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

solving a modified consensus problem of linear multi agent systems a distributed protocol is proposed for a modified consensus problem of a network of agents that have the same continuous time linear dynamics each agent estimates its own state using its output information and then sends the estimated state to its neighbor agents for the purpose of reaching a consensus the modified consensus problem requires the group decision value to be a linear function of initial states and initial estimated states of all agents in the network and the transformation matrix associated with this linear function not to be a zero matrix it is proved that under the proposed control protocol the modified consensus problem can be solved if and only if the system matrices of the agent s dynamics are stabilizable and detectable the input matrix is not a zero matrix and the communication topology graph has a spanning tree the proposed protocol can also be extended to multi agent systems where agents are described by discrete time linear dynamics the corresponding necessary and sufficient conditions are provided as well

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

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

correlations between zeros of a random polynomial we obtain exact analytical expressions for correlations between real zeros of the kac random polynomial we show that the zeros in the interval 1 1 are asymptotically independent of the zeros outside of this interval and that the straightened zeros have the same limit translation invariant correlations then we calculate the correlations between the straightened zeros of theo 1 random polynomial

universal fluctuations of zeros of chaotic wavefunctions wavefunctions of one and two dimensional quantum systems can be parametrized by a finite number of zeros lying in phase space we study correlations of these zeros for fully chaotic systems in terms of a statistical model based on random polynomials excellent agreement is found for the two point correlation function and nearest neighbour spacing distribution of this model and the results obtained for wavefunctions of dynamical systems we conjecture that these correlation functions are valid for any chaotic system after rescaling the phase space distances unfolding some consequences for the distribution of zeros due to time reversal symmetry are also discussed

optimal reconstruction of images from localized phase the importance of localized phase in signal representation is investigated the convergence rate of the pocs algorithm projection onto convex sets used for image reconstruction from spectral phase is defined and analyzed and the characteristics of images optimally reconstructed from phase only information are presented it is concluded that images of geometric form are most efficiently reconstructed from their spectral phase whereas images of symmetric form have the poorest convergence characteristics the transition between the two extremes is shown to be continuous the results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach and suggest possible compression schemes

consensus seeking over markovian switching networks with time varying delays and uncertain topologies stochastic consensus problems for linear time invariant multi agent systems over markovian switching networks with time varying delays and topology uncertainties are dealt with by using the linear matrix inequality method and the stability theory of markovian jump linear system we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the markov process provided the union of topologies associated with the positive recurrent states of the markov process admits a spanning tree and the agent dynamics is stabilizable feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying delays numerical examples are given to show the feasibility of theoretical results

the zeros of random polynomials further results and applications we consider the density of the zeros of random polynomials with nonzero mean correlated gaussian coefficients we show that for most communication problems the original result by hammersley 1956 can be expressed in a simpler form in order to illustrate the usefulness of the presented theory two applications are considered first the zeros of frequency selective ricean fading channels are investigated second the zeros of the transfer function corresponding to channel impulse response estimates obtained by a least squares approach are calculated for both applications implications for equalizer design are discussed

density of complex critical points of a real random so m 1 polynomial we study the density of complex critical points of a real random so m 1 polynomial in m variables in a previous paper macdonald in j stat phys 136 5 807 2009 the author used the poincare lelong formula to show that the density of complex zeros of a system of these real random polynomials rapidly approaches the density of complex zeros of a system of the corresponding complex random polynomials the su m 1 polynomials in this paper we use the kac rice formula to prove an analogous result the density of complex critical points of one of these real random polynomials rapidly approaches the density of complex critical points of the corresponding complex random polynomial in one variable we give an exact formula and a scaling limit formula for the density of critical points of the real random so 2 polynomial as well as for the density of critical points of the corresponding complex random su 2 polynomial

stochastic consentability of linear systems with time delays and multiplicative noises this paper develops stochastic consentability of linear multiagent systems with time delays and multiplicative noises first the stochastic stability for stochastic differential delay equations driven by multiplicative noises is examined and the existence of the positive definite solution for a class of generalized algebraic riccati equations gares is established then sufficient conditions are deduced for the mean square and almost sure consentability and stabilization based on the developed stochastic stability and gares consensus protocols are designed for linear multiagent systems with undirected and leader following topologies it is revealed that multiagent consentability depends on certain characterizing system parameters including linear system dynamics communication graph channel uncertainties and time delay of the deterministic term it is shown that a second order integrator multiagent system is unconditionally mean square and almost surely consentable for any given noise intensities and time delay and that the mean square and almost sure consensus can be achieved by carefully choosing the control gain according to certain explicit conditions

secular determinants of random unitary matrices we consider the characteristic polynomials of random unitary matrices u drawn from various circular ensembles in particular the statistics of the coefficients of these polynomials are studied the variances of these secular coefficients are given explicitly for arbitrary dimension and continued analytically to arbitrary values of the level repulsion exponent the latter secular coefficients are related to the traces of powers of u by newton s well known formulae while the traces tend to have gaussian distributions and to be statistically independent among one another in the limit as the matrix dimension grows large the secular coefficients exhibit strong mutual correlations due to newton s mixing of traces to coefficients these results might become relevant for current efforts at combining semiclassics and random matrix theory in quantum treatments of classically chaotic dynamics

stable protocol admissible synchronizability for high order singular complex networks with switching topologies abstract stable protocol admissible synchronization analysis and design problems for singular complex networks with both connected switching topologies and jointly connected switching topologies are investigated firstly a singular observer type synchronization protocol is introduced where the errors of protocol states among neighboring agents are applied to make complex networks satisfy a specific separation principle which can simplify synchronization analysis and design problems then by the orthonormal projection operators between the synchronization subspace and the complement synchronization subspace stable protocol admissible synchronization problems are transformed into admissible ones of multiple subsystems with lower dimensions and an approach is given to determine the synchronization function furthermore stable protocol admissible synchronizability criteria for connected switching topology cases and jointly connected switching topology cases are proposed respectively finally two numerical examples are given to demonstrate the effectiveness of theoretical results

random analytic chaotic eigenstates the statistical properties of random analytic functions z are investigated as a phase space model for eigenfunctions of fully chaotic systems we generalize to the plane and to the hyperbolic plane a theorem concerning the equidistribution of the zeros of z previously demonstrated for a spherical phase space su 2 polynomials for systems with time reversal symmetry the number of real roots is computed for the three geometries in the semiclassical regime the local correlation functions are shown to be universal independent of the system considered or the geometry of phase space in particular the autocorrelation function of is given by a gaussian function the connections between this model and the gaussian random function hypothesis as well as the random matrix theory are discussed

distribution of roots of random polynomials we consider polynomials of high degree with random coefficients which appear in the context of quantum chaotic dynamics and investigate various conditions under which their roots tend to concentrate near the unit circle in the complex plane correlation functions of roots are computed analytically we also investigate a certain class of random polynomials whose roots cover in a uniform way the riemann sphere special emphasis is devoted to the influence of symmmetries

chaotic analytic zero points exact statistics for those of a random spin state a natural statistical ensemble of 2j points on the unit sphere can be associated via the majorana representation with a random quantum state of spin j and an exact expression is obtained here for the general k point correlation function in this ensemble the pair correlation in the large j limit takes the relatively simple form where and is the angular separation of the pair of points on the sphere it appears from the numerical work of others that in this limit these statistics are typical of the zero points of analytic functions associated with chaotic quantum dynamical systems

necessary and sufficient conditions for consensus of double integrator multi agent systems with measurement noises an average consensus protocol is proposed for continuous time double integrator multi agent systems with measurement noises under fixed topologies the time varying control gain is employed to attenuate noises the closed loop system is therefore a time varying linear stochastic differential equation by determining the state transition matrix of this closed loop system the dynamic characteristics of the multi agent system can be fully described it is proved that in the noisy communication environment the average consensus can be achieved if and only if the communication topology is a balanced and strongly connected graph and the time varying control gain satisfies the stochastic approximation type conditions under the proposed protocol the position of each agent is convergent in mean square to a common random variable whose mathematical expectation is the average of initial positions and initial velocities of all agents in the system while each agent s velocity is convergent in mean square to a common random variable whose mathematical expectation and variance are both zero

hamilton decompositions of regular expanders a proof of kelly s conjecture for large tournaments abstract a long standing conjecture of kelly states that every regular tournament on n vertices can be decomposed into n 1 2 edge disjoint hamilton cycles we prove this conjecture for large n in fact we prove a far more general result based on our recent concept of robust expansion and a new method for decomposing graphs we show that every sufficiently large regular digraph g on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge disjoint hamilton cycles this enables us to obtain numerous further results e g as a special case we confirm a conjecture of erd s on packing hamilton cycles in random tournaments as corollaries to the main result we also obtain several results on packing hamilton cycles in undirected graphs giving e g the best known result on a conjecture of nash williams we also apply our result to solve a problem on the domination ratio of the asymmetric travelling salesman problem which was raised e g by glover and punnen as well as alon gutin and krivelevich

stochastic consensus seeking with noisy and directed inter agent communication fixed and randomly varying topologies we consider consensus seeking of networked agents on directed graphs where each agent has only noisy measurements of its neighbors states stochastic approximation type algorithms are employed so that the individual states converge both in mean square and almost surely to the same limit we further generalize the algorithm to networks with random link failures and prove convergence results

parametric statistics of zeros of husimi representations of quantum chaotic eigenstates and random polynomials local parametric statistics of zeros of husimi representations of quantum eigenstates are introduced it is conjectured that for a classically fully chaotic system one should use the model of parametric statistics of complex roots of gaussian random polynomials which is exactly solvable as demonstrated below for example the velocities derivatives of zeros of husimi function with respect to an external parameter are predicted to obey a universal non maxwellian distribution where is the mean square velocity the conjecture is demonstrated numerically in a generic chaotic system with two degrees of freedom dynamical formulation of the zero flow in terms of an integrable many body dynamical system is given as well

shape from moments an estimation theory perspective this paper discusses the problem of recovering a planar polygon from its measured complex moments these moments correspond to an indicator function defined over the polygon s support previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given in this paper we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given similar to methods found in array processing system identification and signal processing we discuss a set of possible estimation procedures that are based on the prony and the pencil methods relate them one to the other and compare them through simulations we then present an improvement over these methods based on the direct use of the maximum likelihood estimator exploiting the above methods as initialization finally we show how regularization and thus maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon

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

exact statistics of complex zeros for gaussian random polynomials with real coefficients k point correlations of complex zeros for gaussian ensembles of random polynomials of order n with real coefficients grprc are calculated exactly following an approach of hannay for the case of gaussian random polynomials with complex coefficients grpcc it is shown that in the thermodynamic limit of gaussian random holomorphic functions all the statistics converge to their grpcc counterparts as one moves off the real axis while close to the real axis the two cases are essentially different special emphasis is given to one and two point correlation functions in various regimes

joint densities of secular coefficients for unitary matrices we determine the joint density of secular coefficients and of the traces of powers for random unitary matrices from dyson s circular ensembles a byproduct are workable unitarity conditions necessary and sufficient for all roots of a polynomial to be unimodular and different these findings will be useful for combinations of random matrix theory with semiclassical approximations in calculating spectral properties of quantum systems whose classical limit is globally chaotic in a first such application we show that reasonable quasi energy spectra result by throwing dice a la random matrix theory to complement restricted knowledge rigorous or from short periodic orbits of the secular polynomial of a unitary floquet matrix

distribution of roots of random real generalized polynomials the average density of zeros for monic generalized polynomials p n z phi z sum nolimits k 1 n c k f k z with real holomorphic f k and real gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative we obtain compact expressions for both the regular component generated by the complex roots and the singular one real roots of the average density of roots the density of the regular component goes to zero in the vicinity of the real axis like lmz we present the low and high disorder asymptotic behaviors then we particularize to the large n limit of the average density of complex roots of monic algebraic polynomials of the form p n z z n sum nolimits k 1 n c k z n k with real independent identically distributed gaussian coefficients having zero mean and dispersion delta 1 sqrt n lambda the average density tends to a simple universal function of 2nlog z and in the domain coth 2 n sin arg z where nearly all the roots are located for largen

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

leader following exponential consensus of fractional order nonlinear multi agents system with hybrid time varying delay a heterogeneous impulsive method abstract in this paper we study the leader following exponential consensus of multi agent system each agent in the system is described by nonlinear fractional order differential equation both the internal delay and coupling delay are taken into consideration the heterogeneous impulsive control is used for ensuring the consensus of all agents based on lyapunov function method and matrix analysis some sufficient conditions for exponential consensus are obtained finally some illustrative examples are given to show the effectiveness of the obtained results

uniqueness of consensus functions for time delayed swarm systems with time varying topologies abstract this paper shows that consensus functions for high order linear swarm systems with time varying interaction topologies and time delays are uniquely determined by initial states if interaction topologies are balanced in addition an explicit expression of the consensus function is presented and the different influences of initial states of agents and protocols on the consensus function are determined respectively

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

power scheduling of universal decentralized estimation in sensor networks we consider the optimal power scheduling problem for the decentralized estimation of a noise corrupted deterministic signal in an inhomogeneous sensor network sensor observations are first quantized into discrete messages then transmitted to a fusion center where a final estimate is generated supposing that the sensors use a universal decentralized quantization estimation scheme and an uncoded quadrature amplitude modulated qam transmission strategy we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power while ensuring a given mean squared error mse performance the proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power for the remaining active sensors their optimal quantization and transmit power levels are determined jointly by individual channel path losses local observation noise variance and the targeted mse performance numerical examples show that in inhomogeneous sensing environment significant energy savings is possible when compared to the uniform quantization strategy

signed zeros of gaussian vector fields density correlation functions and curvature we calculate correlation functions of the signed density of zeros of gaussian distributed vector fields we are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract riemann cartan or riemannian manifold as an application we discuss one and two point functions the zeros of a two dimensional gaussian vector field model the distribution of topological defects in the high temperature phase of two dimensional systems with orientational degrees of freedom such as superfluid films thin superconductors and liquid crystals

exact statistical properties of the zeros of complex random polynomials the zeros of complex gaussian random polynomials with coefficients such that the density in the underlying complex space is uniform are known to have the same statistical properties as the zeros of the coherent state representation of one dimensional chaotic quantum systems we extend the interpretation of these polynomials by showing that they also arise as the wavefunction for a quantum particle in a magnetic field constructed from a random superposition of states in the lowest landau level a study of the statistical properties of the zeros is undertaken using exact formulae for the one and two point distribution functions attention is focused on the moments of the two point correlation in the bulk the variance of a linear statistic and the asymptotic form of the two point correlation at the boundary a comparison is made with the same quantities for the eigenvalues of complex gaussian random matrices

hamilton decompositions of regular tournaments we show that every sufficiently large regular tournament can a lmost completely be decomposed into edge disjoint hamilton cycles more precisely for each 0 every regular tournament g of sufficiently large ordern contains at least 1 2 n edge disjoint hamilton cycles this gives an approximate solution to a conjecture of kelly from 1968 our result also extends to almost regular tournaments

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

real roots of random polynomials universality close to accumulation points we identify the scaling region of a width o n 1 in the vicinity of the accumulation points t 1 of the real roots of a random kac like polynomial of large degree n we argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent identically distributed coefficients ci as long as the second moment e c2i is finite in particular we reveal a gradual in contrast to the previously reported abrupt and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value n e ci scaled as n n 1 2

quantum chaotic dynamics and random polynomials we investigate the distribution of roots of polynomials of high degree with random coefficients which among others appear naturally in the context of quantum chaotic dynamics it is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane in order to further increase this tendency we study in detail the particular case of self inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle correlation functions of these roots are also computed analytically and compared to the correlations of eigenvalues of random matrices the problem of ergodicity of chaotic wavefunctions is also considered for that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space while these results are consistent with random matrix theory predictions they provide a new and different insight into the problem of quantum ergodicity special attention is devoted to the role of symmetries in the distribution of roots of random polynomials

the chaotic analytic function in contrast to a stationary gaussian random function of a real variable which is free to have any correlation function the closest analogous analytic random function in the complex plane has no true freedom it is statistically unique since it has arisen only recently as an apparently universal feature in the physical context of quantum chaos i refer to it here as the chaotic analytic function i note that it is implied by the assumption that a quantum chaotic wavefunction has gaussian randomness and has a constant value for the average of its wigner function in phase space interpreted literally this shows that the chaotic analytic function is the bargmann function of a pure white noise wavefunction more physically if constant is replaced by smooth on the scale of a planck area these assumptions are the semiclassical ones made by berry for chaotic eigenstates the analysis shows that the chaotic analytic function is still obtained semiclassically

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

continuum percolation for gaussian zeroes and ginibre eigenvalues we study continuum percolation on certain negatively dependent point processes on r 2 specifically we study the ginibre ensemble and the planar gaussian zero process which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion for the ginibre ensemble we establish the uniqueness of infinite cluster in the supercritical phase for the gaussian zero process we establish that a non trivial critical radius exists and we prove the uniqueness of infinite cluster in the supercritical regime

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

a mean square consensus protocol for linear multi agent systems with communication noises and fixed topologies the mean square consensus of linear multi agent systems with communication noises is studied in this note each agent is modeled by a continuous time linear time invariant dynamics and the fixed communication topology is described by a digraph the proposed consensus protocol is composed of two parts the agent s own state feedback and the relative states between agent and its neighbor agents due to the existence of communication noises the relative states cannot be obtained accurately to attenuate the noise effect a time varying gain vector a t k is applied to the inaccurate relative states it is proved that 1 if the communication topology has a spanning tree and every node has at least one parent node then the proposed protocol can solve the mean square consensus problem if and only if a t satisfies 0 a s ds and 0 a2 s ds and all roots of the polynomial whose coefficients are the elements of vector k are in the left half complex plane 2 if the communication topology has a spanning tree and there exists one node without any parent node then the condition 0 a2 s ds is only sufficient but not necessary and 3 if the communication topology has no spanning tree then the proposed protocol cannot solve the mean square consensus problem

on the distribution of zeros of chaotic wavefunctions wavefunctions in a phase space representation can be expressed as entire functions of their zeros if the phase space is compact these zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics besides an understanding of their statistical properties may prove to be useful in the analytical calculations of the wavefunctions in quantum chaotic systems this motivates us to pursue the present study which by a numerical statistical analysis shows that both long range correlations as well as short range correlations exist between zeros while the latter turn out to be universal and parametric independent the former seem to be system dependent and are significantly affected by various parameters i e symmetry localization etc furthermore for the delocalized quantum dynamics the distribution of these zeros seem to mimic that of the zeros of the random functions as well as random polynomials

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

periodic orbit quantization of baker s map we consider the resummation of the semiclassical selberg zeta function for quantized maps on compact phase space specifically the quantized baker s map in particular we demonstrate that the semiclassical periodic orbit expansion leads to an effectively finite polynomial for the spectrum of the quantum map however the coefficients are not self inverse as required by unitarity an extension of the semiclassical approximation by including corrections due to the discontinuities of the classical map improves the situation the improved polynomial is closer to being self inverse but the eigenphases remain complex slightly better results are obtained if the functional equation is imposed on the semiclassical expansion

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

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

continuous time stochastic consensus this paper investigates the continuous time multi agent consensus with stochastic communication noises each agent can only use its own and neighbors information corrupted by random noises to design its control input to attenuate the communication noises we consider the stochastic approximation type and the kalman bucy filtering based protocols by using the tools of stochastic analysis and algebraic theory the asymptotic properties of these two kinds of protocols are analyzed firstly for the stochastic approximation type protocol we clarify the relationship between the convergence rate of the consensus error and a representative class of consensus gains in both mean square and probability one secondly we propose kalman bucy filtering based consensus protocols each agent uses kalman bucy filters to get asymptotically unbiased estimates of neighbors states and the control input is designed based on the protocol with precise communication and the certainty equivalence principle the iterated logarithm law of estimation errors is developed it is shown that if the communication graph has a spanning tree then the consensus error is bounded above by o t 1 in mean square and by o t 1 2 log log t 1 2 almost surely finally the superiority of the kalman bucy filtering based protocol over the stochastic approximate type protocol is studied both theoretically and numerically

convergence rates of discrete time stochastic approximation consensus algorithms graph related limit bounds abstract in this paper we study the convergence rates of the discrete time stochastic approximation consensus algorithms over sensor networks with communication noises under general digraphs basic results of stochastic analysis and algebraic graph theory are used to investigate the dynamics of the consensus error and the mean square and sample path convergence rates of the consensus error are both given in terms of the graph and noise parameters especially calculation methods to estimate the mean square limit bounds are presented under balanced digraphs and sufficient conditions on the network topology and the step sizes are given to achieve the fast convergence rate for the sample path limit bounds estimation methods are also presented under undirected graphs

how many zeros of a random polynomial are real we provide an elementary geometric derivation of the kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients we show that the expected number of real zeros is simply the length of the moment curve 1 t tn projected onto the surface of the unit sphere divided by the probability density of the real zeros is proportional to how fast this curve is traced out we then relax kac s assumptions by considering a variety of random sums series and distributions and we also illustrate such ideas as integral geometry and the fubini study metric

containment control of multi agent systems in a noisy communication environment the containment problem of first order and second order integral multi agent systems with communication noises is investigated in this paper motivated by the previous work a time varying gain a t is introduced to attenuate the noise effect it is proved that the proposed protocol can solve the mean square containment problem if the following conditions hold 1 the communication topology graph has a spanning forest whose roots are leaders of the multi agent system 2 0 a t dt 3 lim t a t 0 moreover if a t is uniformly continuous these conditions are necessary for ensuring the mean square containment in addition the proposed protocol is also extended to allow the case where each agent has its own gain a i t it is proved that the mean square containment problem can still be solved if all agent dependent gains are infinitesimals of the same order as time goes to infinity finally two simulation examples are provided to demonstrate the effectiveness of the proposed protocols

zeros of the i i d gaussian power series a conformally invariant determinantal process consider the zero set of the random power series f z p anz n with i i d complex gaussian coefficientsan we show that these zeros form a determinantal process more precisely their joint intensity can be written as a minor of the bergman kernel we show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent 0 1 valued random variables xk where p xk 1 r 2k moreover the set of absolute values of the zeros of f has the

consensus conditions of continuous time multi agent systems with additive and multiplicative measurement noises this work is concerned with the consensus problem of multi agent systems with additive and multiplicative measurement noises by developing general stochastic stability lemmas for nonautonomous stochastic differential equations stochastic weak and strong consensus conditions are investigated under fixed and time varying topologies respectively for the case with fixed topologies and additive noises the necessary and sufficient conditions for almost sure strong consensus are given it is revealed that almost sure strong consensus and mean square strong consensus are equivalent under general digraphs and almost sure weak consensus implies mean square weak consensus under undirected graphs if multiplicative noises appear then small noise intensities do not affect the control gain to guarantee stochastic strong consensus for the case with time varying topologies sufficient consensus conditions are given under the periodically connected condition of the topology flow

intrinsic ordering of quasienergy states for mixed regular chaotic quantum systems zeros of the husimi distribution a method is proposed which allows an intrinsic ordering of the quasienergy states for a time periodic quantum system according to the number of essential zeros of the husimi distribution in phase space the corresponding classical system shows a typical mixed dynamics with coexisting regular and chaotic regions in phase space the ordering of states allows a straightforward comparison with semiclassical quantities moreover a direct connection of the organization of zeros with the underlying classical phase space dynamics is demonstrated

density of complex zeros of a system of real random polynomials we study the density of complex zeros of a system of real random so m 1 polynomials in m variables we show that the density of complex zeros of this random polynomial system with real coefficients rapidly approaches the density of complex zeros in the complex coefficients case we also show that the behavior the scaled density of complex zeros near m of the system of real random polynomials is different in the m 2 case than in the m 1 case the density approaches infinity instead of tending linearly to zero

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

bifurcations of periodic orbits and uniform approximations we derive uniform approximations for contributions to gutzwiller s periodic orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space there orbits lie close together and give collective contributions while the individual contributions of gutzwiller s type would diverge at the bifurcation new results for the tangent the period doubling and the period tripling bifurcation are given they are obtained by going beyond the local approximation and including higher order terms in the normal form of the action the uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results

correlation functions for random complex zeroes strong clustering and local universality we prove strong clustering of k point correlation functions of zeroes of gaussian entire functions in the course of the proof we also obtain universal local bounds for k point functions of zeroes of arbitrary nondegenerate gaussian analytic functions in the second part of the paper we show that strong clustering yields the asymptotic normality of fluctuations of some linear statistics of zeroes of gaussian entire functions in particular of the number of zeroes in measurable domains of large area this complements our recent results from the paper fluctuations in random complex zeroes

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

admissible l2 consensus for singular time delayed swarm systems with external disturbances abstract admissible consensus analysis and design problems for high order linear time invariant singular swarm systems with time delays and external disturbances are investigated firstly by the state space decomposition a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances which describe the absolute motions of singular swarm systems as a whole then an l 2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents and linear matrix inequality criteria for admissible l 2 consensus and consensualization are shown finally numerical simulations are presented to demonstrate theoretical results

synchronization and convergence of linear dynamics in random directed networks recently methods in stochastic control are used to study the synchronization properties of a nonautonomous discrete time linear system x k 1 g k x k where the matrices g k are derived from a random graph process the purpose of this note is to extend this analysis to directed graphs and more general random graph processes rather than using lyapunov type methods we use results from the theory of inhomogeneous markov chains in our analysis these results have been used successfully in deterministic consensus problems and we show that they are useful for these problems as well sufficient conditions are derived that depend on the types of graphs that have nonvanishing probabilities for instance if a scrambling graph occurs with nonzero probability then the system synchronizes

time reversal symmetry and random polynomials we analyse the density of roots of random polynomials where each complex coefficient is constructed of a random modulus and a fixed deterministic phase the density of roots is shown to possess a singular component only in the case for which the phases increase linearly with the index of coefficients this means that contrary to earlier belief eigenvectors of a typical quantum chaotic system with some antiunitary symmetry will not display a clustering curve in the stellar representation moreover a class of time reverse invariant quantum systems is shown for which spectra display fluctuations characteristic of orthogonal ensemble while eigenvectors confer to predictions of unitary ensemble