a functional equation for the specular reflection of rays this paper aims to generalize the radiosity method when applied to specular reflection within the field of thermics the radiosity method is also called the standard procedure the integral equation for incident energy which is usually derived for diffuse reflection is replaced by a more appropriate functional equation the latter is used to solve some specific problems and it is shown that all the classical features of specular reflection for example the existence of image sources are embodied within this equation this equation can be solved with the ray tracing technique despite the implemented mathematics being quite different several interesting features of the energy field are presented

hierarchical geodesic models in diffeomorphisms hierarchical linear models hlms are a standard approach for analyzing data where individuals are measured repeatedly over time however such models are only applicable to longitudinal studies of euclidean data this paper develops the theory of hierarchical geodesic models hgms which generalize hlms to the manifold setting our proposed model quantifies longitudinal trends in shapes as a hierarchy of geodesics in the group of diffeomorphisms first individual level geodesics represent the trajectory of shape changes within individuals second a group level geodesic represents the average trajectory of shape changes for the population our proposed hgm is applicable to longitudinal data from unbalanced designs i e varying numbers of timepoints for individuals which is typical in medical studies we derive the solution of hgms on diffeomorphisms to estimate individual level geodesics the group geodesic and the residual diffeomorphisms we also propose an efficient parallel algorithm that easily scales to solve hgms on a large collection of 3d images of several individuals finally we present an effective model selection procedure based on cross validation we demonstrate the effectiveness of hgms for longitudinal analysis of synthetically generated shapes and 3d mri brain scans

boundary reconstruction in binary images using splines in image analysis it is often required to reconstruct the boundary of an object in a noisy image this paper presents a new method which relies on flexibility and computational simplicity of b spline curves to reconstruct a smooth connected boundary in a noisy binary image boundary inference is based on oriented distance functions yielding the estimator which is interpreted as a posterior expected boundary of the underlying random set the performance of the method and its dependence on the image quality and model specification are studied on simulated data the method is applied to reconstruct the skin air boundary in digitised analogue mammogram images highlightswe present a new method for boundary reconstruction in noisy images using b spline curves the method is bayesian and uses oriented distance functions for inference the resulting estimator can be interpreted as a posterior expected boundary we study the performance of the method on simulated data we apply the method to reconstruct the skin air boundary in mammogram images

hilbert schmidt lower bounds for estimators on matrix lie groups for atr deformable template representations of observed imagery model the variability of target pose via the actions of the matrix lie groups on rigid templates in this paper we study the construction of minimum mean squared error estimators on the special orthogonal group so n for pose estimation due to the nonflat geometry of so n the standard bayesian formulation of optimal estimators and their characteristics requires modifications by utilizing hilbert schmidt metric defined on gl n a larger group containing so n a mean squared criterion is defined on so n the hilbert schmidt estimate hse is defined to be a minimum mean squared error estimator restricted to so n the expected error associated with the hse is shown to be a lower bound called the hilbert schmidt bound hsb on the error incurred by any other estimator analysis and algorithms are presented for evaluating the hse and the hsb in cases of both ground based and airborne targets

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

adaptive finite time bipartite consensus for second order multi agent systems with antagonistic interactions abstract this paper is concerned with the adaptive finite time bipartite consensus problems for networked second order multi agent systems with antagonistic interactions and unknown external disturbances a signed undirected graph is used to describe the interactions among agents for the leaderless case continuous nonlinear distributed protocols with adaptive update laws are given which can not only guarantee the bipartite steady state errors of any two agents converge to a small region in finite time but also eliminate the chattering problem then the proposed algorithm is extended to solve the adaptive finite time bipartite consensus tracking problem for leader follower case by designing distributed finite time estimator simulation example is included to show the effectiveness of the presented methods

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

signed consensus problems on networks of agents with fixed and switching topologies abstractthis paper deals with signed consensus problems for networks of agents in the presence of both fixed and switching topologies by specifying signs for the agents they are divided into two groups and are enabled to reach agreement on a consensus value which is the same in modulus for both groups but not in sign using nearest neighbour interaction rules we propose the distributed protocols and address their exponential convergence problem it is shown that the quasi strong connectivity of fixed networks or joint quasi strong connectivity of switching networks can provide a necessary and sufficient guarantee for all agents to achieve signed consensus exponentially fast in particular the signed consensus results can include as special cases those of bipartite consensus in signed networks with fixed and switching topologies numerical simulations are also provided to illustrate the exponential convergence performance of the proposed signed consensus protocols

distributed exponential finite time coordination of multi agent systems containment control and consensus in this paper exponential finite time coordination problems of multi agent systems are investigated including containment control and consensus the theoretical basis is that a class of nonlinear systems has favourable finite time convergence characteristic for the objective of containment control the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time for the objective of consensus a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time the distinguished features of this paper lie in the following two points 1 a smaller settling time of the lyapunov function is obtained which manifests in a faster convergence rate than the traditional one and 2 the weakly connected topology considered in this paper is more general than the o

a penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

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

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

gaussian process morphable models models of shape variations have become a central component for the automated analysis of images an important class of shape models are point distribution models pdms these models represent a class of shapes as a normal distribution of point variations whose parameters are estimated from example shapes principal component analysis pca is applied to obtain a low dimensional representation of the shape variation in terms of the leading principal components in this paper we propose a generalization of pdms which we refer to as gaussian process morphable models gpmms we model the shape variations with a gaussian process which we represent using the leading components of its karhunen loeve expansion to compute the expansion we make use of an approximation scheme based on the nystrom method the resulting model can be seen as a continuous analog of a standard pdm however while for pdms the shape variation is restricted to the linear span of the example data with gpmms we can define the shape variation using any gaussian process for example we can build shape models that correspond to classical spline models and thus do not require any example data furthermore gaussian processes make it possible to combine different models for example a pdm can be extended with a spline model to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the pdm we introduce a simple algorithm for fitting a gpmm to a surface or image this results in a non rigid registration approach whose regularization properties are defined by a gpmm we show how we can obtain different registration schemes including methods for multi scale or hybrid registration by constructing an appropriate gpmm as our approach strictly separates modeling from the fitting process this is all achieved without changes to the fitting algorithm to demonstrate the applicability and versatility of gpmms we perform a set of experiments in typical usage scenarios in medical image analysis and computer vision the model based segmentation of 3d forearm images and the building of a statistical model of the face to complement the paper we have made all our methods available as open source

development of an energy boundary element formulation for computing high frequency sound radiation from incoherent intensity boundary conditions an energy boundary element analysis ebea formulation is presented for calculating sound radiation at high frequency from a radiator with arbitrary shape the ebea development presented in this paper compliments previous energy finite element analysis efea developments for computing high frequency vibration of structures immersed in an acoustic medium from the efea solution the structural vibrational energy throughout the structure and the acoustic power radiated from each surface element in contact with the surrounding fluid are computed the ebea utilizes the information for the acoustic power radiated from each element of the outer surface of the structure as a boundary condition in order to compute the acoustic field in an unbound medium with no damping that surrounds the radiating structure since the structural vibration between different elements is considered as incoherent in the efea the acoustic intensity associated with each surface element that radiates in the surrounding medium is also considered as incoherent between different elements in the ebea formulation the governing integral equation of ebea is established and a numerical solution is presented the present method is validated by comparing ebea results to analytical solutions and to numerical results from an axi symmetric hp finite element code with infinite acoustic elements suitable for structural acoustic computations good correlation is demonstrated for all the analyses

modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions abstractthis paper addresses the modulus consensus in a network of singularly perturbed systems all of which own multi time scales characteristics the interactions among the agents are collaborat

nonlinear finite time bipartite consensus protocol for multi agent systems associated with signed graphs in this paper finite time multi agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative a nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time if the signed graph is structurally balanced then the final consensus states of all agents are the same in modulus but not in sign otherwise if the signed graph is structurally unbalanced then the states of all agents converge to zero moreover the final consensus states of agents can be provided uniformly regarding a signed average quantity that depends on both the initial states of agents and the topology structure of the whole multi agent network numerical simulations illustrate that the protocol is effective in achieving the finite time consensus of agents under signed graphs and can particularly solve the finite time average consensus problem of agents when their associated graph has all positive edge weights

a new class of finite time nonlinear consensus protocols for multi agent systems this paper is devoted to investigating the finite time consensus problem for a multi agent system in networks with undirected topology a new class of global continuous time invariant consensus protocols is constructed for each single integrator agent dynamics with the aid of lyapunov functions in particular it is shown that the settling time of the proposed new class of finite time consensus protocols is upper bounded for arbitrary initial conditions this makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents finally a numerical simulation example is presented as a proof of concept

high dimensional image registration using symmetric priors this paper is about warping a brain image from one subject the object image so that it matches another the template image a high dimensional model is used whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image bayesian statistics are used to obtain a maximum a posteriori map estimate of the deformation field the validity of any registration method is largely based upon the constraints or in this instance priors incorporated into the model describing the transformations in this approach we assume that the priors should have some form of symmetry in that priors describing the probability distribution of the deformations should be identical to those for the inverses i e warping brain a to brain b should not be different probabilistically from warping b to a the fundamental assumption is that the probability of stretching a voxel by a factor of n is considered to be the same as the probability of shrinking n voxels by a factor of n 1 in the bayesian framework adopted here the priors are assumed to have a gibbs form where the gibbs potential is a penalty function that embodies this symmetry the penalty function of choice is based upon the singular values of the jacobian having a lognormal distribution this enforces a continuous one to one mapping a gradient descent algorithm is presented that incorporates the above priors in order to obtain a map estimate of the deformations we demonstrate this approach for the two dimensional case but the principles can be extended to three dimensions a number of examples are given to demonstrate how the method works

a nonlinear merging protocol for consensus in multi agent systems on signed and weighted graphs in this paper we investigate the multi agent consensus for networks with undirected graphs which are not connected especially for the signed graph in which some edge weights are positive and some edges have negative weights and the negative weight graph whose edge weights are negative we propose a novel nonlinear merging consensus protocol to drive the states of all agents to converge to the same state zero which is not dependent upon the initial states of agents if the undirected graph whose edge weights are positive is connected then the states of all agents converge to the same state more quickly when compared to most other protocols while the undirected graph whose edge weights might be positive or negative is unconnected the states of all agents can still converge to the same state zero under the premise that the undirected graph can be divided into several connected subgraphs with more than one node furthermore we also discuss the impact of parameter r presented in our protocol current results can further deepen the understanding of consensus processes for multi agent systems

towards a coherent statistical framework for dense deformable template estimation summary the problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge we provide a careful definition and analysis of a well defined statistical model based on dense deformable templates for grey level images of deformable objects we propose a rigorous bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting the model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class we illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

diffusion for global optimization in r n we seek a global minimum of u mathbb r n to mathbb r the solution to d dt x t nabla u x t will find local minima using the idea of simulated annealing we consider th

comparison of an integral equation on energy and the ray tracing technique in room acoustics this paper deals with a comparison of two room acoustic models the first one is an integral formulation stemming from power balance and the second is the ray tracing technique with a perfectly diffuse reflection law the common assumptions to both models are the uncorrelated wave hypothesis and the perfectly diffuse reflection law the latter allows the use of these methods for nondiffuse fields beyond the validity domain of sabine s formula comparisons of numerical simulations performed with the softwares rayon and ceres point out that these results are close to each other and finally a formal proof is proposed showing that both methods are actually equivalent

distributed consensus control for linear multi agent systems with discontinuous observations this article addresses the distributed consensus problem of linear multi agent systems with discontinuous observations over a time invariant undirected communication topology under the assumption that each agent can only intermittently share its outputs with the neighbours a class of distributed observer type of protocols are designed and utilised to achieve consensus by using appropriate matrix decomposition it is shown that consensus in the closed loop multi agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent from a multiple lyapunov functions approach it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value furthermore a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected particularly the questions of what kind of agen

a nonlinear variational problem for image matching minimizing a nonlinear functional is presented as a way of obtaining a planar mapping that matches two similar images a smoothing term is added to the nonlinear functional to penalize discontinuous and irregular solutions one option for the smoothing term is a quadratic form generated by a linear differential operator the functional is then minimized using the fourier representation of the planar mapping with this representation the quadratic form is diagonalized another option is a quadratic form generated via a basis of compactly supported wavelets in both cases a natural approximation scheme is described both quadratic forms are shown to impose the same smoothing however in terms of the finite dimensional approximations it is easier to accommodate local deformations using the wavelet basis

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

bayesian technique for image classifying registration in this paper we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues usual image registration models which are based on a single global intensity similarity criterion fail to register such images as they are blind to local deviations of intensity dependencies such a limitation is also encountered in contrast enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption in this paper we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies defined in a bayesian framework the similarity criterion is a mixture of probability distributions describing dependencies on two classes the model also includes a class map which locates pixels of the two classes and weighs the two mixture components the registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem it is solved using a gradient descent algorithm in the problem formulation and resolution the image deformation and the class map are estimated simultaneously leading to an original combination of registration and classification that we call image classifying registration whenever sufficient information about class location is available in applications the registration can also be performed on its own by fixing a given class map finally we illustrate the interest of our model on two real applications from medical imaging template based segmentation of contrast enhanced images and lesion detection in mammograms we also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations of intensity dependencies while keeping a good registration accuracy

statistical region snake based segmentation adapted to different physical noise models algorithms for object segmentation are crucial in many image processing applications during past years active contour models snakes have been widely used for finding the contours of objects this segmentation strategy is classically edge based in the sense that the snake is driven to fit the maximum of an edge map of the scene we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image the algorithms developed in a maximum likelihood approach are based on the calculation of the statistics of the inner and the outer regions defined by the snake it has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known we demonstrate that this approach is still efficient when no boundary s edge exists in the image we also show that one can obtain fast algorithms by transforming the summations over a region for the calculation of the statistics into summations along the boundary of the region finally we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach

an acoustic boundary element method based on energy and intensity variables for prediction of high frequency broadband sound fields a boundary element method is formulated in terms of time averaged energy and intensity variables the approach is applicable to high modal density fields but is not restricted to the usual low absorption diffuse and quasiuniform assumptions a broadband acoustic energy intensity source is the basic building block for the method a directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately a distribution of infinitesimal uncorrelated directional sources is used to model the boundaries of an enclosure these sources are discretized in terms of boundary elements a system of equations results from applying boundary conditions in terms of incident reflected and absorbed intensity the unknown source power for each element is determined from this system of equations a two dimensional model problem is used to demonstrate and verify the method exact numerical solutions were also obtained for this model problem the results show that spatially varying mean square pressure levels are accurately predicted at very low computational cost

an integral formulation with random parameters adapted to the study of the vibrational behaviour of structures in the middle and high frequency field the fundamentals of a new boundary element formulation applied to the study of structural dynamics on a wide frequency range is proposed in this paper random geometrical parameters are introduced to the integral representations in order to model the increasing sensitivity of the harmonic vibrational responses to any parameter perturbation when the frequency increases it is shown that the significant unknowns of the formulation are the expectations of the square boundary kinematic unknowns indeed these variables are able to describe accurately the responses of the structures in the low frequency field and deliver a smooth response in the middle and high frequency field corresponding to the global trend of the structural dynamic response in this frequency domain the formulation is established for isolated and assembled one two and three dimensional structures numerical applications illustrate the effectiveness of the method

a statistical model for signature verification a bayesian model for off line signature verification involving the representation of a signature through its curvature is developed the prior model makes use of a spatial point process for specifying the knots in an approximation restricted to a buffer region close to a template curvature along with an independent time warping mechanism in this way prior shape information about the signature can be built into the analysis the observation model is based on additive white noise superimposed on the underlying curvature the approach is implemented using markov chain monte carlo and applied to a collection of documented instances of william shakespeare s signature

finite time consensus for stochastic multi agent systems in this article we study the finite time consensus in probability for stochastic multi agent systems first we give the nonlinear consensus protocol for multi agent systems with gaussian white noise and define the concept of finite time consensus in probability second we prove that multi agent systems can achieve the finite time consensus in probability under five different kinds of communication topologies by using graph theory stochastic lyapunov theory and probability theory finally some simulation examples are provided to illustrate the effectiveness of the theoretical results

interval bipartite consensus of networked agents associated with signed digraphs this paper solves consensus problems for networked agents whose interactions with each other are described by signed digraphs the laplacian matrix of a signed digraph is studied by introducing rooted cycles and the relationship between it and the spanning tree condition is addressed in particular the laplacian matrix of a signed digraph with spanning trees is positive stable if and only if there is at least one negative rooted cycle otherwise it has exactly one zero eigenvalue if and only if either there exist no rooted cycles or all existing rooted cycles are positive it is shown that all agents reach interval bipartite consensus if their associated signed digraph has a spanning tree further the consensus values of all agents depend only on the initial states of those agents which are associated with root vertices the developed consensus results are applicable for multi agent systems with both continuous time and discrete time dynamics illustrative examples are provided to demonstrate interval bipartite consensus performances for multi agent systems associated with different signed digraphs which all contain spanning trees but are not strongly connected

a new random boundary element formulation applied to high frequency phenomena the basis of a new boundary element method adapted to wide frequency range applications is proposed in this paper the formulation employs the frequency domain dynamic fundamental solutions of the problems random geometrical parameters are introduced in the integral equations these equations are then modified to exhibit the products of the different kinematic variables the expectations of the new equations with respect to the latter random variables are considered and the new variables of the formulation are the different stochastic moments force displacement variables this formulation is applied to different structures such as beams rods and assembled one dimensional systems

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

graphical templates for model registration a new method of model registration is proposed using graphical templates a graph of landmarks is chosen in the template image all possible candidates for these landmarks are found in the data image using local operators a dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time this combination of local operators to describe points of interest landmarks and a graph to describe their geometric orientation in the plane yields fast and precise matches of the model to the data with no initialization required

a method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

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

convergence properties of the gibbs sampler for perturbations of gaussians 1993 and smith and roberts 1993 a host of other applications of these methods in the context of hierarchical bayesian models is described in all these examples the question arises as to the rate of convergence of the markov chain there is no unified theory to answer this question especially in the case of continuous densities on r n and currently many different approaches are being attempted for the different types of simulation methods one direction of research uses doeblin type bounds on bounded sets together with geometric drift conditions or some form of lyapounov functions to obtain rather general results on exponential convergence for continuous n densities on r see mengersen and tweedie 1996 for the metropolis algorithm and rosenthal 1995 for the gibbs sampler these results are then applied to certain special cases and yield bounds on the rate of convergence in variational norm distance another approach analyzes a discretized version of the problem using general discrete state space markov chain techniques see frieze kannan and polson 1994 finally there are attempts to use spectral analysis to obtain rates of convergence in the l sense where the markov chain operator is considered 2 as a bounded operator in the hilbert space of square integrable functions

transcale average consensus of directed multi vehicle networks with fixed and switching topologies abstractthis paper contributes to solving a class of so called transcale average consensus problems for directed networks of vehicles with single integrator dynamics it generalises the idea of average consensus by taking into account the measurement scale of every vehicle s information state using the nearest neighbour interaction rules distributed algorithms are presented which are shown with the ability to achieve the transcale average consensus for directed networks associated with balanced graphs such consensus results are applicable to networks in the presence of both fixed topology and switching topologies which are also illustrated via simulation tests moreover improved algorithms and results of consensus are given for directed networks associated with unbalanced graphs

existence and consistency of wasserstein barycenters in this paper based on the frechet mean we define a notion of barycenter corresponding to a usual notion of statistical mean we prove the existence of wasserstein barycenters of random distributions defined on a geodesic space e d we also prove the consistency of this barycenter in a general setting that includes taking barycenters of empirical versions of the distributions or of a growing set of distributions

a hybrid method for vibroacoustics based on the radiative energy transfer method a hybrid method is proposed to predict the noise radiated in the high frequency range by a structure whose vibratory behavior is rather in the low frequency range this problem meets for instance when the structure radiates inside some closed acoustical spaces the proposed approach is called hybrid as it couples two methods valid on different frequency bands respectively used for the structural and acoustical systems low frequency structural approaches generally provide the velocity field on the vibrating surface while methods adapted to high frequency acoustical studies are based on energy data so the main difficulty for the coupling is a problem of data compatibility in the proposed hybrid method the radiated noise is predicted by using the radiative energy transfer method which is an energy boundary integral method basically equivalent to the known ray tracing method for acoustic applications adequate equivalent energy sources are estimated on the surface of the vibrating structure from the surface pressure and velocity fields these sources are then introduced in the integral equation of the radiative energy transfer method the approach is applied to predict the radiation of a ribbed plate sandwiched between two absorbant panels good agreement is observed with the results given by the boundary element method generally speaking the hybrid method can be considered to apply the radiative energy transfer method for high frequency acoustical predictions from the knowledge of the vibratory behavior of a structure

an efficient 2d deformable objects detection and location algorithm abstract this paper presents a complete method for the automatic detection and location of two dimensional objects even in the presence of noise occlusion cluttering and or deformations this method is based on shape information extracted from the edges gradient and only needs a template of the object to be located a new generalized hough transform is proposed to automatically locate rigid objects in the presence of noise occlusion and or cluttering a bayesian scheme uses this rigid objects location algorithm to obtain the deformation of the object the whole method is invariant to rotation scale displacement and minor deformations several examples with real images are presented to show the validity of the method

prediction of sound level at high frequency bands by means of a simplified boundary element method a simplified boundary element method bem for dealing with high frequency sound is proposed the boundary integral equation is modified into a quadratic form to enable the prediction of sound levels in the one third octave band analysis monopole and dipole source terms in the conventional bem are transformed into the auto and cross spectra of two vibrating sources in which the cross spectra are eventually neglected by assuming that the correlation coefficients involved are negligible the present method is compared with the rayleigh integral for calculating the sound pressure radiated from a baffled panel in terms of the application limit the characteristic length of the boundary element and the applicable frequency range can be determined by the lower limit value of the correlation coefficient as a test example the field pressure radiated from a partially vibrating sphere is predicted and the resultant trend is in good agreement with the analytic solution as far as the related correlation coefficient satisfies the assumption the overdetermination process for overcoming nonuniqueness in exterior radiation problems is unnecessary in the present method because phase information can be ignored the results of the calculation show that the proposed method is acceptable for solving the exterior radiation problem at a high frequency range in a timely manner

extension of the statistical modal energy distribution analysis for estimating energy density in coupled subsystems abstract the present article deals with an extension of the statistical modal energy distribution analysis smeda method to estimate kinetic and potential energy density in coupled subsystems the smeda method uses the modal bases of uncoupled subsystems and focuses on the modal energies rather than the global energies of subsystems such as sea statistical energy analysis this method permits extending sea to subsystems with low modal overlap or to localized excitations as it does not assume the existence of modal energy equipartition we demonstrate that by using the modal energies of subsystems computed by smeda it is possible to estimate energy distribution in subsystems this approach has the same advantages of standard sea as it uses very short calculations to analyze damping effects the estimation of energy distribution from smeda is applied to an academic case and an industrial example

deformation based curved shape representation in this paper we introduce a deformation based representation space for curved shapes in mathbb r n given an ordered set of points sampled from a curved shape the proposed method represents the set as an element of a finite dimensional matrix lie group variation due to scale and location are filtered in a preprocessing stage while shapes that vary only in rotation are identified by an equivalence relationship the use of a finite dimensional matrix lie group leads to a similarity metric with an explicit geodesic solution subsequently we discuss some of the properties of the metric and its relationship with a deformation by least action furthermore invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function thereafter two possible approaches are presented to solve the point correspondence estimation problem finally we propose an adaptation of k means clustering for shape analysis in the proposed representation space experimental results show that the proposed representation is robust to uninformative cues e g local shape perturbation and displacement in comparison to state of the art methods it achieves a high precision on the swedish and the flavia leaf datasets and a comparable result on mpeg 7 kimia99 and kimia216 datasets

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

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

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

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation