auxiliary variable methods for markov chain monte carlo with applications abstract suppose that one wishes to sample from the density x using markov chain monte carlo mcmc an auxiliary variable u and its conditional distribution u x can be defined giving the joint distribution x u x u x a mcmc scheme that samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches the revolutionary algorithm of swendsen and wang is one such example besides reviewing the swendsen wang algorithm and its generalizations this article introduces a new auxiliary variable method called partial decoupling two applications in bayesian image analysis are considered a binary classification problem in which partial decoupling out performs swendsen wang and single site metropolis methods and a positron emission tomography pet reconstruction that uses the gray level prior of geman and mcclure a generalized swendsen wang algorithm is developed for this problem which reduces the computing time to the point where mcmc is a viab

graph homology and stability of coupled oscillator networks there are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph laplacian some examples of such models include the kuramoto and kuramoto sakaguchi equations as well as the swing equations which govern the behavior of generators coupled in an electrical network we show that the index calculation can be related to a dual calculation which is done on the first homology group of the graph rather than the vertex space we also show that this representation is computationally attractive for relatively sparse graphs where the dimension of the first homology group is low as is true in many applications we also give explicit formulae for the dimension of the unstable manifold to a phase locked solution for graphs containing one or two loops as an application we present some novel results for the kuramoto model defined on a ring and compute the longest possible edge length for a stable solution

a version of the swendsen wang algorithm for restoration of images degraded by poisson noise abstract an algorithm for restoration of images degraded by poisson noise is proposed the algorithm belongs to the family of markov chain monte carlo methods with auxiliary variables we explicitly use the fact that medical images consist of finitely many often relatively few grey levels the continuous scale of grey levels is discretized in an adaptive way so that a straightforward application of the swendsen wang phys rev lett 58 1987 86 algorithm becomes possible partial decoupling method due to higdon j am statist assoc 93 1998 442 585 is also incorporated into the algorithm simulation results suggest that the algorithm is reliable and efficient

opinion dynamics in social networks with hostile camps consensus vs polarization most of the distributed protocols for multi agent consensus assume that the agents are mutually cooperative and trustful and so the couplings among the agents bring the values of their states closer opinion dynamics in social groups however require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents which are usually characterized by repulsive couplings and may lead to clustering of the opinions a simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by c altafini who examined first order consensus algorithms over static signed graphs this protocol establishes modulus consensus where the opinions become the same in modulus but may differ in signs in this paper we extend the modulus consensus model to the case where the network topology is an arbitrary time varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph for cut balanced graphs not only sufficient but also necessary conditions for modulus consensus are given

event driven multi consensus of multi agent networks with repulsive links due to diversification in environment a network of agents may have several emergent behaviors this paper introduces an event driven paradigm for realizing multi consensus which as a generic version of group cluster consensus depends both on the initial underlying topology and initial states for the network feature we resort to a distributed event driven paradigm since event driven control has advantages on communication reduction and control energy saving moreover to relax assumption on network topology repulsive links are exploited at event instants to facilitate multiple coordination to realize multi consensus we design a distributed event driven controller based on coupled intra subgroup and extra subgroup information in this context with different control strengths the finial value of man would be varying this phenomenon matches the principle of multi consensus in the current study based on lasalle s invariance principle we prove that under the proposed event driven configuration the joint cooperation and competition contributes to multi consensus provided that the sampling period is no larger than a positive threshold it is shown there is no further requirement on network topologies in pursuit of multiple coordination this paper studies multiple coordination of multi agent networks under an event driven paradigm for an undirected connected graph a node clustering scheme is first adopted to ensure a relatively strong degree of connectivity within each potential subgroup and some repulsive effect is used to deal with the extra subgroup links to reduce unnecessary communication a distributed event driven controller is designed via coupled intra subgroup and extra subgroup information based on the lasalle s invariance principle it is shown that under the proposed event driven control configuration multi agent networks can realize multi consensus without any balanced requirement on the underlying topologies simulation work is presented to validate the theoretical results

gibbs sampling for bayesian non conjugate and hierarchical models by using auxiliary variables summary we demonstrate the use of auxiliary or latent variables for sampling non standard densities which arise in the context of the bayesian analysis of non conjugate and hierarchical models by using a gibbs sampler their strategic use can result in a gibbs sampler having easily sampled full conditionals we propose such a procedure to simplify or speed up the markov chain monte carlo algorithm the strength of this approach lies in its generality and its ease of implementation the aim of the paper therefore is to provide an alternative sampling algorithm to rejection based methods and other sampling approaches such as the metropolis hastings algorithm

collision free consensus in multi agent networks this paper addresses the collision free consensus problem in a network of agents with single integrator dynamics distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision free among agents during the evolution of the multi agent networks the novelty of the proposed algorithms lies in the definition of neighbors for each agent which is different from the usual sense that neighbors are selected by the distance between agents in the state space in the proposed strategies the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order the consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis meanwhile by realizing the relations between order preservation and collision free a systematic analysis framework on order preservation and hence collision free for agents in arbitrary dimension is provided based on tools from monotone systems theory illustrated numerical examples are presented to validate the effectiveness of the proposed strategies

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

mri tissue classification using high resolution bayesian hidden markov normal mixture models magnetic resonance imaging mri is used to identify the major tissues within a subject s brain classification is usually based on a single image providing one measurement for each volume element or voxel in a discretization of the brain a simple model views each voxel as homogeneous belonging entirely to one of the three major tissue types gray matter white matter or cerebrospinal fluid the measurements are normally distributed with means and variances depending on the tissue types of their voxels because nearby voxels tend to be of the same tissue type a markov random field model can be used to capture the spatial similarity of voxels a more realistic model takes into account the fact that some voxels are not homogeneous and contain tissues of more than one type our approach to this problem is to construct a higher resolution image in which each voxel is divided into subvoxels and subvoxels are in turn assumed to be homogeneous and to follow a markov random field model in the present work

bipartite and cooperative output synchronizations of linear heterogeneous agents this paper investigates cooperative output synchronization and bipartite output synchronization of a group of linear heterogeneous agents in a unified framework for a structurally balanced signed graph we prove that the bipartite output synchronization is equivalent to the cooperative output synchronization over an unsigned graph whose adjacency matrix is obtained by taking the absolute value of each entry in the adjacency matrix of the signed graph we obtain a new h criterion which is sufficient for both cooperative output synchronization and bipartite output synchronization

a descriptor approach to robust leader following output consensus of uncertain multi agent systems with delay in this technical note a descriptor approach to leader following output consensus of multi agent systems with both stationary and dynamic leaders is given in the presence of transmission delay and model uncertainty the proposed method can deal with stable and unstable agents described by general linear models to this end a new proportional derivative integral pid consensus protocol for the closed loop multi agent system is proposed under a directed graph applying this consensus protocol to the multi agent system leads to a time delay closed loop equation of neutral type to deal with the resulting neutral system a descriptor model transformation is used to derive delay dependent sufficient conditions for the existence of the consensus protocol in terms of certain linear matrix inequalities lmi the application of the proposed method is illustrated in a teleoperation system simulation results are given to show the effectiveness of the proposed approach

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

persistent flows in deterministic chains this paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents an arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l 1 norm convergence of the infinite backward products to a rank one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states we discuss two balance conditions on the interactions between agents which generalize the arc balance and cut balance conditions in the literature respectively the proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant we prove that in both cases global consensus is reached if and only if the persistent graph which consists of all the persistent arcs contains a directed spanning tree the convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place the results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self confidence of the agents

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

applied nonparametric statistics 2nd ed 1991 applied nonparametric statistics 2nd ed technometrics vol 33 no 3 pp 364 365

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

a necessary and sufficient condition for consensus of continuous time agents over undirected time varying networks the average consensus problem of continuous time agents in undirected time varying networks is studied the network is allowed to be disconnected a notion called infinite integral connectivity is proposed based on the notion a necessary and sufficient condition for achieving consensus is given that is when the network topology is described by an undirected time varying graph g t the agents achieve consensus if and only if the infinite integral graph of g t over 0 is connected this criterion does not hold for directed networks

flocking of multi agent systems with multiple groups in this paper we consider the flocking problem of multi agent systems with multiple groups first some algorithms using local information are designed to divide the agents into any pre assigned number of groups in fixed and switching heterogeneous networks respectively based on algebraic graph theory and barbalat s lemma convergence criteria are established to ensure velocity alignment and cohesion of each subgroup as well as collision avoidance between any agents in the whole group second an algorithm for homogeneous networks is studied simulation examples are finally presented to verify the effectiveness of our theoretical results

alternating subspace spanning resampling to accelerate markov chain monte carlo simulation this article provides a simple method to accelerate markov chain monte carlo sampling algorithms such as the data augmentation algorithm and the gibbs sampler via alternating subspace spanning resampling assr the assr algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency the methodology is illustrated with bayesian estimation for analysis of censored data from fractionated experiments the relationships between assr and existing methods are also discussed

an analysis of swendsen wang and related sampling methods convergence rates statistical efficiency and sampling costs are studied for the original and extended swendsen wang methods of generating a sample path s j j 1 with equilibrium distribution with r distinct elements on a finite state space x of size n 1 given s j 1 each method uses auxiliary random variables to identify the subset of x from which s j is to be randomly sampled let min and max denote respectively the smallest and largest elements in and let n denote the number of elements in with value max for a single auxiliary variable uniform sampling from the subset and n 1 n r min n r max 1 our results show rapid convergence and high statistical efficiency for large min max or n r n 1 and slow convergence and poor statistical efficiency for small min max and n r n 1 other examples provide additional insight for extended swendsen wang methods with non uniform subset sampling the analysis identifies the properties of a decomposition of x that favour fast convergence and high statistical efficiency in the absence of exploitable special structure subset sampling can be costly regardless of which of these methods is employed

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

a comparison of tests for the k sample non decreasing alternative this paper compares by means of monte carlo simulations three non parametric tests to detect a non decreasing trend in location parameters the three tests are the jonckheere terpstra test the cuzick test and the le test we estimated power for each test across a wide variety of non decreasing location parameters under four different types of distributions none of the tests produced an overwhelmingly higher power over their two competitors

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

delay independent incremental stability in time varying monotone systems satisfying a generalized condition of two sided scalability monotone systems generated by delay differential equations with explicit time variation are of importance in the modeling of a number of significant practical problems including the analysis of communications systems population dynamics and consensus protocols in such problems it is often of importance to be able to guarantee delay independent incremental asymptotic stability whereby all solutions converge toward each other asymptotically thus allowing the asymptotic properties of all trajectories of the system to be determined by simply studying those of some particular convenient solution it is known that the classical notion of quasimonotonicity renders time delayed systems monotone however this is not sufficient alone to obtain such guarantees in this work we show that by combining quasimonotonicity with a condition of scalability motivated by wireless networks it is possible to guarantee incremental asymptotic stability for a general class of systems that includes a variety of interesting examples furthermore we obtain as a corollary a result of guaranteed convergence of all solutions to a quantifiable invariant set enabling time invariant asymptotic bounds to be obtained for the trajectories even if the precise values of time varying parameters are unknown

decomposed slice sampling for factorized distributions abstract slice sampling provides an automatical adjustment to match the characteristics of the distribution although this method has made great success in many situations it becomes limited when the distribution is complex inspired by higdon 1 in this paper we present a decomposed sampling framework based on slice sampling called decomposed slice sampling dss we suppose that the target distribution can be divided into two multipliers so that information in each term can be used respectively the first multiplier is used in the first step of dss to obtain horizontal slices and the last term is used in the second step simulations on four simple distributions indicate the effectiveness of our method compared with slice sampling and hamiltonian monte carlo on gaussian distributions in different dimensions and ten real world datasets the proposed method achieves better performance

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

consensus of multiagent systems with distance dependent communication networks in this paper we study the consensus problem of discrete time and continuous time multiagent systems with distance dependent communication networks respectively the communication weight between any two agents is assumed to be a nonincreasing function of their distance first we consider the networks with fixed connectivity in this case the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough we show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound second we study the networks with distance dependent connectivity it is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range with the validity of some conditions related to the property of the initial communication graph we prove that consensus can be achieved asymptotically third we present some applications of the main results to opinion consensus problems and formation control problems finally several simulation examples are presented to illustrate the effectiveness of the theoretical findings

systems of ordinary differential equations which generate an order preserving flow a survey of results this article consists of a survey of results concerning the qualitative behavior of solutions of systems of ordinary differential equations which generate an order preserving flow we restrict our consideration to partial orderings on r n induced by any one of its orthants a flow preserves ordering if any two solutions x t and y t are ordered x t leqq y t for all t 0 whenever x 0 leqq y 0 many of the important results for such systems have only recently been obtained principally by m w hirsch who pointed out the tendency of their solutions to converge to equilibrium less well known are some global geometric constraints on the stable manifold of an equilibrium and the existence of heteroclinic orbits connecting ordered equilibria a particularly striking result for this class of systems is the easily computable necessary and sufficient condition for stability of an equilibrium one of our main goals is to show that by allowing partial orderings on r n generated by orthants

the evolution of beliefs over signed social networks we study the evolution of opinions or beliefs over a social network modeled as a signed graph the sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends positive links or enemies negative links pairs of nodes are randomly selected to interact over time and when two nodes interact each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link this model generalizes the degroot model to account for negative links when two adversaries interact their opinions go in opposite directions we provide conditions for convergence and divergence in expectation in mean square and in almost sure sense and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph we establish a no survivor theorem stating that the difference in opinions of any two nodes diverges whenever opinions in the network diverge as a whole we also prove a live or die lemma indicating that almost surely the opinions either converge to an agreement or diverge finally we extend our analysis to cases where opinions have hard lower and upper limits in these cases we study when and how opinions may become asymptotically clustered to the belief boundaries and highlight the crucial influence of strong or weak structural balance of the underlying network on this clustering phenomenon

delay independent asymptotic stability in monotone systems monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties it is known that under the property of quasimonotonicity time delayed systems become monotone and some remarkable properties have been reported for such systems these include for example the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays nevertheless extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity and it has been conjectured that these can be relaxed our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay independent stability in particular one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as t rightarrow infty then the system is globally asymptotically stable for arbitrary bounded time varying delays this follows from a more general result derived in the paper that allows to quantify delay independent regions of attraction which can be used to prove global asymptotic stability for various classes of systems these also recover various known delay independent stability results that are discussed within the paper

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

nonlinear second order multi agent systems subject to antagonistic interactions without velocity constraints abstract this paper studies the nonlinear second order multi agent systems without velocity information while subject to antagonistic interactions among the reciprocal agents when being free of nonlinear disturbances a necessary and sufficient condition for the consensus resp stability problem is presented which essentially shows that the coupling weights and topology structure suffice to assure the consensus resp stability of the agents whereas nonzero eigenvalues of the laplacian matrix also act a crucial role provided that merely the absolute information of the auxiliary variable is demanded the derived results implicitly manifest that structurally balanced graph resp isolated structurally balanced graph or containing the in isolated structurally balanced subgraph is merely the necessary condition for the consensus resp stability of the agents within the second order dynamical setting in the presence of nonlinear dynamics we explicitly extend the derived results with the help of the lyapunov based technique under quite mild assumptions furthermore some comparisons are presented in contrast to some of the existing literature finally numerical examples are given to validate the efficiency of the obtained results

distributed consensus of heterogeneous multi agent systems with fixed and switching topologies in this article we study distributed consensus of heterogeneous multi agent systems with fixed and switching topologies the analysis is based on graph theory and nonnegative matrix theory we propose two kinds of consensus protocols based on the consensus protocol of first order and second order multi agent systems some necessary and sufficient conditions that the heterogeneous multi agent system solves the consensus problems under different consensus protocols are presented with fixed topology we also give some sufficient conditions for consensus of the heterogeneous multi agent system with switching topology simulation examples are provided to demonstrate the effectiveness of the theoretical results

parameter expansion for data augmentation abstract viewing the observed data of a statistical model as incomplete and augmenting its missing parts are useful for clarifying concepts and central to the invention of two well known statistical algorithms expectation maximization em and data augmentation recently liu rubin and wu demonstrated that expanding the parameter space along with augmenting the missing data is useful for accelerating iterative computation in an em algorithm the main purpose of this article is to rigorously define a parameter expanded data augmentation px da algorithm and to study its theoretical properties the px da is a special way of using auxiliary variables to accelerate gibbs sampling algorithms and is closely related to reparameterization techniques we obtain theoretical results concerning the convergence rate of the px da algorithm and the choice of prior for the expansion parameter to understand the role of the expansion parameter we establish a new theory for iterative conditional sampling under the tra

recent directions in matrix stability abstract matrix stability has been intensively investigated in the past two centuries we review work that has been done in this topic focusing on the great progress that has been achieved in the last decade or two we start with classical stability criteria of lyapunov routh and hurwitz and lienard and chipart we then study recently proven sufficient conditions for stability with particular emphasis on p matrices we investigate conditions for the existence of a stable scaling for a given matrix we review results on other types of matrix stability such as d stability additive d stability and lyapunov diagonal stability we discuss the weak principal submatrix rank property shared by lyapunov diagonally semistable matrices we also discuss the uniqueness of lyapunov scaling factors maximal lyapunov scaling factors cones of real positive semidefinite matrices and their applications to matrix stability and inertia preserving matrices

on the consensus and bipartite consensus in high order multi agent dynamical systems with antagonistic interactions abstract the aim of this paper is to address consensus and bipartite consensus for a group of homogeneous agents under the assumption that their mutual interactions can be described by a weighted signed connected and structurally balanced communication graph this amounts to assuming that the agents can be split into two antagonistic groups such that interactions between agents belonging to the same group are cooperative and hence represented by nonnegative weights while interactions between agents belonging to opposite groups are antagonistic and hence represented by nonpositive weights in this framework bipartite consensus can always be reached under the stabilizability assumption on the state space model describing the dynamics of each agent on the other hand nontrivial standard consensus may be achieved only under very demanding requirements both on the laplacian associated with the communication graph and on the agents description in particular consensus may be achieved only if there is a sort of equilibrium between the two groups both in terms of cardinality and in terms of the weights of the conflicting interactions amongst agents

importance sampling for simulation of markovian physical processes transient markov chains are sometimes simulated to estimate rare event probabilities for illustration chains defined by an airborne particle dispersion model are used to estimate the probabilities that released particles reach various locations such estimated probabilities are needed for many purposes including exposure calculations for affected populations and optimization of detector placement by using experimental designs for simulation runs and embedding fitted regression models of output data in importance sampling transition kernels convergence is improved by factors of tens to hundreds

a criterion for exponential consensus of time varying non monotone nonlinear networks in this technical note we present new results on exponential consensus for continuous time nonlinear time varying networks a key feature in the following is that the monotonicity property is not required unlike most of existing literature on the subject moreover we give an estimate of the exponential rate of convergence towards the agreement manifold finally representative example and counterexample are given

a goodness of fit test for logistic regression models based on case control data summary we test the logistic regression assumption under a case control sampling plan after reparameterisation the assumed logistic regression model is equivalent to a two sample semiparametric model in which the log ratio of two density functions is linear in data by identifying this model with a biased sampling model we propose a kolmogorov smirnovtype statistic to test the validity of the logistic link function moreover we point out that this test statistic can also be used in mixture sampling we present a bootstrap procedure along with some results on simulation and on analysis of two real datasets

spatial bayesian variable selection with application to functional magnetic resonance imaging we propose a procedure to undertake bayesian variable selection and model averaging for a series of regressions located on a lattice for those regressors that are in common in the regressions we consider using an ising prior to smooth spatially the indicator variables representing whether or not the variable is zero or nonzero in each regression this smooths spatially the probabilities that each independent variable is nonzero in each regression and indirectly smooths spatially the regression coefficients we discuss how single site sampling schemes can be used to evaluate the joint posterior distribution the approach is applied to the problem of functional magnetic resonance imaging in medical statistics where massive datasets arise that require prompt processing here the ising prior with a three dimensional neighborhood structure is used to smooth spatially activation maps from regression models of blood oxygenation the ising prior also has the advantage of allowing incorporation of anatomic prio

intrinsic reduced attitude formation with ring inter agent graph this paper investigates the reduced attitude formation control problem for a group of rigid body agents using feedback based on relative attitude information under both undirected and directed cyc

positron emission tomography by markov chain monte carlo with auxiliary variables we propose a new algorithm for positron emission tomography pet image reconstruction the algorithm belongs to the family of markov chain monte carlo methods with auxiliary variables the idea is to iteratively generate hidden variables at one step and use them for image restoration at another step the well known model of vardi et al j amer statist assoc 80 1985 8 for pet is combined with the bayesian model of lasota and niemiro pattern recognition 36 2003 931 for the underlying images this latter model takes advantage of the fact that medical images often consist of relatively few grey levels of unknown intensity the algorithm of lasota and niemiro pattern recognition 36 2003 931 is used in the image restoration part of the pet algorithm essentially as a noise filtering and smoothing device it is now equipped with an additional data reconstruction step we include simulation results which suggest that the method is truly reliable we also describe a version of the basic algorithm in which a random simulation step is replaced by computation of expected value similarly as in the em algorithm

on limits of powers of certain absolutely row stochastic matrices abstract we consider limits of powers of matrices that are absolutely row stochastic matrices a such that a is row stochastic we give graph theoretic criteria when such limits exist and if so determine their value in particular we show that for aperiodic connected matrices that satisfy opposition bipartiteness obipness a perron frobenius property holds here we call a obip also called structural balance in the literature when nodes in the graph corresponding to a can be partitioned into two groups such that within group links are non negative and across group links are non positive

bayesian mode regression using mixtures of triangular densities abstract bayesian semiparametric models for mean and median regressions abound but a void for mode regressions exists we fill this gap by nonparametrically modeling the error distribution in such regressions that entails constructing prior distributions on densities which exhibit flexibility while fixing the mode at 0 such priors exist when constraining the mean and median but to our knowledge there is none for the mode our solution with mixtures of triangular distributions results in a conditionally conjugate prior on the space of unimodal untruncated convex densities consistency properties of the resulting modal estimators are studied followed by simulated and real data illustrations

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

controllability improvement for multi agent systems leader selection and weight adjustment abstractfor an uncontrollable system adding leaders and adjusting edge weights are two methods to improve controllability in this paper the controllability of multi agent systems under directed topologies is studied especially on the leader selection problem and the weight adjustment problem for a multi agent system necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed to improve controllability by adjusting edge weights the system is supposed to be structurally controllable which holds if and only if the communication topology contains a spanning tree it is also proved that the number of the fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix in addition a leader selection algorithm and a weight adjustment algorithm are presented simulation examples are provided to illustrate the theoretical results

graphical gaussian shape models and their application to image segmentation this paper presents a novel approach to shape modeling and a model based image segmentation procedure tailor made for the proposed shape model a common way to represent shape is based on so called key points and leads to shape variables which are invariant with respect to similarity transformations we propose a graphical shape model which relies on a certain conditional independence structure among the shape variables most often it is sufficient to use a sparse underlying graph reflecting both nearby and long distance key point interactions graphical shape models allow for specific shape modeling since e g for the subclass of decomposable graphical gaussian models both model selection procedures and explicit parameter estimates are available a further prerequisite to a successful application of graphical shape models in image analysis is provided by the toolbox of markov chain monte carlo methods offering highly flexible and effective methods for the exploration of a specified distribution for bayesian image segmentation based on a graphical gaussian shape model we suggest applying a hybrid approach composed of the well known gibbs sampler and the more recent slice sampler shape modeling as well as image analysis are demonstrated for the segmentation of vertebrae from two dimensional slices of computer tomography images

convergence rate for discrete time multiagent systems with time varying delays and general coupling coefficients multiagent systems mass are ubiquitous in our real world there is an increasing attention focusing on the consensus or synchronization problem of mass over the past decade although there are numerous results reported on the convergence of a discrete time mas based on the infinite products of matrices few results are on the convergence rate because of the switching topology the traditional eigenvalue analysis and the lyapunov function methods are both invalid for the convergence rate analysis of an mas with a switching topology therefore the estimation of the convergence rate for a discrete time mas with time varying delays remains a difficult problem to overcome the essential difficulty of switching topology this paper aims at developing a contractive set approach to analyze the convergence rate of a discrete time mas in the presence of time varying delays and generalized coupling coefficients using the proposed approach we obtain an upper bound of the convergence rate under the condition of joint connectivity in particular the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients which have been widely applied in the existing works on this topic as an application of the main results we will show that the classical vicsek model with time delays can realize synchronization if the initial topology is connected

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

convergence analysis of directed signed networks via an m matrix approach abstractthis paper aims at solving convergence problems on directed signed networks with multiple nodes where interactions among nodes are described by signed digraphs the convergence analysis is

controllability of multi agent systems with directed and weighted signed networks abstract this paper studies the controllability of multi agent systems with signed networks which are represented by directed weighted signed graphs the adjacency weights of network depict the property of interactions positive weight means cooperative interaction while negative weight antagonistic interaction first by using switching equivalent transformation the controllability of three kinds of signed networks is studied structurally balanced anti balanced and strictly unbalanced it is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network then a graph theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks furthermore some necessary and sufficient conditions are given for the controllability of generic linear multi agent systems in addition several examples are presented to illustrate the theoretical results

likelihood analysis of spatial point patterns summary the likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns approximation methods of the normalizing factor of gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness or hardness of repulsive interactions the approximations are useful up to a considerably high density the validity of our procedure is demonstrated by some computer experi ments some real data are analysed

asymptotic behaviours of a class of threshold models for collective action in social networks a class of dynamic threshold models is proposed for describing the upset of collective actions in social networks the agents of the network have to decide whether to undertake certain action or no

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

equilibrium topology of multi agent systems with two leaders it is typical in containment control problems to assume that there is no conflict of interest among leaders in this paper we consider the situation where there is conflict between leaders namely the leaders compete to attract followers the strategies of each leader are defined by choosing at most k followers to propagate their information then we formulate a standard two player zero sum game by using graph theory and matrix theory we further prove that each player will choose exactly k followers when the game achieves a nash equilibrium it is noteworthy that the interaction graph here is generated from the conflict between leaders and then the nash equilibrium point of the game corresponds to the equilibrium topology for the case of choosing one follower a necessary and sufficient condition for an interaction graph to be the equilibrium topology is derived moreover we can obtain the equilibrium topology directly if followers interaction graph is a circulant graph or a graph with a center vertex simulation examples are provided to validate the effectiveness of the theoretical results

bayesian methods for hidden markov models markov chain monte carlo mcmc sampling strategies can be used to simulate hidden markov model hmm parameters from their posterior distribution given observed data some mcmc methods used in practice for computing likelihood conditional probabilities of hidden states and the most likely sequence of states can be improved by incorporating established recursive algorithms the most important of these is a set of forward backward recursions calculating conditional distributions of the hidden states given observed data and model parameters i show how to use the recursive algorithms in an mcmc context and demonstrate mathematical and empirical results showing a gibbs sampler using the forward backward recursions mixes more rapidly than another sampler often used for hmms iintroduce an augmented variables technique for obtaining unique state labels in hmms and finite mixture models i show how recursive computing allows the statistically efficient use of mcmc output when estimating the hidden states i

fully bayesian estimation of gibbs hyperparameters for emission computed tomography data in recent years many investigators have proposed gibbs prior models to regularize images reconstructed from emission computed tomography data unfortunately hyperparameters used to specify gibbs priors can greatly influence the degree of regularity imposed by such priors and as a result numerous procedures have been proposed to estimate hyperparameter values from observed image data many of these procedures attempt to maximize the joint posterior distribution on the image scene to implement these methods approximations to the joint posterior densities are required because the dependence of the gibbs partition function on the hyperparameter values is unknown here the authors use recent results in markov chain monte carlo mcmc sampling to estimate the relative values of gibbs partition functions and using these values sample from joint posterior distributions on image scenes this allows for a fully bayesian procedure which does not fix the hyperparameters at some estimated or specified value but enables uncertainty about these values to be propagated through to the estimated intensities the authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source the authors consider two different markov random field mrf models the power model and a line site model as applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography spect phantom

continuous time consensus under persistent connectivity and slow divergence of reciprocal interaction weights in this paper we present new results on consensus for continuous time multiagent systems we introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete time consensus protocols slow divergence of reciprocal interaction weights generalizes the assumption of cut balanced interactions we show that under these two assumptions the continuous time consensus protocol succeeds the states of all the agents converge asymptotically to a common value moreover our proof allows us to give an estimate of the rate of convergence towards the consensus we also provide examples that make us think that both of our assumptions are tight

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed

stability criteria for matrices in this paper we study the stability of matrices using technologies of special matrices analysis several simple criteria for the stability for the matrix a aij cn n which is not diagonally dominant are obtained by aid of simple algebraic conditions of aij only