit we show that a nd represents the best of both worlds zero bias and low variance at the cost of a slow convergence rate rescaling the weights balances the variance versus the rate of bias reduction convergence rate in contrast a nc because of its constant weights converges fast but presents a different bias variance tradeoff for the same number of iterations iota p shorter runs smaller iota lead to high bias but smaller variance larger number p of runs to average over for a static nonrandom network with gaussian noise we compute the optimal gain for a nc to reach in the shortest number of iterations iota p with high probability 1 delta epsiv delta consensus epsiv residual bias our results hold under fairly general assumptions on the random link failures and communication noise

linearized oscillation theorems for certain nonlinear delay partial difference equations this paper is concerned with the nonlinear delay partial difference equation am 1 n am n 1 am n pm nf am k n 1 0 where k and l are nonnegative integers and m n 0 1 some linearized oscillation theorems for this equation are obtained i e we will prove that under some conditions on f this equation has the same oscillatory character as an associated linear equation an existence result for positive solutions of this equation is obtained also

structural modeling and convergence analysis of consensus based time synchronization algorithms over networks this paper raises a quite general problem how to characterize necessary conditions of bounded convergence namely the divergence conditions of a consensus based time synchronization cbts algorithm over a network with random communication delays we firstly present a unified structural model of cbts algorithms then we fit different cbts algorithms such as dcts ats wmts and lsts into the same structural model with just different algorithm parameters to characterize divergence conditions we focus on the algorithm structure and algorithm parameters rather than the topology graph of the network by studying the asymptotic property of the relative drift estimation error of cbts algorithms we discover almost sure divergence conditions and mean square divergence conditions of cbts algorithms using these conditions we clearly point out that the dcts algorithm is divergent the ats algorithm is divergent almost surely the wmts algorithm is mean square divergent but the lsts overcomes all of these divergence conditions the results of this paper provide a fundamental guideline for designing future time synchronization algorithms

quantized data based distributed consensus under directed time varying communication topology distributed average consensus dac is investigated for multiagent systems mass with directed time varying communication topology and quantized communication data we propose a communication feedback based distributed consensus protocol suitable for directed time varying topologies to deal with the inconsistency between the internal state of each agent s encoder and the output of its neighbors decoder and give rigorous analysis for the consensus of the mas the consensus protocols are designed based on uniform quantizers with scaling a finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure the exponential consensus by properly choosing system parameters in addition the lower bound is proved to be merely 1 bit for the directed fixed topology case no matter how large the agent number is a numerical example is presented to demonstrate the results obtained

mantel haenszel type inference for cumulative odds ratios with a stratified ordinal response this article proposes a mantel haenszel type estimator of an assumed common cumulative odds ratio in a proportional odds model for an ordinal response with several 2 x c contingency tables it is useful for instance for comparing two treatments on an ordinal response for data from several centers when the data are highly sparse the estimator has behavior similar to the mantel haenszel estimator of a common odds ratio for several 2 x 2 tables it is consistent under the ordinary asymptotic framework in which the number of tables is fixed and unlike the maximum likelihood ml estimator also under sparse asymptotics in which the number of tables grows with the sample size simulations reveal a considerable difference between it and the ml estimator when each table has few observations efficiency comparisons suggest that little efficiency loss occurs compared to the ml estimator when the data are not sparse tests and estimators are presented for detecting and handling heterogeneity in the odds ratios and generalizations are available for stratified r x c contingency tables

asymptotic agreement in distributed estimation each of several agents updates his estimate of the same random variable whenever he makes a new observation or receives the estimate made by another agent in turn each agent transmits his estimate to a randomly chosen subset of the other agents a subset of agents forms a communicating ring if for every pair underline m underline p of ring members there is a sequence of ring members underline m underline m 1 underline m 2 underline m n 1 underline p such that underline m i sends his estimate to underline m i 1 infinitely often if each ring member knows that he is a ring member then the estimates of all the ring members asymptotically agree however this common limit can depend upon the order in which estimates are transmitted

consensus seeking in multi agent systems with multiplicative measurement noises abstract in this paper the consensus problems of the continuous time integrator systems under noisy measurements are considered the measurement noises which appear when agents measure their neighbors states are modeled to be multiplicative by multiplication of the noises here the noise intensities are proportional to the absolute value of the relative states of an agent and its neighbor by using known distributed protocols for integrator agent systems the closed loop system is described in the vector form by a singular stochastic differential equation for the fixed and switching network topology cases constant consensus gains are properly selected such that mean square consensus and strong consensus can be achieved especially exponential mean square convergence of agents states to the common value is derived for the fixed topology case in addition asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied simulations shed light on the effectiveness of the proposed theoretical results

impulsive consensus algorithms for second order multi agent networks with sampled information in this paper the distributed consensus problem for second order continuous time multi agent networks with sampled data communication is investigated motivated by impulsive control strategy two kinds of impulsive distributed consensus algorithm are proposed these algorithms only utilize the sampled information and are implemented at sampled times by using the stability theory of impulsive systems and properties of the laplacian matrix necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks it is shown that the control gains the sampling period and the eigenvalues of the laplacian matrix of the communication graph play key roles in achieving the consensus a numerical example is given to illustrate the results

seeking consensus in networks of linear agents communication noises and markovian switching topologies the stochastic consensus problem of linear multi input multi output mimo multi agent systems mass with communication noises and markovian switching topologies is studied in this technical note the agent s full state is first estimated by the state observer and then the estimated state is exchanged with neighbor agents through a noisy communication environment the communication topology is randomly switching and the switching law is described by a continuous time markovian chain then a consensus protocol is proposed for this mas and some sufficient conditions are obtained for ensuring the mean square and almost sure consensus in addition if the communication topology is fixed some necessary and sufficient conditions for the mean square consensus can be obtained according to whether or not each agent in the system has parents

residuals and diagnostics for ordinal regression models a surrogate approach ordinal outcomes are common in scientific research and everyday practice and we often rely on regression models to make inference a long standing problem with such regression analyses is the lack

on convergence rate of leader following consensus of linear multi agent systems with communication noises this note further studies the previously proposed consensus protocol for linear multi agent systems with communication noises each agent is allowed to have its own time varying gain to attenuate the effect of communication noises therefore the common assumption that all agents have the same noise attenuation gain is not necessary it has been proved that if all noise attenuation gains are infinitesimal of the same order then the mean square leader following consensus can be reached furthermore the convergence rate of the multi agent system has been investigated if the noise attenuation gains belong to a class of functions which are bounded above and below by t beta beta in 0 1 asymptotically then the second moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by t beta asymptotically

the oscillation of partial difference equations with continuous arguments abstract for the partial difference equations and we shall obtain sufficient conditions for the oscillation of all solutions of these equations

distributed consensus algorithms in sensor networks quantized data and random link failures the paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures to achieve consensus dither small noise is added to the sensor states before quantization when the quantizer range is unbounded countable number of quantizer levels stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable we show that the mean squared error mse can be made arbitrarily small by tuning the link weight sequence at a cost of the convergence rate of the algorithm to study dithered consensus with random links when the range of the quantizer is bounded we establish uniform boundedness of the sample paths of the unbounded quantizer this requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer this is accomplished by splitting the state vector of the quantizer in two components one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace the proofs use maximal inequalities for submartingale and supermartingale sequences from these we derive probability bounds on the excursions of the two subsequences from which probability bounds on the excursions of the quantizer state vector follow the paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels the size of the quantization steps the desired probability of saturation and the desired level of accuracy away from consensus finally the paper illustrates the quantizer design with a numerical study

prediction of functional status for the elderly based on a new ordinal regression model the functional mobility of the elderly is a very important factor in aging research and prognostic information is valuable in making clinical and health care policy decisions we develop a predictive model for the functional status of the elderly based on data from the second longitudinal study of aging lsoa ii the functional status is an ordinal response variable the ordered probit model has been moderately successful in analyzing such data however its reliance on the normal distribution for its latent variable hinders its accuracy and potential in this paper we focus on the prediction of conditional quantiles of the functional status based on a more general transformation model the proposed estimation procedure does not rely on any parametric specification of the conditional distribution functions aiming to reduce model misspecification errors in the prediction cross validation within the lsoa ii data shows that our prediction intervals are more informative than those from the ordered probit

oscillation in nonlinear difference equations abstract in this paper we shall discuss oscillatory behavior of the solutions of difference equations including the self adjoint second order linear equation and the discrete version of the nonlinear wave equation our work is to give sufficient conditions such that every nontrivial solution of the equations oscillates

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

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

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper