an infinite dimensional morse theory with applications in this paper we construct an infinite dimensional extraordinary cohomology theory and a morse theory corresponding to it these theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension several applications are given to hamiltonian systems the onedimensional wave equation of vibrating string type and systems of elliptic partial differential equations 0 introduction let e be a real hilbert space with an inner product and let be a twice continuously differentiable functional denote the frechet derivative and the gradient of at x by x and x respectively where as usual x y x y y e recall that a point x0 e is said to be critical if x0 0 or equivalently if x0 0 the level c r will be called regular if 1 c contains no critical points and critical if x0 0 for some x0 1 c let a b a b be two regular levels of denote m 1 a b and consider the restriction of to m in morse theory one is interested in the local topological structure of the level sets of m near a critical point and in the relation between this local structure and the topological structure of the set m to be more specific suppose that x0 m is an isolated critical point of then one defines a sequence of critical groups of at x0 by setting cq x0 hq c u u x0 q 0 1 2 0 1 where c x0 c x e x c hq is the q th singular homology group with coefficients in some field f and u is a neighbourhood of x0 define the morse index of x0 to be the maximal dimension of a subspace of e on which the quadratic form x0 y y is negative definite one shows that if x0 is a nondegenerate critical point i e if x0 e e is invertible then cq x0 f received by the editors march 20 1995 1991 mathematics subject classification primary 58e05 secondary 34c25 35j65 35l05 55n20 58f05

periodic solutions of weakly coupled superlinear systems abstract by the use of a higher dimensional version of the poincare birkhoff theorem we are able to generalize a result of jacobowitz 15 and hartman 14 thus proving the existence of infinitely many periodic solutions for a weakly coupled superlinear system

on superquadratic periodic systems with indefinite linear part abstract we consider a second order periodic system with an indefinite linear part and a potential function which is superquadratic but does not satisfy the ar condition using morse critical groups we show that the system has at least one nontrivial solution

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

periodic solutions of second order equations via rotation numbers abstract we consider the problem of the existence and multiplicity of periodic solutions associated to a class of scalar equations of the form x f t x 0 the class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable piecewise linear systems we show how a rotation number approach together with the poincare birkhoff theorem and the phase plane analysis of the spiral properties allows to obtain multiplicity results in terms of the gap between the rotation numbers of the referred piecewise linear systems at zero and at infinity these systems may also be resonant in particular our approach can be used to deal with the problems without both global existence of the cauchy problems associated to the equation and the sign assumption on f the typical example is a partially superlinear second order equation our main result generalizes some classical results of jacobowitz and hartman among others

the cardinality balanced multi target multi bernoulli filter and its implementations it is shown analytically that the multitarget multibernoulli member recursion proposed by mahler has a significant bias in the number of targets to reduce the cardinality bias a novel multibernoulli approximation to the multi target bayes recursion is derived under the same assumptions as the member recursion the proposed recursion is unbiased in addition a sequential monte carlo smc implementation for generic models and a gaussian mixture gm implementation for linear gaussian models are proposed the latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

periodic solutions of classical hamiltonian systems without palais smale condition abstract in this paper we study the existence of periodic solutions for classical hamiltonian systems without the palais smale condition we prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions moreover we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function v

multiple solutions of perturbed superquadratic second order hamiltonian systems abstract in this paper the author proves the existence of infinitely many distinct t periodic solutions of the perturbed second order hamiltonian systems q v q f t under the condition that v is c and superquadratic via minimax methods we also obtain similar results for general nonautonomous second order hamiltonian systems and perturbed lagrangian systems keywords invariance asymmetry a priori growth estimates multiple periodic solutions

multiobject tracking for generic observation model using labeled random finite sets this paper presents an exact bayesian filtering solution for the multiobject tracking problem with the generic observation model the proposed solution is designed in the labeled random finite set framework using the product styled representation of labeled multiobject densities with the standard multiobject transition kernel and no particular simplifying assumptions on the multiobject likelihood computationally tractable solutions are also devised by applying a principled approximation involving the replacement of the full multiobject density with a labeled multi bernoulli density that minimizes the kullback leibler divergence and preserves the first order moment to achieve the fast performance a dynamic grouping procedure based implementation is presented with a step by step algorithm the performance of the proposed filter and its tractable implementations are verified and compared with the state of the art in numerical experiments

periodic solutions of autonomous newtonian systems partially asymptotically linear at infinity abstract the goal of this article is to study the existence continuation and global bifurcation of autonomous newtonian systems partially asymptotically linear at infinity the main idea is to prove a kind of splitting lemma and apply the degree for s 1 equivariant gradient maps defined by rybicki 1994 in 16

periodic solutions of superquadratic hamiltonian systems with bounded forcing terms on etudie l existence et la multiplicite des solutions periodiques pour le systeme hamiltonien z z t z ou z r r 2n z dz dt j o j j o j etant la matrice identite dans r n

periodic solutions of large norm of hamiltonian systems abstract hamiltonian systems of ordinary differential equations are studied the only assumption made on the hamiltonian is appropriately rapid growth at infinity it is proved that for any given period there is an unbounded sequence of periodic solutions of the system having the given period

on the classical dynamics of strongly driven anharmonic oscillators abstract we investigate the dynamics of periodically driven anharmonic oscillators in particular we consider values of the coupling strength which are orders of magnitude higher than those required for the overlap of primary resonances we observe a division of phase space into a regular and a stochastic region both regions are separated by a sharp chaos border which sets an upper limit to the stochastic heating of particles its dependence on the coupling strength is studied we construct perpetual adiabatic invariants governing regular motion a bifurcation mechanism leading to the annihilation of resonances is explained

periodic solutions for a class of superquadratic hamiltonian systems abstract we prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second order hamiltonian systems by applying condition c to critical point theory and some new solvability conditions of nontrivial periodic solutions are obtained

periodic and subharmonic solutions for a class of superquadratic hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic hamiltonian systems by the minimax methods in critical point theory specially a local link theorem due to li and willem and the generalized mountain pass theorem respectively

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

generalized labeled multi bernoulli approximation of multi object densities in multiobject inference the multiobject probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects exact computation of the multiobject density is generally intractable and tractable implementations usually require statistical independence assumptions between objects in this paper we propose a tractable multiobject density approximation that can capture statistical dependence between objects in particular we derive a tractable generalized labeled multi bernoulli glmb density that matches the cardinality distribution and the first moment of the labeled multiobject distribution of interest it is also shown that the proposed approximation minimizes the kullback leibler divergence over a special tractable class of glmb densities based on the proposed glmb approximation we further demonstrate a tractable multiobject tracking algorithm for generic measurement models simulation results for a multiobject track before detect example using radar measurements in low signal to noise ratio snr scenarios verify the applicability of the proposed approach

fixed lag smoothing for bayes optimal knowledge exploitation in target tracking in this work we are interested in the improvements attainable when multiscan processing of external knowledge is performed over a moving time window we propose a novel algorithm that enforces the state constraints by using a fixed lag smoothing procedure within the prediction step of the bayesian recursion for proving the improvements we utilize differential entropy as a measure of uncertainty and show that the approach guarantees a lower or equal posterior differential entropy than classical single step constrained filtering simulation results using examples for single target tracking are presented to verify that a sequential monte carlo implementation of the proposed algorithm guarantees an improved tracking accuracy

periodic solutions of semilinear duffing equations with impulsive effects abstract in this paper we are concerned with the existence of periodic solutions for semilinear duffing equations with impulsive effects firstly for its autonomous equation any motion of the solution is same as the motion of the corresponding equation without impulses until it meets the first impulse time under the influence of impulses these two motions are likely to be quite different we introduce some reasonable assumptions on the impulsive functions to control these differences such that the information valid for the equation without impulses can always be used for the impulsive one basing on poincare birkhoff twist theorem we prove the existence of infinitely many periodic solutions secondly as for the nonautonomous equation where the autonomous case is taken as an auxiliary one we find the relation between the solutions of these two equations and then obtain the existence of infinitely many periodic solutions also by poincare birkhoff twist theorem lastly an example with special impulses satisfying the above assumptions is given

analytic implementations of the cardinalized probability hypothesis density filter the probability hypothesis density phd recursion propagates the posterior intensity of the random finite set rfs of targets in time the cardinalized phd cphd recursion is a generalization of the phd recursion which jointly propagates the posterior intensity and the posterior cardinality distribution in general the cphd recursion is computationally intractable this paper proposes a closed form solution to the cphd recursion under linear gaussian assumptions on the target dynamics and birth process based on this solution an effective multitarget tracking algorithm is developed extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques the proposed cphd implementations not only sidestep the need to perform data association found in traditional methods but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard phd filter our implementations only have a cubic complexity but simulations suggest favorable performance compared to the standard joint probabilistic data association jpda filter which has a nonpolynomial complexity

a continuation approach to superlinear periodic boundary value problems this paper deals with the problem of the existence of t periodic solutions for the first order differential system x i t x 1 1 where f 0 t x r r is a caratheodory function in what follows we prove some results for the solvability of the periodic bvp in the case when the dimension of the space is even such a limitation is motivated by our interest in applications to the second order equation d g t u u o 1 2 which takes the form of 1 1 when it is written as the equivalent system u v 0 g t u v 1 3

periodic and subharmonic solutions for a class of superquadratic second order hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic second order hamiltonian systems by the minimax methods in critical point theory especially a local linking theorem due to luan and mao and the generalized mountain pass theorem due to rabinowitz

infinitely many periodic solutions for second order hamiltonian systems in this paper we study the existence of infinitely many periodic solutions for second order hamiltonian systems u uv t u 0 where v t u is either asymptotically quadratic or superquadratic as u

on the bolza problem abstract we consider the following boundary value problem x v x 0 x 0 x 0 x t x 1 where t 0 x 0 x 1 r n are given we prove that this problem has infinitely many solutions provided v is even and superquadratic

a bahri lions theorem revisited abstract in 1988 a bahri and p l lions a bahri p l lions morse index of some min max critical points i application to multiplicity results comm pure appl math 41 1988 1027 1037 studied the following elliptic problem u u p 2 u f x u u h 0 1 where is a bounded smooth domain of r n 2 p 2 n 2 n 2 and f x u is not assumed to be odd in u they proved the existence of infinitely many solutions under an appropriate growth restriction on f in the present paper we improve this result by showing that under the same growth assumption on f the problem admits in fact infinitely many sign changing solutions in addition we derive an estimate on the number of their nodal domains we also deal with the corresponding fourth order equation 2 u u p 2 u f x u with both dirichlet and navier boundary conditions as well as with strongly coupled elliptic systems

periodic solutions of duffing s equations with superquadratic potential abstract this paper is devoted to the study of harmonic and subharmonic solutions for the second order scalar nonlinear duffing s equation x g x p t x x where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g x sign x as x among other results we prove the existence of infinitely many harmonic and subharmonic solutions of any order p p t and if the potential g x of g x satisfies certain conditions of superquadratic growth at the new existence results can be applied to situations in which the more classical superlinear growth condition g x x as x is not satisfied in this manner various preceding theorems are improved and sharpened see the introduction for more details proofs are based on a generalized version of the poincare birkhoff twist theorem due to w ding

on distances in uniformly random networks the distribution of euclidean distances in poisson point processes is determined the main result is the density function of the distance to the n nearest neighbor of a homogeneous process in ropfm which is shown to be governed by a generalized gamma distribution the result has many implications for large wireless networks of randomly distributed nodes

joint detection and estimation of multiple objects from image observations the problem of jointly detecting multiple objects and estimating their states from image observations is formulated in a bayesian framework by modeling the collection of states as a random finite set analytic characterizations of the posterior distribution of this random finite set are derived for various prior distributions under the assumption that the regions of the observation influenced by individual objects do not overlap these results provide tractable means to jointly estimate the number of states and their values from image observations as an application we develop a multi object filter suitable for image observations with low signal to noise ratio snr a particle implementation of the multi object filter is proposed and demonstrated via simulations

range image segmentation by dynamic neural network architecture abstract in this paper a dynamic neural network architecture for jump and crease edge detection in range images is proposed here the weights are based on fractional differentiation whose derivative index is varied from zero to one in discrete steps a set of edge pixels is selected as seed pixels at the start after convolving the neural edge operator at a very small derivative index these are then linked progressively to real edge pixels extracted in subsequent stages of fractional differentiation the robustness of this technique in identifying the crease edge pixels is demonstrated on a synthetic range image data with added noise in a precisely controlled environment then the technique is tested on a set of real world range image data

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

distributed fusion with multi bernoulli filter based on generalized covariance intersection in this paper we propose a distributed multiobject tracking algorithm through the use of multi bernoulli mb filter based on generalized covariance intersection g ci our analyses show that the g ci fusion with two mb posterior distributions does not admit an accurate closed form expression to solve this problem we first approximate the fused posterior as the unlabeled version of delta generalized labeled mb distribution referred to as generalized mb gmb distribution then to allow the subsequent fusion with another mb posterior distribution e g fusion with a third sensor node in the sensor network or fusion in the feedback working mode we further approximate the fused gmb posterior distribution as an mb distribution which matches its first order statistical moment the proposed fusion algorithm is implemented using sequential monte carlo technique and its performance is highlighted by numerical results

determination of the attitude of 3d objects from a single perspective view a method for finding analytical solutions to the problem of determining the attitude of a 3d object in space from a single perspective image is presented its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model and on the search for the model attitude consistent with these projections the geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight degree equation in the general case using simple logical rules it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3d objects because few admissible hypotheses are retained from the interpolation of the three line segments line matching by the prediction verification procedure is thus less complex

the labeled multi bernoulli filter this paper proposes a generalization of the multi bernoulli filter called the labeled multi bernoulli filter that outputs target tracks moreover the labeled multi bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi bernoulli filter by exploiting the conjugate prior form for labeled random finite sets the proposed filter can be interpreted as an efficient approximation of the delta generalized labeled multi bernoulli filter it inherits the advantages of the multi bernoulli filter in regards to particle implementation and state estimation it also inherits advantages of the delta generalized labeled multi bernoulli filter in that it outputs labeled target tracks and achieves better performance

periodic and subharmonic solutions of second order hamiltonian systems abstract some solvability conditions of periodic solutions and subharmonic solutions are obtained for a class of new superquadratic non autonomous second order hamiltonian systems by the minimax methods in critical point theory

visual tracking in background subtracted image sequences via multi bernoulli filtering this correspondence presents a novel method for simultaneous tracking of multiple non stationary targets in video our method operates directly on the video data and does not require any detection we propose a multi target likelihood function for the background subtracted grey scale image data which admits multi target conjugate priors this allows the multi target posterior to be efficiently propagated forward using the multi bernoulli filter our method does not need any training pattern or target templates and makes no prior assumptions about object types or object appearance case studies from the caviar dataset show that our method can automatically track multiple targets and quickly finds targets entering or leaving the scene

model indexing and object recognition using 3d viewpoint invariance object recognition and location of 3d objects from range data are described based on invariant representations of characteristic views of single objects depth data is processed to remove outliers then smoothed and segmented into surface patches fitted by polynomial equations mathematical invariants are derived from groups of these surface patches and used for indexing a model database stored in the form of a kd tree the pose of the known object may then be determined from the euclidean centre and orientation of the higher order surfaces formed from the feature groups the approach is complete scalable and extendable the robustness of the method is evaluated in terms of the stability and discriminatory power of the representation and the accuracy of the determined pose

existence and multiplicity of periodic solutions for a class of second order hamiltonian systems we study the existence and multiplicity of periodic solutions of the following second order hamiltonian system email protected t email protected k t u t w t u t 0 the existence of a nontrivial periodic solution is obtained when w is asymptotically linear at infinity and the existence of infinitely many periodic solutions is also obtained when w is superlinear

a novel joint multitarget estimator for multi bernoulli models in this paper the joint multitarget jom estimator proposed for the joint target detection and tracking jott filter is reformulated for the gaussian mixture gm implementations of the multitarget multi bernoulli member filters for this purpose a mode finding algorithm is employed to search for the most significant mode of a gm density thus the maximum a posterior map estimates of bernoulli targets are determined in addition the multi bernoulli versions of the two conflicting objective functions for the pareto optimal value of the unknown jom estimation constant are derived simulations compare the performance of the proposed jom estimator with that of the marginal multitarget mam estimator in a multitarget tracking scenario where the probability of target detection is a function of target states the simulation results demonstrate that the proposed jom estimator outperforms the mam estimator under moderately low observable conditions this is because the incomplete cost function of the mam estimator is not adequate to obtain accurate cardinality estimates of targets without considering how well targets are localized nevertheless the proposed jom estimator may suffer from track termination latency more than the mam estimator due to the definition of its cost function

infinitely many periodic solutions for a second order nonautonomous system in this paper we are interested in multiplicity results for a second order nonautonomous system infinitely many solutions follow from a recent variational principle by b ricceri

morse indices of critical manifolds generated by min max methods with compact lie group actions and applications we derive some upper and lower bounds for morse indices of critical manifolds generated by min max principles for functionals invariant under a general compact lie group or a finite group action the results generalize the similar results in the nonequivariant no group action case in doing so we also generalize the extension theorem of dugundji type in the nonequivariant case to the equivariant group action case as an application we obtain a precise growth estimate for the whole sequence of critical values given by the min max procedure for some superquadratic second order differential equations it is well known that this growth estimate is crucial in showing the existence of multiple solutions of some superquadratic perturbed hamiltonian systems and equations

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

borsuk ulam theorems for arbitrary s1 actions and applications abstract an s to the first power version of the borsuk ulam theorem is proved for a situation where fix s to the first power may be nontrivial the proof is accomplished with the aid of a new relative index theory applications are given to intersection theorems and the existence of multiple critica points is established for a class of functionals invariant under an s to the first power symmetry minimax arguments from the calculus of variations serve as an important tool in establishing the existence of nonlinear vibrations of discrete mechanical systems as modelled by hamilton s equations in these arguments one obtains the solutions of the differential equations as critical points of an associated lagrangian by minimaxing the lagrangian over appropriate classes of sets intersection theorems such as are proved in this paper play a crucial role in this process in addition to obtaining some intersection theorems this report illustrates their use by proving an existence theorem for multiple critical points of the functional invarianet under an s to the first power symmetry group

void probabilities and cauchy schwarz divergence for generalized labeled multi bernoulli models the generalized labeled multi bernoulli glmb is a family of tractable models that alleviates the limitations of the poisson family in dynamic bayesian inference of point processes in this paper we derive closed form expressions for the void probability functional and the cauchy schwarz divergence for glmbs the proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a glmb while the proposed analytic cauchy schwarz divergence provides a tractable measure of similarity between glmbs we demonstrate the use of both results on a partially observed markov decision process for glmbs with cauchy schwarz divergence based reward and void probability constraint

recognition of occluded polyhedra from range images abstract occlusion remains a major hindrance for automatic recognition of 3 d objects in this paper we address the occlusion problem in the context of polyhedral object recognition from range data a novel approach is presented for object recognition based on sound occlusion guided reasoning for feature distortion analysis and perceptual organization this type of reasoning enables us to maximize the amount of information extracted from the scene data thus leading to robust and efficient recognition the proposed approach is based on a multi stage matching process which attempts to recognize scene objects according to their order in the occlusion hierarchy i e an object is recognized before those that are occluded by it such a strategy helps in resolving some occlusion induced ambiguities in feature distortion analysis furthermore it leads to verification of object pose hypotheses with greater confidence matching is based on a hypothesize cluster and verify approach hypotheses are generated using an occlusion tolerant composite feature a fork which is a pair of non parallel edges that belong to the same surface generated hypotheses are then clustered and verified using a robust pixel based technique indexing is performed using distortion adaptive bounds on a rich set of viewpoint invariant fork attributes for high selectivity even in the presence of heavy occlusion performance of the system is demonstrated using complex multi object scenes

periodic solutions of second order superquadratic hamiltonian systems with potential changing sign ii abstract we consider the periodic solutions of the second order hamiltonian system x x h t v x with v being positive and superquadratic at infinity h being c 1 2 periodic sign changing and all zeros being simple some existence and multiplicity results of periodic solutions are given

multiplicity of periodic solutions for a class of second order perturbed hamiltonian systems abstract consider the following second order perturbed hamiltonian systems u t f u u g t u t r u 0 u t u 0 u t 0 t 0 where f u k u w u k w c 2 r n r g c 2 r r n r with g t t u g t u k and w is even but g t u maybe has no parity in u assume that w is superquadratic and g is subquadratic at the infinity and k satisfies pinched condition the existence of infinitely many periodic solutions of the above perturbed systems is proved via the bolle s perturbation method which is a generalization of 21 theorem 1 2 and 3 theorem 2 in some sense

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

periodic solutions of partially superquadratic second order hamiltonian systems abstract we consider the periodic solutions of the hamiltonian system x v x with v being superquadratic in some directions at infinity some theorems on periodic solutions for superquadratic v are generalized

periodic and subharmonic solutions of a class of superquadratic hamiltonian systems abstract periodic solutions and infinitely distinct subharmonic solutions are obtained for a class of nonconvex and nonautonomous superquadratic hamiltonian systems z j h z z t by using the minimax methods in critical point theory

existence of forced oscillations for some nonlinear differential equations abstract this article studies the existence of t periodic solutions for systems of nonlinear second order ordinary differential equations assuming function v to be superquadratic it is shown that this system possesses infinitely many t periodic solutions the proof of this result rests on showing that certain homotopy groups of level sets of the functional associated with the system are not trivial some more general results concerning systems of another type are also presented

periodic solutions of superlinear impulsive differential equations a geometric approach abstract a geometric method is introduced to study superlinear second order differential equations with impulsive effects basing on a reference continuous polar lifting of a planar orientation preserving homeomorphism we prove via the poincare birkhoff twist theorem the existence of infinitely many periodic solutions of conservative superlinear second order equations with the finite twist impulsive terms we also prove by developing a new twist fixed point theorem the existence of periodic solutions for non conservative superlinear second order equations with degenerate impulsive terms

labeled random finite sets and multi object conjugate priors the objective of multi object estimation is to simultaneously estimate the number of objects and their states from a set of observations in the presence of data association uncertainty detection uncertainty false observations and noise this estimation problem can be formulated in a bayesian framework by modeling the hidden set of states and set of observations as random finite sets rfss that covers thinning markov shifts and superposition a prior for the hidden rfs together with the likelihood of the realization of the observed rfs gives the posterior distribution via the application of bayes rule we propose a new class of rfs distributions that is conjugate with respect to the multiobject observation likelihood and closed under the chapman kolmogorov equation this result is tested on a bayesian multi target tracking algorithm

a periodic solution for a second order asymptotically linear hamiltonian system abstract we study the existence of a periodic solution of the following second order hamiltonian system u t f t u t 0 t 0 t where f t x k t x w t x assuming that k satisfies the pinching condition and w is asymptotically linear at infinity the existence of a nontrivial periodic solution is obtained via the mountain pass theorem

models for point processes observed with noise summary consider a pair of point processes x and y where x is regarded as a true point process and y is an imperfect observation of x for the transformation from x to y we consider a number of disturbance mechanisms covering random thinning displacement censoring of the displaced points and superposition of extra points we present the conditional likelihood of y given x when both point processes are observed the likelihood may be used for inference about the disturbance mechanisms the likelihood is a sum typically with very many terms and we discuss an approximation with a small number of terms the results are applied to an example where x denotes a set of true positions of tree tops and y denotes tree top positions estimated by template matching in a digital image obtained by high resolution aerial photography the parameters governing the various disturbance mechanisms are estimated from the conditional likelihood

periodic solutions for hamiltonian systems without ambrosetti rabinowitz condition and spectrum 0 abstract in this paper we consider the superquadratic second order hamiltonian system u t a t u t h t u t 0 t r our main results here allow the classical ambrosetti rabinowitz superlinear condition to be replaced by a general superquadratic condition and 0 lies in a gap of b where b d 2 d t 2 a t we will study the ground state periodic solutions for this problem the main idea here lies in an application of a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou

on a notion of category depending on a functional part i theory and application to critical point theory abstract we introduce the notion of category depending on a fixed functional f defined on a topological space this notion permits us to obtain a better lower bound to the number of critical points of f than the bound obtained with the lusternik schnirelman category we also introduce the notion of truncated category depending on the functional f which permits us to obtain a lower bound to the number of critical points of unbounded functionals finally we extend our result after having introduced the notions of relative category and limit relative category depending on the functional f

on forced vibrations of a semilinear wave equation without assumptions of monotonicity abstract we prove the existence of infinitely many periodic solutions of a forced wave equation with dirichlet boundary conditions for a large class of non monotone nonlinear terms

edge region based segmentation of range images in this correspondence we present a new computationally efficient three dimensional 3 d object segmentation technique the technique is based on the detection of edges in the image the edges can be classified as belonging to one of the three categories fold edges semistep edges defined here and secondary edges the 3 d image is sliced to create equidepth contours edcs three types of critical points are extracted from the edcs a subset of the edge pixels is extracted first using these critical points the edges are grown from these pixels through the application of some masks proposed in this correspondence the constraints of the masks can be adjusted depending on the noise present in the image the total computational effort is small since the masks are applied only over a small neighborhood of critical points edge regions furthermore the algorithm can be implemented in parallel as edge growing from different regions can be carried out independently of each other

fusion of labeled rfs densities with minimum information loss this paper addresses fusion of labeled random finite set lrfs densities according to the criterion of minimum information loss mil the mil criterion amounts to minimizing the weighted sum of kullback leibler divergences klds with the fused density appearing as righthand argument of the klds the optimal fused density following the mil rule is the linear opinion pool of local ones however such results cannot be directly applied to the marginalized delta generalized labeled multi bernoulli m delta glmb and labeled multi bernoulli lmb densities since the resulting fused densities are not belonging to the same family of local ones thus cannot be adopted in the context of bayesian filtering which requires the conjugacy of prior in order to overcome such difficulties when lrfs densities are m delta glmb or lmb the mil rule is further elaborated by imposing the constraint that the fused density be in the same family of local ones the resulting fusion rules are derived in closed form and the error of replacing the optimal fused density with the best m delta glmb lmb one is theoretically analyzed the derivation of mil fusion of m delta glmb lmb densities is based on the assumption that their label spaces have been matched which however cannot be satisfied in the majority of practical applications it is shown theoretically that label matching can be solved as a separate problem with respect to lrfs density fusion by resorting to the mil criterion finally the performance of the proposed fusion approach is assessed via simulation experiments concerning distributed multitarget tracking dmt on a sensor network

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

symplectic transformations and periodic solutions of hamiltonian systems abstract symplectic transformations with a kind of homogeneity are introduced which enable us to give a unified approach to some existence problems on the periodic solutions for the first and second order hamiltonian systems

labeled random finite sets and the bayes multi target tracking filter an analytic solution to the multi target bayes recursion known as the delta generalized labeled multi bernoulli delta glmb filter has been recently proposed by vo and vo in labeled random finite sets and multi object conjugate priors ieee trans signal process vol 61 no 13 pp 3460 3475 2014 as a sequel to that paper the present paper details efficient implementations of the delta glmb multi target tracking filter each iteration of this filter involves an update operation and a prediction operation both of which result in weighted sums of multi target exponentials with intractably large number of terms to truncate these sums the ranked assignment and k th shortest path algorithms are used in the update and prediction respectively to determine the most significant terms without exhaustively computing all of the terms in addition using tools derived from the same framework such as probability hypothesis density filtering we present inexpensive relative to the delta glmb filter look ahead strategies to reduce the number of computations characterization of the l 1 error in the multi target density arising from the truncation is presented

finding the k shortest paths we give algorithms for finding the k shortest paths not required to be simple connecting a pair of vertices in a digraph our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges in time o m n log n k we can also find the k shortest paths from a given source s to each vertex in the graph in total time o m n log n kn we describe applications to dynamic programming problems including the knapsack problem sequence alignment maximum inscribed polygons and genealogical relationship discovery

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

3 d object recognition using bipartite matching embedded in discrete relaxation the authors show how large efficiencies can be achieved in model based 3 d vision by combining the notions of discrete relaxation and bipartite matching the computational approach presented is capable of pruning large segments of search space an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations the time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided the algorithms do not take more than a couple of iterations even for objects with more than 30 surfaces

critical point theory for indefinite functionals with symmetries letxbe a hilbert space and c1 x r be strongly indefinite assume in addition that a compact lie groupgacts orthogonally onxand that is invariant in order to find critical points of we develop the limit relative category of fournieret al in the equivariant context we use this to prove two generalizations of the symmetric mountain pass theorem and a linking theorem in the case of the mountain pass theorem the mountain range is allowed to lie in a subspace of infinite codimension also other conditions of the classical symmetric mountain pass theorem forg z 2 due to ambrosetti and rabinowitz can be weakened considerably for example we are able to deal with infinite dimensional fixed point spaces the proofs consist of a direct reduction to a relative borsuk ulam type theorem this provides a new proof even for the classical mountain pass theorem the abstract critical point theorems are applied to an elliptic system with dirichlet boundary conditions we only need a weak version of the usual superquadraticity condition the linking theorem can be applied to asymptotically linear hamiltonian systems which are symmetric with respect to a generalized symplectic group action

nonlinear oscillations and boundary value problems for hamiltonian systems we prove the existence of solutions of various boundary value problems for nonautonomous hamiltonian systems with forcing terms begin gathered dot x t h p t x t p t g t hfill dot p t h x t x t p t f t hfill end gathered

dependence correlation and gaussianity in independent component analysis independent component analysis ica is the decomposition of a random vector in linear components which are as independent as possible here independence should be understood in its strong statistical sense it goes beyond second order decorrelation and thus involves the non gaussianity of the data the ideal measure of independence is the mutual information and is known to be related to the entropy of the components when the search for components is restricted to uncorrelated components this paper explores the connections between mutual information entropy and non gaussianity in a larger framework without resorting to a somewhat arbitrary decorrelation constraint a key result is that the mutual information can be decomposed under linear transforms as the sum of two terms one term expressing the decorrelation of the components and one expressing their non gaussianity our results extend the previous understanding of these connections and explain them in the light of information geometry we also describe the local geometry of ica by re expressing all our results via a gram charlier expansion by which all quantities of interest are obtained in terms of cumulants