coupled visual and kinematic manifold models for tracking in this paper we consider modeling data lying on multiple continuous manifolds in particular we model the shape manifold of a person performing a motion observed from different viewpoints along a view circle at a fixed camera height we introduce a model that ties together the body configuration kinematics manifold and visual observations manifold in a way that facilitates tracking the 3d configuration with continuous relative view variability the model exploits the low dimensionality nature of both the body configuration manifold and the view manifold where each of them are represented separately the resulting representation is used for tracking complex motions within a bayesian framework in which the model provides a low dimensional state representation as well as a constrained dynamic model for both body configuration and view variations experimental results estimating the 3d body posture from a single camera are presented for the humaneva dataset and other complex motion video sequences

some entire solutions to the competitive reaction diffusion system abstract this manuscript focuses on the study of the classical lotka volterra competitive reaction diffusion system morita and tachibana 2009 19 proved the existence of entire solutions of this system they used traveling front solutions the lower bound of the proportion between two components of which is positive to construct these entire solutions in order to reasonably explain this positive lower bound we investigate it based on the eigenvalues of the linearized system and show some sufficient and necessary conditions particularly if the parameters in the system satisfy some conditions then the positive lower bound spontaneously holds when the ratio is zero we also construct new entire solutions based on the super sub solution method the comparison theorem and a pair of exact traveling front solutions in addition another kind of entire solutions is revealed by the combination of traveling front solutions their reflects and the solutions of the diffusion free system

a regularized approach for geodesic based semisupervised multimanifold learning geodesic distance as an essential measurement for data dissimilarity has been successfully used in manifold learning however most geodesic distance based manifold learning algorithms have two limitations when applied to classification 1 class information is rarely used in computing the geodesic distances between data points on manifolds and 2 little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances in this paper we regard geodesic distance as a kind of kernel which maps data from linearly inseparable space to linear separable distance space in doing this a new semisupervised manifold learning algorithm namely regularized geodesic feature learning algorithm is proposed the method consists of three techniques a semisupervised graph construction method replacement of original data points with feature vectors which are built by geodesic distances and a new semisupervised dimension reduction method for feature vectors experiments on the mnist usps handwritten digit data sets mit cbcl face versus nonface data set and an intelligent traffic data set show the effectiveness of the proposed algorithm

time periodic traveling wave solutions for periodic advection reaction diffusion systems abstract we study the existence uniqueness and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection reaction diffusion systems under certain conditions we prove that there exists a maximal wave speed c such that for each wave speed c c there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system it is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co moving frame coordinate we also show that the traveling wave solutions with wave speed c c are asymptotically stable in certain sense in addition we establish the nonexistence of time periodic traveling waves with speed c c

traveling wave front for a two component lattice dynamical system arising in competition models abstract we study traveling front solutions for a two component system on a one dimensional lattice this system arises in the study of the competition between two species with diffusion or migration if we divide the habitat into discrete regions or niches we consider the case when the nonlinear source terms are of lotka volterra type and of monostable case we first show that there is a positive constant the minimal wave speed such that a traveling front exists if and only if its speed is above this minimal wave speed then we show that any wave profile is strictly monotone moreover under some conditions we show that the wave profile is unique up to translations for a given wave speed finally we characterize the minimal wave speed by the parameters in the system

analytical properties and exact solutions of the lotka volterra competition system the lotka volterra competition system with diffusion is considered the painleve property of this system is investigated exact traveling wave solutions of the lotka volterra competition system are found periodic solutions expressed in terms of the weierstrass elliptic function are also given

traveling wave solutions of lotka volterra competition systems with nonlocal dispersal in periodic habitats this paper is concerned with space periodic traveling wave solutions of the following lotka volterra competition system with nonlocal dispersal and space periodic dependence partial derivative u 1 partial derivative t integral r n kappa y x u 1 t y dy u 1 t x u 1 a 1 x b 1 x u 1 c 1 x u 1 x is an element of r n partial derivative u 2 partial derivative t integral r n kappa y x u 2 t y dy u 1 t x u 2 a 2 x b 2 x u 2 c 2 x u 2 x is an element of r n under suitable assumptions the system admits two semitrivial space periodic equilibria u 1 x 0 and 0 u 2 x where u 1 x 0 is linearly and globally stable and 0 u 2 x is linearly unstable with respect to space periodic perturbations by sub and supersolution techniques and comparison principals we show that for any given xi is an element of sn 1 there exists a continuous periodic traveling wave solution of the form u 1 t x u 2 t x phi 1 x ct xi ct xi 4 phi 2 x ct xi ct xi connecting u 1 0 and 0 u 2 and propagating in the direction of xi with speed c c xi where c xi is the spreading speed of the system in the direction of moreover for c c xi we also prove the asymptotic stability and uniqueness of traveling wave solution using squeezing techniques c 2016 elsevier inc all rights reserved

asymptotic stability of the critical pulled front in a lotka volterra competition model abstract we prove that the critical pulled front of lotka volterra competition systems is nonlinearly asymptotically stable more precisely we show that perturbations of the critical front decay algebraically with rate t 3 2 in a weighted l space our proof relies on pointwise semigroup methods and utilizes in a crucial way that the faster decay rate t 3 2 is a consequence of the lack of an embedded zero of the evans function at the origin for the linearized problem around the critical front

wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations linear diffusion is an established model for spatial spread in biological systems including movement of cell populations however for interacting closely packed cell populations simple diffusion is inappropriate because different cell populations will not move through one another rather a cell will stop moving when it encounters another cell in this paper i introduce a nonlinear diffusion term that reflects this phenomenon known as contact inhibition of migration i study this term in the context of two competing cell populations one of which has a proliferative advantage over the other this is motivated by the very early stages of solid tumour growth i focus in particular on travelling wave solutions corresponding to moving interfaces between the two cell populations numerical simulations indicate that there are wavefront solutions for wave speeds above a critical minimum value and i present linear analysis that explains the selection of wave speeds by initial conditions i obtain an approximation to the shape of these waves for high speeds and show that the minimum speed arises via quite new behaviour in the travelling wave equations with the proportion of cells of each type approaching a step function as the wave speed decreases towards the minimum exploiting this structure i use singular perturbation theory to investigate the wave shape for speeds close to the minimum

online similarity learning for visual tracking a novel metric learning approach is proposed to improve the visual tracking performance a computational efficient solution of the proposed learning method is derived the proposed metric learning method can reduce the classification errors incorporating metric learning in visual tracking applications has been demonstrated to be able to improve tracking performance however the optimal metric is mainly derived based on annotated feature vectors by studying their magnitude and intersection angle in complex scenarios the magnitude of feature samples may change drastically confining the matching performance of the distance metric moreover most distance learning methods are optimized in a time consuming iterative way which limits their applications in real time visual tracking to address these problems this paper proposes a novel metric called sphere similarity metric which normalizes the magnitude of feature vectors and measures the distance between pairs of vectors by their intersection angle such metric is robust even when the magnitude of feature vectors changes drastically in complex scenarios we formulate the proposed metric by a convex matrix function which does not require adapting samples magnitude iteratively and can be optimized in a closed form with low computational complexity additionally the proposed similarity metric can be learned in an online manner which accelerates the learning process and improves the tracking accuracy in visual tracking applications experimental results on synthetic data and benchmark video sequences show that the proposed metric learning method achieves better classification accuracy and its application in visual tracking outperforms the state of the art tracking methods

the asymptotic behavior of solutions of a system of reaction diffusion equations which models the belousov zhabotinskii chemical reaction abstract we investigate the boundary value problem u t 2 u x 2 u 1 u rv v t 2 v x 2 buv u t v t 0 u t 1 and v t t 0 where r 0 b 0 0 and x r this system has been proposed by murray as a model for the propagation of wave fronts of chemical activity in the belousov zhabotinskii chemical reaction here u and v are proportional to the concentrations of bromous acid and bromide ion respectively we determine the global stability of the constant solution u v 1 0 furthermore we introduce a moving coordinate and for each fixed x r we investigate the asymptotic behavior of u x ct t and v x ct t as t for both large and small values of the wave speed c 0

3d human motion tracking with a coordinated mixture of factor analyzers a major challenge in applying bayesian tracking methods for tracking 3d human body pose is the high dimensionality of the pose state space it has been observed that the 3d human body pose parameters typically can be assumed to lie on a low dimensional manifold embedded in the high dimensional space the goal of this work is to approximate the low dimensional manifold so that a low dimensional state vector can be obtained for efficient and effective bayesian tracking to achieve this goal a globally coordinated mixture of factor analyzers is learned from motion capture data each factor analyzer in the mixture is a locally linear dimensionality reducer that approximates a part of the manifold the global parametrization of the manifold is obtained by aligning these locally linear pieces in a global coordinate system to enable automatic and optimal selection of the number of factor analyzers and the dimensionality of the manifold a variational bayesian formulation of the globally coordinated mixture of factor analyzers is proposed the advantages of the proposed model are demonstrated in a multiple hypothesis tracker for tracking 3d human body pose quantitative comparisons on benchmark datasets show that the proposed method produces more accurate 3d pose estimates over time than those obtained from two previously proposed bayesian tracking methods

on an advection reaction diffusion competition system with double free boundaries modeling invasion and competition of aedes albopictus and aedes aegypti mosquitoes abstract based on the invasion of the aedes albopictus mosquitoes and the competition between ae albopictus and ae aegypti mosquitoes in the united states we consider an advection reaction diffusion competition system with two free boundaries consisting of an invasive species ae albopictus with density u and a local species ae aegypti with density v in which u invades the environment with leftward front x g t and rightward front x h t in the case that the competition between the two species is strong weak and species v wins over species u the solution u v converges uniformly to the semi positive equilibrium 0 1 while the two fronts satisfy that lim t g t h t g h r in the case that the competition between the two species is weak we show that when the advection coefficients are less than fixed thresholds there are two scenarios for the long time behavior of solutions i when the initial habitat h 0 4 1 2 1 and the initial value of u is sufficiently small the solution u v converges uniformly to the semi positive equilibrium 0 1 with the two fronts g h r ii when the initial habitat h 0 4 1 2 1 the solution u v converges locally uniformly to the interior equilibrium with the two fronts g h r in addition we propose an upper bound and a lower bound for the asymptotic spreading speeds of the leftward and rightward fronts numerical simulations are also provided to confirm our theoretical results

the stability of traveling wave front solutions of a reaction diffusion system we investigate the behavior of solutions of the problem begin gathered frac partial x partial t f x y frac d partial 2x partial zeta 2 quad frac partial y

tracking people on a torus we present a framework for monocular 3d kinematic pose tracking and viewpoint estimation of periodic and quasi periodic human motions from an uncalibrated camera the approach we introduce here is based on learning both the visual observation manifold and the kinematic manifold of the motion using a joint representation we show that the visual manifold of the observed shape of a human performing a periodic motion observed from different viewpoints is topologically equivalent to a torus manifold the approach we introduce here is based on the supervised learning of both the visual and kinematic manifolds instead of learning an embedding of the manifold we learn the geometric deformation between an ideal manifold conceptual equivalent topological structure and a twisted version of the manifold the data experimental results show accurate estimation of the 3d body posture and the viewpoint from a single uncalibrated camera

global asymptotic stability of lotka volterra 3 species reaction diffusion systems with time delays abstract this paper is concerned with three 3 species time delayed lotka volterra reaction diffusion systems and their corresponding ordinary differential systems without diffusion the time delays may be discrete or continuous and the boundary conditions for the reaction diffusion systems are of neumann type the goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady state solution for each of the three model problems these conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays the result of global asymptotic stability implies that each of the three model systems coexists is permanent and the trivial and all semitrivial solutions are unstable our approach to the problem is based on the method of upper and lower solutions for a more general reaction diffusion system which gives a common framework for the 3 species model problems some global stability results for the 2 species competition and prey predator reaction diffusion systems are included in the discussion

stability of traveling wavefronts for a discrete diffusive lotka volterra competition system abstract in this paper we study a discrete diffusive lotka volterra competition system it is known that this system has traveling wavefronts we prove that the traveling wavefronts are exponentially stable when the initial perturbation around the traveling wavefronts decays exponentially as x but can be arbitrarily large in other locations the approach we use here is the comparison principle and the weighted energy method

minimal speed selection of traveling waves to the lotka volterra competition model abstract in this paper the minimal speed determinacy of traveling wave fronts of a two species competition model of diffusive lotka volterra type is investigated first a cooperative system is obtained from the classical lotka volterra competition model then we apply the upper lower solution technique on the cooperative system to study the traveling waves as well as its minimal speed selection mechanisms linear or nonlinear new types of upper and lower solutions are established previous results for the linear speed selection are extended and novel results on both linear and nonlinear selections are derived

efficient isometric multi manifold learning based on the self organizing method geodesic distance as an essential measurement for data similarity has been successfully used in manifold learning however many geodesic based isometric manifold learning algorithms such as the isometric feature mapping isomap and geonlm fail to work on data that distribute on clusters or multiple manifolds this limits their applications because practical data sets generally distribute on multiple manifolds in this paper we propose a new isometric multi manifold learning method called multi manifold proximity embedding mpe which can be efficiently optimized using the gradient descent method or the self organizing method compared with the previous methods the proposed method has two steps which can isometrically learn data distributed on several manifolds and is more accurate in preserving both the intra manifold and the inter manifold geodesic distances the effectiveness of the proposed method in recovering the nonlinear data structure and clustering is demonstrated through experiments on both synthetically and real data sets

the minimal wave speed to the lotka volterra competition model abstract this paper focuses on selection mechanisms of the minimal speed of traveling waves to the lotka volterra reaction diffusion model we first establish general conditions for the linear and nonlinear selection by way of an upper and lower solution method then some explicit criteria are derived by subtly constructing formulas of upper and lower solutions the obtained conditions substantially improve or complement the corresponding results in the known references

entire solutions of diffusive lotka volterra system abstract this work is concerned with the existence of entire solutions of the diffusive lotka volterra competition system on the real line we prove the existence of some entire solutions that are asymptotic as t to a traveling wave consisting of a single species depending on system parameters these entire solutions evolve into two ore more stacked invasion waves as t our results cover both the weak and strong competition case in the weak competition case the existence of a class of entire solutions that forms a 4 dimensional manifold is proved

learning representations from multiple manifolds the problem we address in this paper is how to learn joint representation from data lying on multiple manifolds we are given multiple data sets and there is an underlying common manifold among the different data sets each data set is considered to be an instance of this common manifold the goal is to achieve an embedding of all the points on all the manifolds in a way that preserves the local structure of each manifold and that at the same time collapses all the different manifolds into one manifold in the embedding space while preserving the implicit correspondences between the points across different data sets we propose a framework to learn embedding of such data which can preserve the intra manifolds local geometric structure and the inter manifolds correspondence structure the proposed solution works as extensions to current state of the art spectral embedding approaches to handling multiple manifolds graphical abstractdisplay omitted highlightsa framework to learn joint embedding space from multiple manifold data is presented intra manifolds geometric structure and inter manifolds structure are preserved implicit correspondence between the points across different data sets is estimated several embedding examples in different data sets are provided current spectral embedding approaches are extended to handle multiple manifolds

a maximum principle for diffusive lotka volterra systems of two competing species abstract using an elementary approach we establish a new maximum principle for the diffusive lotka volterra system of two competing species which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function the first derivative of another function and a quadratic nonlinearity this maximum principle gives a priori estimates for the total mass of the two species moreover applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions

existence and stability of time periodic traveling waves for a periodic bistable lotka volterra competition system abstract this paper is concerned with the time periodic lotka volterra competition diffusion system u t d 1 t u x x u r 1 t a 1 t u b 1 t v v t d 2 t v x x v r 2 t a 2 t u b 2 t v x r t 0 where d i t r i t a i t b i t c 2 r are t periodic functions 0 1 i 1 2 under certain conditions the system admits two stable semi trivial periodic solutions p t 0 and 0 q t and a unique coexistence periodic solution u 0 t v 0 t which is unstable and satisfies 0 u 0 t p t and 0 v 0 t q t for t 0 t in this paper we prove that the system admits a time periodic traveling wave solution u x t v x t u x c t t v x c t t connecting two periodic solutions p t 0 and 0 q t as x where c is the wave speed by using a dynamical method we show that the time periodic traveling wave solution u x c t t v x c t t is asymptotically stable and unique modulo translation for front like initial values

traveling curved fronts of bistable lotka volterra competition diffusion systems in r 3 this paper is concerned with the existence and other qualitative properties of three dimensional traveling curved fronts for bistable lotka volterra competition diffusion systems in r 3 it is first shown that there exists a traveling front of convex polyhedral shape to such systems which is asymptotically stable then by taking the limits of such solutions as lateral surfaces go to infinity one proves the existence as well as the uniqueness of a three dimensional traveling curved front for any given g c s 1 with min 0 2 g 0