simultaneous partial inverses and decoding interleaved reed solomon codes this paper introduces the simultaneous partial inverse problem spi for polynomials and develops its application to decoding interleaved reed solomon codes beyond half the minimum distance while closely related both to standard key equations and to well known pade approximation problems the spi problem stands out in several respects first the spi problem has a unique solution up to a scale factor which satisfies a natural degree bound second the spi problem can be transformed monomialized into an equivalent spi problem where all moduli are monomials third the spi problem can be solved by an efficient algorithm of the berlekamp massey type fourth decoding interleaved reed solomon codes or subfield evaluation codes beyond half the minimum distance can be analyzed in terms of a partial inverse condition for the error pattern if that condition is satisfied then the true error locator polynomial is the unique solution of a standard key equation and can be computed in many different ways including the well known multi sequence berlekamp massey algorithm and the spi algorithm of this paper two of the best performance bounds from the literature the schmidt sidorenko bossert bound and the roth vontobel bound are generalized to hold for the partial inverse condition and thus to apply to several different decoding algorithms

distributed rotating formation control of multi agent systems this paper investigates collective rotating motions of second order multi agent systems we first consider rotating consensus problems using local relative information we propose a protocol and give a necessary and sufficient condition for rotating consensus of the system then we consider rotating formation control problems with the help of lyapunov theory for complex systems we propose rotating formation protocols and give sufficient conditions to make all agents move with a specific structure in a circular channel finally simulation results are provided to demonstrate the effectiveness of our theoretical results

thermodynamics and statistical analysis of gaussian random fields gaussian fields are considered as gibbsian fields thermodynamic functions are calculated for them and the variational principle is proved as an application we get an approximation of log likelihood and an information theoretic interpretation of the asymptotic behaviour of the maximum likelihood estimator for gaussian markov fields

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

relaxation algorithms for map estimation of gray level images with multiplicative noise the authors present a comparison between stochastic and deterministic relaxation algorithms for maximum a posteriori estimation of gray level images modeled by noncausal gauss markov random fields gmrf and corrupted by film grain noise the degradation involves nonlinear transformation and multiplicative noise parameters for the gmrf model were estimated from the original image using maximum likelihood techniques to overcome modeling errors a constraint minimization approach is suggested for estimating the parameters to ensure the positivity of the power spectral density function real image experiments with various noise variances and magnitudes of the nonlinear transformation are presented

multiresolution gauss markov random field models for texture segmentation this paper presents multiresolution models for gauss markov random fields gmrfs with applications to texture segmentation coarser resolution sample fields are obtained by subsampling the sample field at fine resolution although the markov property is lost under such resolution transformation coarse resolution non markov random fields can be effectively approximated by markov fields we present two techniques to estimate the gmrf parameters at coarser resolutions from the fine resolution parameters one by minimizing the kullback leibler distance and another based on local conditional distribution invariance we also allude to the fact that different gmrf parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first and second order cases we apply this multiresolution model to texture segmentation different texture regions in an image are modeled by gmrfs and the associated parameters are assumed to be known parameters at lower resolutions are estimated from the fine resolution parameters the coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution we use the iterated conditional mode icm minimization at all resolutions our experiments with synthetic brodatz texture and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm

decentralized control of vehicle formations this paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory the vehicles exchange information according to a pre specified communication digraph g a feedback control is designed using relative information between a vehicle and its in neighbors in g we prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that g has a rooted directed spanning tree we show the direct relationship between the rate of convergence to formation and the eigenvalues of the directed laplacian of g various special situations are discussed including symmetric communication graphs and formations with leaders several numerical simulations are used to illustrate the results

extendability tests for multidimensional covariance sequences the problem of extendibility of multidimensional covariance sequences and the equivalent problem of the existence of maximum entropy me spectral estimates are analyzed using some recent results on the valid parameter space of gaussian markov random fields gmrfs for several nontrivial examples explicit conditions for extendability and using those conditions sketches of the space of extendible covariance sequences are obtained for the general case a cutting plane algorithm is proposed as an alternative to the two existing numerical procedures for ascertaining extendibility namely the linear programming procedure and the expanding hull algorithm the duality between the valid parameter space and the space of extendible covariances and the relationship between those two spaces and the space of admissible covariances for finite size data sequences are examined the connection between extendability and maximum likelihood ml estimation is established and some properties extendibility of covariances specified over increasing window sizes are presented

containment control for second order multi agent systems with time varying delays abstract this paper considers the containment control problem for second order multi agent systems with time varying delays both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated sufficient conditions on the communication digraph the feedback gains and the allowed upper bound of the delays to ensure containment control are given in the case that the leaders are stationary the lyapunov razumikhin function method is used in the case that the leaders are dynamic the lyapunov krasovskii functional method and the linear matrix inequality lmi method are jointly used a novel discretized lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is which leads to a better result on the allowed upper bound of the delays to ensure containment control finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

two dimensional spectrum estimation using noncausal autoregressive models two dimensional 2 d spectrum estimation from raw data is of interest in signal and image processing a parametric technique for spectrum estimation using 2 d noncausal autoregressive ncar models is given the ncar models characterize the statistical dependency of the observation at location s on its neighbors in all directions this modeling assumption reduces the spectrum estimation problem to two subproblems the choice of appropriate structure of the ncar model and the estimation of parameters in ncar models by assuming that the true structure of the ncar model is known we first analyze the existence and uniqueness of gaussian maximum likelihood gml estimates of ncar model parameters due to the noncausal nature of the models the computation of gml estimates is burdensome by assuming specific boundary conditions computationally tractable expressions are obtained for the likelihood function expressions for the asymptotic covariance matrix of the gml estimates as well as the simultaneous confidence bands for the estimated spectrum using gml estimates are derived finally the usefulness of the method is illustrated by computer simulation results

noncausal 2 d spectrum estimation for direction finding a two dimensional noncausal autoregressive ncar plus additive noise model based spectrum estimation method is presented for planar array data typical of signals encountered in array processing applications since the likelihood function for ncar plus noise data is nonlinear in the model parameters and is further complicated by the unknown variance of the additive noise computationally intensive gradient search algorithms are required for computing the estimates if a doubly periodic lattice is assumed the complexity of the approximate maximum likelihood ml equation is significantly reduced without destroying the theoretical asymptotic properties of the estimates and degrading the observed accuracy of the estimated spectra initial conditions for starting the approximate ml computation are suggested experimental results that can be used to evaluate the signal plus noise approach and compare its performance to those of signal only methods are presented for gaussian and simulated planar array data statistics of estimated spectrum parameters are given and estimated spectra for signals with close spatial frequencies are shown the approximate ml parameter estimate s asymptotic properties such as consistency and normality are established and lower bounds for the estimate s errors are derived assuming that the data are gaussian

brief paper multi agent consensus with diverse time delays and jointly connected topologies this paper investigates consensus problems in networks of continuous time agents with diverse time delays and jointly connected topologies for convergence analysis of the networks a class of lyapunov krasovskii functions is constructed which contains two parts one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past by a contradiction approach sufficient conditions are derived under which all agents reach consensus even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected the obtained conditions are composed of a sum of decoupled parts corresponding to each possible connected component of the communication topology finally numerical examples are included to illustrate the obtained results

contiguity of the whittle measure for a gaussian time series for a stationary time series whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete fourier transforms of the data at certain frequencies whittle s likelihood has been widely used in the literature for con structing estimators in this paper we show that for a gaussian time series the whittle measure is mutually contiguous with the actual distribution of the data as a consequence most asymptotic properties of estimators and test statistics derived under the whittle measure can be carried over to the actual distribution

brief paper robust consensus of multi agent systems with diverse input delays and asymmetric interconnection perturbations the consensus problem of second order multi agent systems with diverse input delays is investigated based on the frequency domain analysis decentralized consensus conditions are obtained for the multi agent system with symmetric coupling weights then the robustness of the symmetric system with asymmetric perturbation is studied a bound of the largest singular value of the perturbation matrix is obtained as the robust consensus condition simulation examples illustrate the design procedure of consensus protocols and validate the correctness of the results

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

consensus of a class of second order multi agent systems with time delay and jointly connected topologies this technical note investigates consensus problems of a class of second order continuous time multi agent systems with time delay and jointly connected topologies we first introduce a neighbor based linear protocol with time delay then we derive a sufficient condition in terms of linear matrix inequalities lmis for average consensus of the system furthermore we discuss the case where the time delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time delay finally simulation results are provided to demonstrate the effectiveness of our theoretical results

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

consensus problems in networks of agents with double integrator dynamics and time varying delays in this article we consider consensus problems in networks of agents with double integrator dynamics and non uniform time varying delays the agent dynamics is adopted as a typical point mass model based on newton s law without assuming that the weighting factors in the information update schemes are non negative we propose two protocols such that both the state and the velocity of agents achieve consensus an equivalent reduced order system is introduced to analyse the convergence of the protocols some necessary and or sufficient conditions for consensus are established in terms of linear matrix inequalities simulation results are provided that demonstrate the effectiveness of our 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