approximate labeling via graph cuts based on linear programming a new framework is presented for both understanding and developing graph cut based combinatorial algorithms suitable for the approximate optimization of a very wide class of markov random fields mrfs that are frequently encountered in computer vision the proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state of the art techniques like the alpha expansion algorithm which is included merely as a special case moreover contrary to alpha expansion the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems for example even for mrfs with nonmetric potentials in addition they are capable of providing per instance suboptimality bounds in all occasions including discrete mrfs with an arbitrary potential function these bounds prove to be very tight in practice that is very close to 1 which means that the resulting solutions are almost optimal our algorithms effectiveness is demonstrated by presenting experimental results on a variety of low level vision tasks such as stereo matching image restoration image completion and optical flow estimation as well as on synthetic problems

invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

structure propagation for image registration mosaicing is a commonly used technique in many medical imaging applications where subimages are stitched together in order to obtain a larger field of view however stitching which involves alignment or registration in overlapping regions is often challenging when the information shared by subimages is absent or small while it is not possible to perform an alignment without overlap using existing techniques imaging artifacts such as distortions towards image boundaries present further complications during registration by decreasing the reliability of available information without taking these into consideration a registration approach might violate the continuity and the smoothness of structures across subimages in this paper we propose a novel registration approach for the stitching of subimages in such challenging scenarios by using a perceptual grouping approach we extend subimages beyond their boundaries by propagating available structures in order to obtain structural maps in the extended regions these maps are then used to establish correspondences between subimages when the shared information is absent small or unreliable using our approach ensures the continuity and the smoothness of structures across subimage boundaries furthermore since only structures are used the proposed method can also be used for the stitching of multi modal images our approach is unique in that it also enables contactless stitching we demonstrate the effectiveness of the proposed method by performing several experiments on synthetic and medical images moreover we show how stitching is possible in the presence of a physical gap between subimages

a modular functor which is universal for quantum computation we show that the topological modular functor from witten chern simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor s state space a computational model based on chern simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model the chief technical advance the density of the irreducible sectors of the jones representation has topological implications which will be considered elsewhere

density of the so 3 tqft representation of mapping class groups we show that for an odd prime r 3 and an integer g 1 in the projective representation given by the so 3 witten reshitikhin turaev theory at an rth root of unity the image of the mapping class group of a surface of genus g is dense

on classification of modular tensor categories we classify all unitary modular tensor categories umtcs of rank 4 there are a total of 35 umtcs of rank 4 up to ribbon tensor equivalence since the distinction between the modular s matrix s and s has both topological and physical significance so in our convention there are a total of 70 umtcs of rank 4 in particular there are two trivial umtcs with s 1 each such umtc can be obtained from 10 non trivial prime umtcs by direct product and some symmetry operations explicit data of the 10 non trivial prime umtcs are given in sect 5 relevance of umtcs to topological quantum computation and various conjectures are given in sect 6

global leader following consensus of a group of general linear systems using bounded controls this paper studies the global leader following consensus problem for a multi agent system with bounded controls the follower agents and the leader agent are all described by a general linear system both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group the feedback law for each input of an agent uses a multi hop relay protocol in which the agent obtains the information of other agents through multi hop paths in the communication network the number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non zero imaginary eigenvalues of the sub system corresponding to the input and the feedback gains are constructed from the adjacency matrix of the communication network it is shown that global leader following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower

consensus in networks of multiagents with cooperation and competition via stochastically switching topologies in this brief we provide some theoretical analysis of the consensus for networks of agents via stochastically switching topologies we consider both discrete time case and continuous time case the main contribution of this brief is that the underlying graph topology is more general in both cases than those appeared in previous papers the weight matrix of the coupling graph is not assumed to be nonnegative or metzler that is in the model discussed here the off diagonal entries of the weight matrix of the coupling graph may be negative this means that sometimes the coupling may not benefit but may prevent the consensus of the coupled agents in the continuous time case the switching time intervals also take a more general form of random variables than those appeared in previous works we focus our study on such networks and give sufficient conditions that ensure almost sure consensus in both discrete time case and continuous time case as applications we give several corollaries under more specific assumptions i e the switching can be some independent and identically distributed i i d random variable series or a markov chain numerical examples are also provided in both discrete time and continuous time cases to demonstrate the validity of our theoretical results

on the equivalence between dissipativity and optimality of discontinuous nonlinear regulators for filippov dynamical systems in this paper we derive guaranteed gain sector and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear nonquadratic performance functional for filippov dynamical systems specifically we consider dynamical systems with lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving filippov set valued maps in addition we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems these results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using clarke gradients and locally lipschitz continuous storage functions furthermore using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for filippov dynamical systems specifically using the extended kalman yakubovich popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate

brief paper distributed containment control for lagrangian networks with parametric uncertainties under a directed graph in this paper we study the distributed containment control problem for networked lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers we propose a distributed adaptive control algorithm combined with distributed sliding mode estimators a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically as a byproduct we show a necessary and sufficient condition on leaderless consensus for networked lagrangian systems under a directed graph numerical simulation results are given to show the effectiveness of the proposed control algorithms

scale and rotation invariant matching using linearly augmented trees we propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching the proposed method enforces pairwise matching consistency defined on trees and high order constraints on all the sites of a template the pairwise constraints admit arbitrary metrics while the high order constraints use l1 norms and therefore can be linearized such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure but different from a general loopy graph its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming the proposed method also works on continuous scale and rotation parameters we can match with a scale up to any large value with the same efficiency our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient accurate and reliable

improved moves for truncated convex models we consider the problem of obtaining an approximate maximum a posteriori estimate of a discrete random field characterized by pairwise potentials that form a truncated convex model for this problem we propose two st mincut based move making algorithms that we call range swap and range expansion our algorithms can be thought of as extensions of swap and expansion respectively that fully exploit the form of the pairwise potentials specifically instead of dealing with one or two labels at each iteration our methods explore a large search space by considering a range of labels that is an interval of consecutive labels furthermore we show that range expansion provides the same multiplicative bounds as the standard linear programming lp relaxation in polynomial time compared to previous approaches based on the lp relaxation for example interior point algorithms or tree reweighted message passing trw our methods are faster as they use only the efficient st mincut algorithm in their design we demonstrate the usefulness of the proposed approaches on both synthetic and standard real data problems

learning coverage control of mobile sensing agents in one dimensional stochastic environments this technical note presents learning coverage control of mobile sensing agents without a priori statistical information regarding random signal locations in a one dimensional space in particular the proposed algorithm controls the usage probability of each agent in a network while simultaneously satisfying an overall network formation topology the proposed control algorithm is rather direct not involving any identification of an unknown probability density function associated to random signal locations our approach builds on diffeomorphic function learning with kernels the almost sure convergence properties of the proposed control algorithm are analyzed using the ode approach numerical simulations for different scenarios demonstrate the effectiveness of the proposed approach

adaptive information collection by robotic sensor networks for spatial estimation this work deals with trajectory optimization for a robotic sensor network sampling a spatio temporal random field we examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories this is a high dimensional multi modal nonsmooth optimization problem known to be np hard even for static fields and discrete design spaces under an asymptotic regime of near independence between distinct sample locations we show that the solutions to a novel generalized disk covering problem are solutions to the optimal sampling problem this result effectively transforms the search for the optimal trajectories into a geometric optimization problem constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots we characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories and provide algorithms which enable the network to find them in a distributed fashion several simulations illustrate our results

profinite completions of burnside type quotients of surface groups using quantum representations of mapping class groups we prove that profinite completions of burnside type surface group quotients are not virtually prosolvable in general further we construct infinitely many finite simple characteristic quotients of surface groups

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

interactive image segmentation based on synthetic graph coordinates in this paper we propose a framework for interactive image segmentation the goal of interactive image segmentation is to classify the image pixels into foreground and background classes when some foreground and background markers are given the proposed method minimizes a min max bayesian criterion that has been successfully used on image segmentation problem and it consists of several steps in order to take into account visual information as well as the given markers without any requirement of training first we partition the image into contiguous and perceptually similar regions superpixels then we construct a weighted graph that represents the superpixels and the connections between them an efficient algorithm for graph clustering based on synthetic coordinates is used yielding an initial map of classified pixels this method reduces the problem of graph clustering to the simpler problem of point clustering instead of solving the problem on the graph data structure as most of the known algorithms from literature do finally having available the data modeling and the initial map of classified pixels we use a markov random field mrf model or a flooding algorithm to get the image segmentation by minimizing a min max bayesian criterion experimental results and comparisons with other methods from the literature are presented on lhi gulshan and zhao datasets demonstrating the high performance and accuracy of the proposed scheme

global minimization for continuous multiphase partitioning problems using a dual approach this paper is devoted to the optimization problem of continuous multi partitioning or multi labeling which is based on a convex relaxation of the continuous potts model in contrast to previous efforts which are tackling the optimal labeling problem in a direct manner we first propose a novel dual model and then build up a corresponding duality based approach by analyzing the dual formulation sufficient conditions are derived which show that the relaxation is often exact i e there exists optimal solutions that are also globally optimal to the original nonconvex potts model in order to deal with the nonsmooth dual problem we develop a smoothing method based on the log sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal dual model and suggests labelings with maximum entropy such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions an expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization numerical experiments also show that our method outperforms several competitive approaches in various aspects such as lower energies and better visual quality

symmetry invariance of multiagent formations in self pursuit structure in the interconnection topology among individuals of a multiagent system plays a fundamental role in the system s steady state and transient behaviors this paper explores how certain interconnection topologies influence symmetry in a multiagent system s trajectories it is shown how circulant connectivity preserves rotation and in particular instances dihedral group symmetries in a formation of locally interacting planar integrators moreover it is revealed to what extent circulant connectivity is also necessary in order that symmetric formations remain symmetric under the multiagent system s dynamics

brief paper decentralized coordination of autonomous swarms using parallel gibbs sampling in this paper we present analysis of a discrete time decentralized stochastic coordination algorithm for a group of mobile nodes called an autonomous swarm on a finite spatial lattice all nodes take their moves by sampling in parallel their locally perceived gibbs distributions corresponding to a pairwise nearest neighbor potential the algorithm has no explicit requirements on the connectedness of the underlying information graph which varies with the swarm configuration it is established that with an appropriate annealing schedule the algorithm results in swarm configurations converging to the global minimizers of a modified potential energy function the extent of discrepancy between the modified and original potential energy functions is determined by the maximum node travel between time steps and when such distance is small the ultimate swarm configurations are close to the global minimizers of the original potential energy simulation results are further presented to illustrate the capability of the sampling algorithm in approximate global optimization for swarms

on the control and estimation over relative sensing networks in this note we consider certain structural aspects of estimation and control over relative sensing networks rsns in this venue using tools from basic algebraic graph theory namely the incidence matrix and cut and cycle spaces of a connect graph we examine transformations among relative sensing topologies for a networked system these transformations are parameterized for noise free as well as noisy networks and their utility in the context of network centric robust control and control reconfigurations is explored

controllability of the multi agent system modeled by the threshold graph with one repeated degree abstract the controllability issue of multi agent systems modeled by a special class of graphs is studied suppose the modeling graph is simple connected and driven by only one controller the author shows that the system is controllable if the graph has exactly two vertices with the same degree and either one of these two vertices is selected to receive the control input this result is extended to the case of the threshold graph that has only one repeated degree specifically it is shown that if the threshold graph has only one repeated degree and its multiplicity is m then m 1 is the minimum number of the controllers required to make the system controllable in addition the necessary and sufficient condition that characterizes the binary control vectors to ensure the controllability of the system is derived

robust synchronization of uncertain linear multi agent systems this paper deals with robust synchronization of uncertain multi agent networks given a network with for each of the agents identical nominal linear dynamics we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics the perturbations are assumed to be stable and bounded in h norm by some a priori given desired tolerance we derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance it is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given single linear system our protocols are expressed in terms of real symmetric solutions of certain algebraic riccati equations and inequalities and also involve weighting factors that depend on the eigenvalues of the graph laplacian for undirected network graphs we show that within the class of such dynamic protocols a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the laplacian we also extend our results to additive nonlinear perturbations with l2 gain bounded by a given tolerance

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

semistability finite time stability differential inclusions and discontinuous dynamical systems having a continuum of equilibria this paper focuses on semistability and finite time semistability for discontinuous dynamical 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 extend the theory of semistability to discontinuous autonomous dynamical systems in particular lyapunov based tests for semistability and finite time semistability for autonomous differential inclusions are established

stochastic stability of continuous time consensus protocols a unified approach to studying convergence and stochastic stability of continuous time consensus protocols cps is presented in this work our method applies to networks with directed information flow both cooperative and noncooperative interactions networks under weak stochastic forcing and those whose topology and strength of connections may vary in time the graph theoretic interpretation of the analytical results is emphasized we show how the spectral properties such as algebraic connectivity and total effective resistance as well as the geometric properties such as the dimension and the structure of the cycle subspace of the underlying graph shape stability of the corresponding cps in addition we explore certain implications of spectral graph theory to cp design in particular we point out that expanders sparse highly connected graphs generate cps whose performance remains uniformly high when the size of the network grows unboundedly similarly we highlight the benefits of using random

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

chern simons witten invariants of lens spaces and torus bundles and the semiclassical approximation we derive explicit formulas for the chern simons witten invariants of lens spaces and torus bundles overs1 for arbitrary values of the levelk most of our results are for the groupg su 2 though some are for more general compact groups we explicitly exhibit agreement of the limiting values of these formulas ask with the semiclassical approximation predicted by the chern simons path integral

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

finite time stabilisation of cyclic formations using bearing only measurements this paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing only sensors since the inter vehicle distance cannot be measured the target formation involves no distance constraints more specifically the target formation considered in this paper is an angle constrained cyclic formation where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre specified to stabilise the target formation we propose a discontinuous control law that only requires the sign information of the angle errors due to the discontinuity of the proposed control law the stability of the closed loop system is analysed by employing a locally lipschitz lyapunov function and nonsmooth analysis tools we prove that the target formation is locally finite time stable with collision avoidance guaranteed

a spatially continuous max flow and min cut framework for binary labeling problems we propose and investigate novel max flow models in the spatially continuous setting with or without i priori defined supervised constraints under a comparative study of graph based max flow min cut we show that the continuous max flow models correspond to their respective continuous min cut models as primal and dual problems in this respect basic conceptions and terminologies from discrete max flow min cut are revisited under a new variational perspective we prove that the associated nonconvex partitioning problems unsupervised or supervised can be solved globally and exactly via the proposed convex continuous max flow and min cut models moreover we derive novel fast max flow based algorithms whose convergence can be guaranteed by standard optimization theories experiments on image segmentation both unsupervised and supervised show that our continuous max flow based algorithms outperform previous approaches in terms of efficiency and accuracy

brief paper the zermelo voronoi diagram a dynamic partition problem we consider a voronoi like partition problem in the plane for a given finite set of generators each element in this partition is uniquely associated with a particular generator in the following sense an agent that resides within a set of the partition at a given time will arrive at the generator associated with this set faster than any other agent that resides anywhere outside this set at the same instant of time the agent s motion is affected by the presence of a temporally varying drift which is induced by local winds currents as a result the minimum time to a destination is not equivalent to the minimum distance traveled this simple fact has important ramifications over the partitioning problem it is shown that this problem can be interpreted as a dynamic voronoi diagram problem where the generators are not fixed but rather they are moving targets to be reached in minimum time the problem is solved by first reducing it to a standard voronoi diagram by means of a time varying coordinate transformation we then extend the approach to solve the dual problem where the generators are the initial locations of a given set of agents distributed over the plane such that each element in the partition consists of the terminal positions that can be reached by the corresponding agent faster than any other agent

nonuniform line coverage from noisy scalar measurements we study the problem of distributed coverage control in a network of mobile agents arranged on a line the goal is to design distributed dynamics for the agents to achieve optimal coverage positions with respect to a scalar density field that measures the relative importance of each point on the line unlike previous work which implicitly assumed the agents know this density field we only assume that each agent can access noisy samples of the field at points close to its current location we provide a simple randomized protocol wherein every agent samples the scalar field at three nearby points at each step and which guarantees convergence to the optimal positions we further analyze the convergence time of this protocol and show that under suitable assumptions the squared distance to the optimal coverage configuration decays as o 1 t with the number of iterations t where the constant scales polynomially with the number of agents n we illustrate these results with simulations

nonuniform coverage and cartograms in this paper we investigate nonuniform coverage of a planar region by a network of autonomous mobile agents we derive centralized nonuniform coverage control laws from uniform coverage algorithms using cartograms transformations that map nonuniform metrics to a near euclidean metric we also investigate time varying coverage metrics and the design of control algorithms to cover regions with slowly varying nonuniform metrics our results are applicable to the design of mobile sensor networks notably when the coverage metric varies as data is collected such as in the case of an information metric the results apply also to the study of animal groups foraging for food that is nonuniformly distributed and possibly changing

distributed adaptive coordination for multiple lagrangian systems under a directed graph without using neighbors velocity information in this paper we study the distributed coordination problem for multiple lagrangian systems in the presence of parametric uncertainties under a directed graph without using neighbors velocity information in the absence of communication we consider two cases namely the distributed containment control problem with multiple stationary leaders and the leaderless synchronization problem in both cases distributed adaptive control algorithms without using neighbors velocity information are proposed the control gains in the algorithms are varying with distributed updating laws furthermore necessary and sufficient conditions on the directed graph are presented respectively such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically in the containment control problem and the systems synchronize asymptotically in the leaderless synchronization problem finally simulation examples are provided to show the effectiveness of the proposed control algorithms

brief paper notes on averaging over acyclic digraphs and discrete coverage control in this paper we study averaging algorithms and coverage control laws in a unified light first we characterize the convergence properties of averaging algorithms over acyclic digraphs with fixed and controlled switching topology second we introduce and study novel discrete coverage control laws which are useful in practical implementations of coverage strategies we characterize the close relationship of the novel discrete control laws with continuous coverage control laws and with averaging algorithms over a class of acyclic digraphs that we term discrete voronoi graphs these results provide a unified framework to model a vast class of distributed optimization problems

dynamical systems that sort lists diagonalize matrices and solve linear programming problems abstract we establish a number of properties associated with the dynamical system h h h n where h and n are symmetric n by n matrices and a b ab ba the most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices we are especially interested in the role of this equation as an analog computer for example we show how to map the data associated with a linear programming problem into h 0 and n in such a way as to have h h h n evolve to a solution of the linear programming problem this result can be applied to find systems which solve a variety of genetic combinatorial optimization problems and it even provides an algorithm for diagonalizing symmetric matrices

linear scale and rotation invariant matching matching visual patterns that appear scaled rotated and deformed with respect to each other is a challenging problem we propose a linear formulation that simultaneously matches feature points and estimates global geometrical transformation in a constrained linear space the linear scheme enables search space reduction based on the lower convex hull property so that the problem size is largely decoupled from the original hard combinatorial problem our method therefore can be used to solve large scale problems that involve a very large number of candidate feature points without using prepruning in the search this method is more robust in dealing with weak features and clutter we apply the proposed method to action detection and image matching our results on a variety of images and videos demonstrate that our method is accurate efficient and robust

exploiting unsupervised and supervised constraints for subspace clustering data in many image and video analysis tasks can be viewed as points drawn from multiple low dimensional subspaces with each subspace corresponding to one category or class one basic task for processing such kind of data is to separate the points according to the underlying subspace referred to as subspace clustering extensive studies have been made on this subject and nearly all of them use unconstrained subspace models meaning the points can be drawn from everywhere of a subspace to represent the data in this paper we attempt to do subspace clustering based on a constrained subspace assumption that the data is further restricted in the corresponding subspaces e g belonging to a submanifold or satisfying the spatial regularity constraint this assumption usually describes the real data better such as differently moving objects in a video scene and face images of different subjects under varying illumination a unified integer linear programming optimization framework is used to approach subspace clustering which can be efficiently solved by a branch and bound bb method we also show that various kinds of supervised information such as subspace number outlier ratio pairwise constraints size prior and etc can be conveniently incorporated into the proposed framework experiments on real data show that the proposed method outperforms the state of the art algorithms significantly in clustering accuracy the effectiveness of the proposed method in exploiting supervised information is also demonstrated

an efficient optimization framework for multi region segmentation based on lagrangian duality we introduce a multi region model for simultaneous segmentation of medical images in contrast to many other models geometric constraints such as inclusion and exclusion between the regions are enforced which makes it possible to correctly segment different regions even if the intensity distributions are identical we efficiently optimize the model using a combination of graph cuts and lagrangian duality which is faster and more memory efficient than current state of the art as the method is based on global optimization techniques the resulting segmentations are independent of initialization we apply our framework to the segmentation of the left and right ventricles myocardium and the left ventricular papillary muscles in magnetic resonance imaging and to lung segmentation in full body x ray computed tomography we evaluate our approach on a publicly available benchmark with competitive results

hough forest random field for object recognition and segmentation this paper presents a new computational framework for detecting and segmenting object occurrences in images we combine hough forest hf and conditional random field crf into hfrf to assign labels of object classes to image regions hf captures intrinsic and contextual properties of objects crf then fuses the labeling hypotheses generated by hf for identifying every object occurrence interaction between hf and crf happens in hfrf inference which uses the metropolis hastings algorithm the metropolis hastings reversible jumps depend on two ratios of proposal and posterior distributions instead of estimating four distributions we directly compute the two ratios using hf in leaf nodes hf records class histograms of training examples and information about their configurations this evidence is used in inference for nonparametric estimation of the two distribution ratios our empirical evaluation on benchmark datasets demonstrates higher average precision rates of object detection smaller object segmentation error and faster convergence rates of our inference relative to the state of the art the paper also presents theoretical error bounds of hf and hfrf applied to a two class object detection and segmentation

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 consensus of fractional order multi agent systems via adaptive pinning control in this paper the leader following consensus problem of fractional order multi agent systems is considered via adaptive pinning control the dynamics of leader and all followers with linear and nonlinear functions are investigated respectively we assume that the node should be pinned if its in degree is less than its out degree in the paper under this assumption and based on the stability theory of fractional order differential systems some leader following consensus criteria are derived which are easily obtained by matrix inequalities the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented the design technique is based on algebraic graph theory and the riccati inequality several simulation examples are presented to demonstrate the effectiveness of the proposed method

asymptotic properties of consensus type algorithms for networked systems with regime switching topologies this paper is concerned with asymptotic properties of consensus type algorithms for networked systems whose topologies switch randomly the regime switching process is modeled as a discrete time markov chain with a finite state space the consensus control is achieved by using stochastic approximation methods in the setup the regime switching process the markov chain contains a rate parameter e 0 in the transition probability matrix that characterizes how frequently the topology switches on the other hand the consensus control algorithm uses a stepsize m that defines how fast the network states are updated depending on their relative values three distinct scenarios emerge under suitable conditions we show that when 0 e o m a continuous time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous time markov chain in this case a scaled sequence of tracking errors converges to a system of switching diffusion when 0 email protected email protected the network topology is almost non switching during consensus control transient intervals and hence the limit dynamic system is simply an autonomous differential equation when email protected email protected the markov chain acts as a fast varying noise and only its averaged network matrices are relevant resulting in a limit differential equation that is an average with respect to the stationary measure of the markov chain simulation results are presented to demonstrate these findings

multi class constrained normalized cut with hard soft unary and pairwise priors and its applications to object segmentation normalized cut is a powerful method for image segmentation as well as data clustering however it does not perform well in challenging segmentation problems such as segmenting objects in a complex background researchers have attempted to incorporate priors or constraints to handle such cases available priors in image segmentation problems may be hard or soft unary or pairwise but only hard must link constraints and two class settings are well studied the main difficulties may lie in the following aspects 1 the nontransitive nature of cannot link constraints makes it hard to use such constraints in multi class settings and 2 in multi class or pairwise settings the output labels have inconsistent representations with given priors making soft priors difficult to use in this paper we propose novel algorithms which can handle both hard and soft both unary and pairwise priors in multi class settings and provide closed form and efficient solutions we also apply the proposed algorithms to the problem of object segmentation producing good results by further introducing a spatial regularity term experiments show that the proposed algorithms outperform the state of the art algorithms significantly in clustering accuracy other merits of the proposed algorithms are also demonstrated

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

a study of parts based object class detection using complete graphs object detection is one of the key components in modern computer vision systems while the detection of a specific rigid object under changing viewpoints was considered hard just a few years ago current research strives to detect and recognize classes of non rigid articulated objects hampered by the omnipresent confusing information due to clutter and occlusion the focus has shifted from holistic approaches for object detection to representations of individual object parts linked by structural information along with richer contextual descriptions of object configurations along this line of research we present a practicable and expandable probabilistic framework for parts based object class representation enabling the detection of rigid and articulated object classes in arbitrary views we investigate learning of this representation from labelled training images and infer globally optimal solutions to the contextual map detection problem using a search with a novel lower bound as admissible heuristic an assessment of the inference performance of belief propagation and tree reweighted belief propagation is obtained as a by product the generality of our approach is demonstrated on four different datasets utilizing domain dependent information cues

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

the two eigenvalue problem and density of jones representation of braid groups 1 the two eigenvalue problem 179 2 hecke algebra representations of braid groups 183 3 duality of jones wenzl representations 186 4 closed images of jones wenzl sectors 188 5 distribution of evaluations of jones polynomials 192 6 fibonacci representations 196

collective inference for extraction mrfs coupled with symmetric clique potentials many structured information extraction tasks employ collective graphical models that capture inter instance associativity by coupling them with various clique potentials we propose tractable families of such potentials that are invariant under permutations of their arguments and call them symmetric clique potentials we present three families of symmetric potentials max sum and majority we propose cluster message passing for collective inference with symmetric clique potentials and present message computation algorithms tailored to such potentials our first message computation algorithm called pass is sub quadratic in the clique size outputs exact messages for max and computes 13 15 approximate messages for potts a popular member of the sum family empirically it is upto two orders of magnitude faster than existing algorithms based on graph cuts or belief propagation our second algorithm based on lagrangian relaxation operates on majority potentials and provides close to exact solutions while being two orders of magnitude faster we show that the cluster message passing framework is more principled accurate and converges faster than competing approaches we extend our collective inference framework to exploit associativity of more general intra domain properties of instance labelings which opens up interesting applications in domain adaptation our approach leads to significant error reduction on unseen domains without incurring any overhead of model retraining

optimal partitioning for spatiotemporal coverage in a drift field abstract we consider the problem of partitioning an area in the plane populated by a team of aerial marine vehicles into a finite collection of non overlapping sets the sets of this partition are in an one to one correspondence with the vehicles under the following rule each point in the given set of the partition can be reached by the corresponding vehicle in this set faster than any other vehicle in the presence of a spatiotemporal drift field consequently a voronoi like partition results which encodes the proximity relations between the vehicles and arbitrary points in the plane with respect to the minimum time to go the construction of this voronoi like partition is based on its interpretation as the intersection of a forest of the cost minimum time to go surfaces emanating from each generator with their common lower envelope the characterization of each cost surface is achieved by means of an efficient expansion scheme of the level sets of the minimum time to go function which utilizes in turn the structure of the optimal synthesis of the minimum time problem without resorting to exhaustive numerical techniques e g fast marching methods we examine the topological characteristics of the partition by using control system theoretic concepts and tools the theoretical developments are illustrated with a number of numerical examples

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

generalized flows for optimal inference in higher order mrf map use of higher order clique potentials in mrf map problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes we propose a new combinatorial algorithm for computing optimal solutions to 2 label mrf map problems with higher order clique potentials the algorithm runs in time o 2 kn 3 in the worst case k is size of clique and n is the number of pixels a special gadget is introduced to model flows in a higher order clique and a technique for building a flow graph is specified based on the primal dual structure of the optimization problem the notions of the capacity of an edge and a cut are generalized to define a flow problem we show that in this flow graph when the clique potentials are submodular the max flow is equal to the min cut which also is the optimal solution to the problem we show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like dual decomposition 1 trws 2 and reduction 3 4 5 the framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques

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

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

cluster consensus in discrete time networks of multiagents with inter cluster nonidentical inputs in this paper cluster consensus of multiagent systems is studied via inter cluster nonidentical inputs here we consider general graph topologies which might be time varying the cluster consensus is defined by two aspects intracluster synchronization the state at which differences between each pair of agents in the same cluster converge to zero and inter cluster separation the state at which agents in different clusters are separated for intra cluster synchronization the concepts and theories of consensus including the spanning trees scramblingness infinite stochastic matrix product and hajnal inequality are extended as a result it is proved that if the graph has cluster spanning trees and all vertices self linked then the static linear system can realize intra cluster synchronization for the time varying coupling cases it is proved that if there exists t 0 such that the union graph across any t length time interval has cluster spanning trees and all graphs has all vertices self linked then the time varying linear system can also realize intra cluster synchronization under the assumption of common inter cluster influence a sort of inter cluster nonidentical inputs are utilized to realize inter cluster separation such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs in addition the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory as an application we employ a modified non bayesian social learning model to illustrate the effectiveness of our results

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

nonsmooth coordination and geometric optimization via distributed dynamical systems emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents for example it is envisioned that groups of agents will perform a variety of useful tasks including surveillance exploration and environmental monitoring this paper deals with basic interactions among mobile agents such as move away from the closest other agent or move toward the furthest vertex of your own voronoi polygon these simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents we characterize the close relationship between these distributed dynamical systems and the disk covering and sphere packing cost functions from geometric optimization our main results are as follows i we characterize the smoothness properties of these geometric cost functions ii we show that the interaction laws are variations of the nonsmooth gradient of the cost functions and iii we establish various asymptotic convergence properties of the laws the technical approach relies on concepts from computational geometry nonsmooth analysis and nonsmooth stability theory

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

grasp geodesic graph based segmentation with shape priors for the functional parcellation of the cortex abstract resting state functional mri is a powerful technique for mapping the functional organization of the human brain however for many types of connectivity analysis high resolution voxelwise analyses are computationally infeasible and dimensionality reduction is typically used to limit the number of network nodes most commonly network nodes are defined using standard anatomic atlases that do not align well with functional neuroanatomy or regions of interest covering a small portion of the cortex data driven parcellation methods seek to overcome such limitations but existing approaches are highly dependent on initialization procedures and produce spatially fragmented parcels or overly isotropic parcels that are unlikely to be biologically grounded in this paper we propose a novel graph based parcellation method that relies on a discrete markov random field framework the spatial connectedness of the parcels is explicitly enforced by shape priors the shape of the parcels is adapted to underlying data through the use of functional geodesic distances our method is initialization free and rapidly segments the cortex in a single optimization the performance of the method was assessed using a large developmental cohort of more than 850 subjects compared to two prevalent parcellation methods our approach provides superior reproducibility for a similar data fit furthermore compared to other methods it avoids incoherent parcels finally the method s utility is demonstrated through its ability to detect strong brain developmental effects that are only weakly observed using other methods

asymptotic optimality of multicenter voronoi configurations for random field estimation this technical note deals with multi agent networks performing estimation tasks consider a network of mobile agents with sensors that can take measurements of a spatial stochastic process using the kriging statistical technique a field estimate may be calculated over the environment with an associated error variance at each point we study a single snapshot scenario in which the spatial process mean is known and each agent can only take one measurement we consider two optimization problems with respect to the measurement locations using as objective functions the maximum error variance and the extended prediction variance as the correlation between distinct locations vanishes we show that circumcenter and incenter voronoi configurations become network configurations that optimize the maximum error variance and the extended prediction variance respectively we also present distributed coordination algorithms that steer the network towards these configurations

a comparative study of energy minimization methods for markov random fields with smoothness based priors among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel labeling tasks such as depth or texture computation it has been known for decades that such problems can be elegantly expressed as markov random fields yet the resulting energy minimization problems have been widely viewed as intractable algorithms such as graph cuts and loopy belief propagation lbp have proven to be very powerful for example such methods form the basis for almost all the top performing stereo methods however the trade offs among different energy minimization algorithms are still not well understood in this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms we investigate three promising methods graph cuts lbp and tree reweighted message passing in addition to the well known older iterated conditional mode icm algorithm our benchmark problems are drawn from published energy functions used for stereo image stitching interactive segmentation and denoising we also provide a general purpose software interface that allows vision researchers to easily switch between optimization methods the benchmarks code images and results are available at http vision middlebury edu mrf

discrete and continuous models for partitioning problems recently variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention since they introduce significantly less artifacts than established graph cut based techniques this work is concerned with the sources of such artifacts we discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples moreover we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method since the employed regularizer is quite tight the considered relaxation generally involves a large computational cost we propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics thus generalizing a method recently proposed by strekalovskiy and cremers ieee conference on computer vision and pattern recognition pp 1905 1911 2011

coordinated path following in the presence of communication losses and time delays this paper addresses the problem of steering a group of vehicles along given spatial paths while holding a desired time varying geometrical formation pattern the solution to this problem henceforth referred to as the coordinated path following cpf problem unfolds in two basic steps first a path following pf control law is designed to drive each vehicle to its assigned path with a nominal speed profile that may be path dependent this is done by making each vehicle approach a virtual target that moves along the path according to a conveniently defined dynamic law in the second step the speeds of the virtual targets also called coordination states are adjusted about their nominal values so as to synchronize their positions and achieve indirectly vehicle coordination in the problem formulation it is explicitly considered that each vehicle transmits its coordination state to a subset of the other vehicles only as determined by the communications topology adopted it is shown that the system that is obtained by putting together the pf and coordination subsystems can be naturally viewed as either the feedback or the cascade connection of the latter two using this fact and recent results from nonlinear systems and graph theory conditions are derived under which the pf and the coordination errors are driven to a neighborhood of zero in the presence of communication losses and time delays two different situations are considered the first captures the case where the communication graph is alternately connected and disconnected brief connectivity losses the second reflects an operational scenario where the union of the communication graphs over uniform intervals of time remains connected uniformly connected in mean to better root the paper in a nontrivial design example a cpf algorithm is derived for multiple underactuated autonomous underwater vehicles auvs simulation results are presented and discussed

edge agreement graph theoretic performance bounds and passivity analysis this work explores the properties of the edge variant of the graph laplacian in the context of the edge agreement problem we show that the edge laplacian and its corresponding agreement protocol provides a useful perspective on the well known node agreement or the consensus algorithm specifically the dynamics induced by the edge laplacian facilitates a better understanding of the role of certain subgraphs e g cycles and spanning trees in the original agreement problem using the edge laplacian we proceed to examine graph theoretic characterizations of the h2 and h performance for the agreement protocol these results are subsequently applied in the contexts of optimal sensor placement for consensus based applications finally the edge laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics

approximation algorithms for classification problems with pairwise relationships metric labeling and markov random fields in a traditional classification problem we wish to assign one of k labels or classes to each of n objects in a way that is consistent with some observed data that we have about the problem an active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified this issue is one of the principal motivations for the framework of markov random fields and it arises in areas such as image processing biometry and document analysis in its most basic form this style of analysis seeks to find a classification that optimizes a combinatorial function consisting of assignment costs based on the individual choice of label we make for each object and separation costs based on the pair of choices we make for two related objects we formulate a general classification problem of this type the metric labeling problem we show that it contains as special cases a number of standard classification frameworks including several arising from the theory of markov random fields from the perspective of combinatorial optimization our problem can be viewed as a substantial generalization of the multiway cut problem and equivalent to a type of uncapacitated quadratic assignment problem we provide the first nontrivial polynomial time approximation algorithms for a general family of classification problems of this type our main result is an o log k log log k approximation algorithm for the metric labeling problem with respect to an arbitrary metric on a set of k labels and an arbitrary weighted graph of relationships on a set of objects for the special case in which the labels are endowed with the uniform metric all distances are the same our methods provide a 2 approximation algorithm

containment control of single integrator network with limited communication data rate this technical note investigates distributed containment control for a single integrator continuous time multi agent system with a limited communication data rate network topology is a directed communication graph the containment control with quantized communication for each follower is designed using only its neighbour s quantized information so that all followers move into the convex hull spanned by the leaders necessary and sufficient criteria which guarantee achievement of containment consensus are given if the communication data rates are unfixed or fixed under a given bound on communication data rate an algorithm is established to achieve the containment consensus finally all the theoretical results are illustrated by numerical simulations

from global finite time linear computations to local edge based interaction rules a network of locally interacting agents can be thought of as performing a distributed computation but not all computations can be faithfully distributed this technical note investigates which global linear transformations can be computed in finite time using local rules with time varying weights i e rules which rely solely on information from adjacent nodes in a network the main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant an optimal control problem is solved for finding the local interaction rules and simulations are performed to elucidate how optimal solutions can be obtained

joint sulcal detection on cortical surfaces with graphical models and boosted priors in this paper we propose an automated approach for the joint detection of major sulci on cortical surfaces by representing sulci as nodes in a graphical model we incorporate markovian relations between sulci and formulate their detection as a maximum a posteriori map estimation problem over the joint space of major sulci to make the inference tractable a sample space with a finite number of candidate curves is automatically generated at each node based on the hamilton jacobi skeleton of sulcal regions using the adaboost algorithm we learn both individual and pairwise shape priors of sulcal curves from training data which are then used to define potential functions in the graphical model based on the connection between adaboost and logistic regression finally belief propagation is used to perform the map inference and select the joint detection results from the sample spaces of candidate curves in our experiments we quantitatively validate our algorithm with manually traced curves and demonstrate the automatically detected curves can capture the main body of sulci very accurately a comparison with independently detected results is also conducted to illustrate the advantage of the joint detection approach

combinatorial optimization of the discretized multiphase mumford shah functional the mumford shah model has been one of the most influential models in image segmentation and denoising the optimization of the multiphase mumford shah energy functional has been performed using level sets methods that optimize the mumford shah energy by evolving the level sets via the gradient descent these methods are very slow and prone to getting stuck in local optima due to the use of gradient descent after the reformulation of the 2 phase mumford shah functional on a graph several groups investigated the hierarchical extension of the graph representation to multi class the discrete hierarchical approaches are more effective than hierarchical or direct multiphase formulation using level sets however they provide approximate solutions and can diverge away from the optimal solution in this paper we present a discrete alternating optimization for the discretized vese chan approximation of the piecewise constant multiphase mumford shah functional that directly minimizes the multiphase functional without recursive bisection on the labels our approach handles the nonsubmodularity of the multiphase energy function and provides a global optimum if the image estimation data term is known apriori

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

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

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments