spacetime texture representation and recognition based on a spatiotemporal orientation analysis this paper is concerned with the representation and recognition of the observed dynamics i e excluding purely spatial appearance cues of spacetime texture based on a spatiotemporal orientation analysis the term spacetime texture is taken to refer to patterns in visual spacetime x y t that primarily are characterized by the aggregate dynamic properties of elements or local measurements accumulated over a region of spatiotemporal support rather than in terms of the dynamics of individual constituents examples include image sequences of natural processes that exhibit stochastic dynamics e g fire water and windblown vegetation as well as images of simpler dynamics when analyzed in terms of aggregate region properties e g uniform motion of elements in imagery such as pedestrians and vehicular traffic spacetime texture representation and recognition is important as it provides an early means of capturing the structure of an ensuing image stream in a meaningful fashion toward such ends a novel approach to spacetime texture representation and an associated recognition method are described based on distributions histograms of spacetime orientation structure empirical evaluation on both standard and original image data sets shows the promise of the approach including significant improvement over alternative state of the art approaches in recognizing the same pattern from different viewpoints

exponential synchronizationlike criterion for state dependent impulsive dynamical networks this paper focuses on the problem of the exponential synchronizationlike criteria for state dependent impulsive dynamical networks sidns two types of sufficient conditions which are applied to ensure every solution intersecting each impulsive surface exactly once are derived for each type of collision conditions combining with comparison principle and inequality techniques some sufficient conditions are obtained to ensure local exponential synchronizationlike for sidn moreover a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed finally an example is given to demonstrate the effectiveness of our results

brief paper synchronization of coupled harmonic oscillators in a dynamic proximity network in this paper we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity we show that the coupled harmonic oscillators can always be synchronized without imposing any network connectivity assumption moreover we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader again without any assumption on connectivity of the followers numerical simulation illustrates the theoretical results

reaching a consensus in a dynamically changing environment convergence rates measurement delays and asynchronous events this paper uses recently established properties of compositions of directed graphs together with results from the theory of nonhomogeneous markov chains to derive worst case convergence rates for the headings of a group of mobile autonomous agents which arise in connection with the widely studied vicsek consensus problem the paper also uses graph theoretic constructions to solve modified versions of the vicsek problem in which there are measurement delays asynchronous events or a group leader in all three cases the conditions under which consensus is achieved prove to be almost the same as the conditions under which consensus is achieved in the synchronous delay free leaderless case

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

oriented structure of the occlusion distortion is it reliable in the energy spectrum of an occlusion sequence the distortion term has the same orientation as the velocity of the occluding signal other works claimed that this oriented structure can be used to distinguish the occluding velocity from the occluded one we argue that the orientation structure of the distortion cannot always work as a reliable feature due to the rapidly decreasing energy contribution this already weak orientation structure is further blurred by a superposition of distinct distortion components we also indicate that the superposition principle of shizawa and mase 1991 for multiple motion estimation needs to be adjusted

second order global consensus in multiagent networks with random directional link failure in this paper we consider the second order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time averaged system a criterion for the second order consensus is derived by constructing a lyapunov function for the time averaged network by associating the solution of random switching nonlinear system with the constructed lyapunov function a sufficient condition for second order globally nonlinear consensus in a multiagent network with random directed interconnections is also established it is required that the second order consensus can be achieved in the time averaged network and the lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments a numerical example is presented to justify the correctness of the theoretical results

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

picard vessiot theory and ziglin s theorem abstract given a hamiltonian system ziglin s theorem is one of the criteria used to study the integrability of the system for this we make use of the variational equations along a known solution in this paper we obtain some consequences of the application of picard vessiot differential galois theory to ziglin s theorem first we present the general results for the case of a finite arbitrary number of degrees of freedom then we pass to the case of two degrees of freedom where the results can be given with more detail under the hypothesis of ziglin s theorem and some additional technical assumptions the main results theorems 1 and 2 relate the integrability of the hamiltonian with the properties of the differential galois group of the picard vessiot extension associated to the normal reduced variational equations for two degrees of freedom it is possible to study also the resonant case theorems 4 and 5 give the full classification of the galois groups and the related extensions in the integrable case a couple of applications are made to recover ito s theorem and to study the lame equation

observer based discrete time nonnegative edge synchronization of networked systems this paper studies the multi input and multi output discrete time nonnegative edge synchronization of networked systems based on neighbors output information the communication relationship among the edges of networked systems is modeled by well known line graph two observer based edge synchronization algorithms are designed for which some necessary and sufficient synchronization conditions are derived moreover some computable sufficient synchronization conditions are obtained in which the feedback matrix and the observer matrix are computed by solving the linear programming problems we finally design several simulation examples to demonstrate the validity of the given nonnegative edge synchronization algorithms

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

the non integrability of the truncated two fixed centres problem in a recent paper published in journal of differential equations irigoyen 2 proved that any truncation of order 3 of the symmetric two fixedcentres problem is not completely integrable through meromorphic integrals the purpose of this note is to point out that in fact neither is any truncationof the asymmetric problem this is deduced from a result published nearlysimultaneously by the authors 1 who established the non integrability ofany truncation of the zonal satellite problem the problem of the two fixed centres with masses equal to m

mean square consensus of stochastic multi agent systems with nonlinear dynamics by distributed event triggered strategy abstractthis paper is concerned with the problem of mean square consensus for nonlinear multi agent systems with state dependent noise perturbations a distributed event triggered mechanism which can be used to reduce the number of controller updates and communication load is developed to apply in stochastic dynamical systems by combining the tools of graph theory and stochastic analysis the sufficient conditions are given to ensure that mean square consensus in the multi agent systems can be achieved exponentially the convergence rate is also analytically derived moreover the feasibility of the proposed distributed event triggered strategy is further verified by exclusion of zeno behaviour finally some numerical examples are given to demonstrate the effectiveness of the obtained results

non integrability of homogeneous two dimensional hamiltonians with velocity dependent potential the non integrability of classes of homogeneous two dimensional hamiltonian systems with a polynomial velocity dependent potential is shown on the basis of ziglin s theorem an analytic expression for the trace of the relevant monodromy matrices is presented which fits the numerical data perfectly an application is made to fokker planck hamiltonians with quadratic and with cubic drift terms

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

relative equilibria and bifurcations in the generalized van der waals 4d oscillator abstract a uniparametric 4 dof family of perturbed hamiltonian oscillators in 1 1 1 1 resonance is studied as a generalization for several models for perturbed keplerian systems normalization by lie transforms only first order is considered here as well as geometric reduction related to the invariants associated to the symmetries is used based on the previous work of the authors a description is given for the lower dimensional relative equilibria in such normalized systems for which we introduce in this context the new concept of moment polytope in addition bifurcations of relative equilibria corresponding to 3d tori are studied in some particular cases where we focus on hamiltonian hopf bifurcations and bifurcations in the 3d van der waals and zeeman systems

non integrability of the truncated toda lattice hamiltonian at any order two sufficient conditions for the non existence of an additional analytic integral are given for hamiltonian systems with non homogeneous polynomial potential of an arbitrary degree an application is made to the truncated three particle toda lattice which is proved to be non integrable at any order

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

orbital behaviour transition from the he non heiles to the three particle toda lattice hamiltonian abstract we examine the orbital behaviour in successive n order approximations 3 n 10 of the three particle toda lattice n 3 corresponding to the henon heiles galactic hamiltonian and in transition models between the 3rd and 4th orders of this expansion by using the poincare consequent method and by computing the e folding rate of the main unstable periodic orbits we locate and quantify the most important instabilities responsible for chaos in systems corresponding to even and odd order expansions

avoiding congestion in cluster consensus of the second order nonlinear multiagent systems in order to avoid congestion in the second order nonlinear leader following multiagent systems over capacity limited paths an approach called cluster lag consensus is proposed which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus it is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold the cluster lag consensus can be achieved furthermore the cluster lag consensus with a time varying communication topology is investigated finally an illustrative example is presented to demonstrate the effectiveness of the theoretical results in particular when the physical sizes of the agents are taken into consideration it is shown that with a rearrangement and a position transformation the multiagent system will reach cluster lag consensus in the new coordinate system this means that all agents in the same cluster will reach consensus on the velocity but their positions may be different and yet their relative positions converge to a constant asymptotically

on the non integrability of some generalized toda lattices abstract we consider a one parameter family of two degrees of freedom generalized toda hamiltonians using ziglin s theorem with some extensions we prove the non existence of an additional single valued analytic integral except for special values of the parameter

signs and approximate magnitudes of lyapunov exponents in continuous time dynamical systems methods for algebraically determining the signs and the magnitudes of lyapunov exponents of a given dynamical system are studied the existence of zero lyapunov exponents for the toda henon heiles and rossler systems are shown the approximate lyapunov spectra of lorenz and rossler systems are computed

on the non integrability of the stark zeeman hamiltonian system in this paper we present a proof of the non integrability in the liouvillian sense of the stark zeeman hamiltonian in particular we generalize the result of kummer and saenz about the non integrability of the pure zeeman hamiltonian the proof we give is an application of the theorem of morales and ramis 1998 about non integrability based on differential galois theory

the structure of multiplicative motions in natural imagery a theoretical investigation of the frequency structure of multiplicative image motion signals is presented e g as associated with translucency phenomena previous work has claimed that the multiplicative composition of visual signals generally results in the annihilation of oriented structure in the spectral domain as a result research has focused on multiplicative signals in highly specialized scenarios where highly structured spectral signatures are prevalent or introduced a nonlinearity to transform the multiplicative image signal to an additive one in contrast in this paper it is shown that oriented structure is present in multiplicative cases when natural domain constraints are taken into account this analysis suggests that the various instances of naturally occurring multiple motion structures can be treated in a unified manner as an example application of the developed theory a multiple motion estimator previously proposed for translation additive transparency and occlusion is adapted to multiplicative image motions this estimator is shown to yield superior performance over the alternative practice of introducing a nonlinear preprocessing step

synchronization of markovian coupled neural networks with nonidentical node delays and random coupling strengths in this paper a general model of coupled neural networks with markovian jumping and random coupling strengths is introduced in the process of evolution the proposed model switches from one mode to another according to a markovian chain and all the modes have different constant time delays the coupling strengths are characterized by mutually independent random variables when compared with most of existing dynamical network models which share common time delay for all modes and have constant coupling strengths our model is more practical because different chaotic neural network models can have different time delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors by designing a novel lyapunov functional and using some inequalities and the properties of random variables we derive several new sufficient synchronization criteria formulated by linear matrix inequalities the obtained criteria depend on mode delays and mathematical expectations and variances of the random coupling strengths as well numerical examples are given to demonstrate the effectiveness of the theoretical results meanwhile right continuous markovian chain is also presented

second order tracking control for leader follower multi agent flocking in directed graphs with switching topology abstract this paper investigates the flocking problem for leader follower multi agent systems in directed graphs with switching topology a decentralized state control rule namely a second order protocol is designed for each agent to track the leader and it is proved that the proposed control scheme can effectively estimate the tracking error of each agent when the leader is active particularly to ensure the tracking error can be estimated the following two questions are solved 1 how many agents are needed to connect to the leader 2 how should these connections be distributed finally a simple example is also given to verify the effectiveness of the proposed theorems

nonintegrability of nonhomogeneous nonlinear lattices we study the integrability of nonlinear lattices with nonhomogeneous polynomial potentials we prove a nonintegrability theorem for these dynamical systems

on the nonintegrability of the generalized van der waals hamiltonian system in this paper we aim to prove that except for the three known cases the uniparametric family of hamiltonian systems defined by the generalized van der waals potential is nonintegrable in the liouville arnold sense the proof is based on the theorem of morales and ramis about nonintegrability by differential galois theory

event based robust control for uncertain nonlinear systems using adaptive dynamic programming in this paper the robust control problem for a class of continuous time nonlinear system with unmatched uncertainties is investigated using an event based control method first the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function under the event based mechanism we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition that is the designed event based controller is robust to the original uncertain system note that the event based controller is updated only when the triggering condition is satisfied which can save the communication resources between the plant and the controller then a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies the stability of the closed loop system with the event based control policy and the augmented control policy is analyzed using the lyapunov approach furthermore we prove that the minimal intersample time is bounded by a nonzero positive constant which excludes zeno behavior during the learning process finally two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

a criterion for the non existence of an additional integral in hamiltonian systems with a homogeneous potential abstract a non integrability criterion on the basis of ziglin s theorem is given for two degrees of freedom hamiltonians with a homogeneous potential of integer degree as simple examples the anisotropic kepler problem and the one dimensional newtonian three body problem are proved to be non integrable a self contained proof of ziglin s theorem n dimensional homogeneous potential version is also given

consensus in correlated random wireless sensor networks this contribution studies the convergence of consensus algorithms in random wireless sensor networks with spatially correlated links aiming at reducing the convergence time we adopt an optimization criterion based on the minimization of the spectral radius of a matrix for which we derive closed form expressions for both directed and undirected topologies we show that the minimization of the spectral radius assuming constant link weights is a convex optimization problem the expressions derived subsume known protocols found in literature

consensus seeking over random weighted directed graphs we examine the consensus problem for a group of agents that communicate via a stochastic information network communication among agents is modeled as a weighted directed random graph that switches periodically the existence of any edge is probabilistic and independent from the existence of any other edge we further allow each edge to be weighted differently sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights

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

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

event triggered control of multiagent systems for fixed and time varying network topologies a decentralized controller that uses event triggered communication scheduling is developed for the leader follower consensus problem under fixed and switching communication topologies to eliminate continuous interagent communication state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors the communication times are based on an event triggered approach and are adapted based on the trade off between the control system performance and the desire to minimize the amount of communication an important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed since the control strategy produces switched dynamics analysis is provided to show that zeno behavior is avoided by developing a positive constant lower bound on the minimum inter event interval a lyapunov based convergence analysis is also provided to indicate bounded convergence of the developed control methodology

analytical non integrability of the truncated two fixed centres problem in the symmetric case abstract the problem of two fixed centres is an integrable hamiltonian system if one truncates the taylor expansion of the potential of this problem in the symmetric case at any order 3 we prove that one obtains a system which does not admit any first integral meromorphic and functionally independent of the energy and the angular momentum the proof is mainly founded on the criterion of non integrability for homogeneous potentials derived by yoshida from ziglin s theorem then we use this result to prove that the vinti problem truncated at any order 3 is analytically non integrable le probleme des deux centres fixes est un systeme hamiltonien integrable si l on tronque a un ordre arbitraire 3 le developpement de taylor du potentiel de ce probleme dans le cas symetrique on montre que le systeme obtenu n admet aucune integrale premiere meromorphe et fonctionnellement independante de l energie et du moment angulaire la demonstration est principalement fondee sur le critere de non integrabilite pour les potentiels homogenes que yoshida a deduit du theoreme de ziglin nous utilisons ensuite ce resultat pour etablir que le probleme de vinti tronque a un ordre arbitraire 3 est non integrable analytiquement

a new asymptotic stability criterion for nonlinear time variant differential equations a new sufficient condition for asymptotic stability of ordinary differential equations is proposed unlike classical lyapunov theory the time derivative along solutions of the lyapunov function may have positive and negative values the classical lyapunov approach may be regarded as an infinitesimal version of the present theorem verification in practical problems is harder than in the classical case an example is included in order to indicate how the present theorem may be applied

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

non integrability of the fourth order truncated toda hamiltonian abstract the integrability of a polynomial hamiltonian derived through the fourth order truncation of the three particle toda lattice is investigated a theorem by ziglin is used to prove that this hamiltonian does not possess a second analytic integral although earlier numerical calculations had suggested its integrability some generalization of this system is also discussed