on some applications of cellular automata abstract cellular automata model corresponding to cattaneo s diffusion is constructed its phase space is given delay is shown to decrease the chaotic damage spread region then cellular automata are used to study a stochastic minority game payoff memory approach introduced by smale is used a corresponding dynamical system is also derived cellular automata model for an epidemic in a population whose individuals are cycling between two places is constructed both cases of uniform and random susceptibilities are included

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

image denoising using the higher order singular value decomposition in this paper we propose a very simple and elegant patch based machine learning technique for image denoising using the higher order singular value decomposition hosvd the technique simply groups together similar patches from a noisy image with similarity defined by a statistically motivated criterion into a 3d stack computes the hosvd coefficients of this stack manipulates these coefficients by hard thresholding and inverts the hosvd transform to produce the final filtered image our technique chooses all required parameters in a principled way relating them to the noise model we also discuss our motivation for adopting the hosvd as an appropriate transform for image denoising we experimentally demonstrate the excellent performance of the technique on grayscale as well as color images on color images our method produces state of the art results outperforming other color image denoising algorithms at moderately high noise levels a criterion for optimal patch size selection and noise variance estimation from the residual images after denoising is also presented

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

bayesian robust tensor factorization for incomplete multiway data we propose a generative model for robust tensor factorization in the presence of both missing data and outliers the objective is to explicitly infer the underlying low candecomp parafac cp rank tensor capturing the global information and a sparse tensor capturing the local information also considered as outliers thus providing the robust predictive distribution over missing entries the low cp rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior while the sparse tensor is modeled by a hierarchical view of student t distribution that associates an individual hyperparameter with each element independently for model learning we develop an efficient variational inference under a fully bayesian treatment which can effectively prevent the overfitting problem and scales linearly with data size in contrast to existing related works our method can perform model selection automatically and implicitly without the need of tuning parameters more specifically it can discover the groundtruth of cp rank and automatically adapt the sparsity inducing priors to various types of outliers in addition the tradeoff between the low rank approximation and the sparse representation can be optimized in the sense of maximum model evidence the extensive experiments and comparisons with many state of the art algorithms on both synthetic and real world data sets demonstrate the superiorities of our method from several perspectives

image classification using correlation tensor analysis images as high dimensional data usually embody large variabilities to classify images for versatile applications an effective algorithm is necessarily designed by systematically considering the data structure similarity metric discriminant subspace and classifier in this paper we provide evidence that besides the fisher criterion graph embedding and tensorization used in many existing methods the correlation based similarity metric embodied in supervised multilinear discriminant subspace learning can additionally improve the classification performance in particular a novel discriminant subspace learning algorithm called correlation tensor analysis cta is designed to incorporate both graph embedded correlational mapping and discriminant analysis in a fisher type of learning manner the correlation metric can estimate intrinsic angles and distances for the locally isometric embedding which can deal with the case when euclidean metric is incapable of capturing the intrinsic similarities between data points cta learns multiple interrelated subspaces to obtain a low dimensional data representation reflecting both class label information and intrinsic geometric structure of the data distribution extensive comparisons with most popular subspace learning methods on face recognition evaluation demonstrate the effectiveness and superiority of cta parameter analysis also reveals its robustness

bv solutions for hyperbolic systems of balance laws with relaxation abstract for hyperbolic systems of balance laws with source manifesting relaxation it is shown that the kawashima condition which yields global classical solutions with smooth initial values near equilibrium is also instrumental in inducing the existence of global admissible bv solutions accommodating shocks

generalized higher order orthogonal iteration for tensor learning and decomposition low rank tensor completion lrtc has successfully been applied to a wide range of real world problems despite the broad successful applications existing lrtc methods may become very slow or even not applicable for large scale problems to address this issue a novel core tensor trace norm minimization ctnm method is proposed for simultaneous tensor learning and decomposition and has a much lower computational complexity in our solution first the equivalence relation of trace norm of a low rank tensor and its core tensor is induced second the trace norm of the core tensor is used to replace that of the whole tensor which leads to two much smaller scale matrix tnm problems finally an efficient alternating direction augmented lagrangian method is developed to solve our problems our ctnm formulation needs only o r n nri log sqrt i n observations to reliably recover an n th order i times i times cdots times i tensor of n rank r r ldots r compared with o ri n 1 observations required by those tensor tnm methods i gg r geq r extensive experimental results show that ctnm is usually more accurate than them and is orders of magnitude faster

patched tube unitary transform for robust tensor completion abstract the aim of the robust tensor completion problem for third order tensors is to recover a low rank tensor from incomplete and or corrupted observations in this paper we develop a patched tubes unitary transform method for robust tensor completion the proposed method is to extract similar patched tubes to form a third order sub tensor and then a transformed tensor singular value decomposition is employed to recover such low rank incomplete and or corrupted sub tensor here the unitary transform matrix for transformed tensor singular value decomposition is constructed by using left singular vectors of the unfolding matrix arising from such sub tensor moreover we establish the perturbation results of the transformed tensor singular value decomposition for patched tubes tensor completion extensive numerical experiments on hyperspectral video and face data sets are presented to demonstrate the superior performance of the proposed patched tubes unitary transform method over testing state of the art robust tensor completion methods

asymptotic stability and relaxation for fast chemistry fluids abstract global existence for multicomponent reactive fluids with fast chemistry is investigated the system of partial differential equations derived from the kinetic theory is symmetrizable hyperbolic parabolic with stiff chemical sources new a priori estimates are obtained uniformly with respect to chemistry relaxation times and lead to asymptotic stability results for well prepared initial conditions convergence towards the chemical equilibrium fluid model when chemistry times go to zero is established as well as error estimates

asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions under the shizuta kawashima condition we show that these solutions approach constant equilibrium state in the lp norm at a rate o t m 2 1 1 p as t tends to infty for p in min m 2 infty moreover we can show that we can approximate with a faster order of convergence theconservative part of the solution in terms of the linearized hyperbolic operator for m 2 and by a parabolic equation in the spirit of chapman enskog expansion the main tool is given by a detailed analysis of the green function for the linearized problem

approximation of the multi dimensional incompressible navier stokes equations by discrete velocity vector bgk models abstract in this paper we prove that a class of discrete velocity vector bgk models can be used as approximations to the multi dimensional incompressible navier stokes equations on the torus the proof relies crucially on two constructions a new symmetrizer and approximate solutions the former renders us a natural setting for energy estimates and the latter is motivated by the maxwell iteration simple and concise stability conditions are also obtained for a number of concrete 2 or 3 dimensional bgk models

epidemic dynamics discrete time and cellular automaton models abstract we present a simple model of population dynamics in the presence of an infection the model is based on discrete time equations for sane and infected populations in interaction and correctly describes the dynamics of the epidemic we find that for some choices of the parameters the model can possess conserved quantities we also propose an ultra discrete cellular automaton version of the model which despite its extremely simple structure still captures the essence of the epidemic dynamics

framelet representation of tensor nuclear norm for third order tensor completion the main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third order tensor recovery in the literature the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete fourier transform matrix and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all fourier transformed matrix frontal slices these fourier transformed matrix frontal slices are obtained by applying the discrete fourier transform on the tubes of the original tensor in this paper we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed because of framelet basis redundancy the representation of each tube is sparsely represented when the matrix slices of the original tensor are highly correlated we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small and the resulting tensor completion can be performed much better the proposed minimization model is convex and global minimizers can be obtained numerical results on several types of multi dimensional data videos multispectral images and magnetic resonance imaging data have tested and shown that the proposed method outperformed the other testing methods

moving object detection using tensor based low rank and saliently fused sparse decomposition in this paper we propose a new low rank and sparse representation model for moving object detection the model preserves the natural space time structure of video sequences by representing them as three way tensors then it operates the low rank background and sparse foreground decomposition in the tensor framework on the one hand we use the tensor nuclear norm to exploit the spatio temporal redundancy of background based on the circulant algebra on the other we use the new designed saliently fused sparse regularizer sfs to adaptively constrain the foreground with spatio temporal smoothness to refine the existing foreground smooth regularizers the sfs incorporates the local spatio temporal geometric structure information into the tensor total variation by using the 3d locally adaptive regression kernel 3d lark what is more the sfs further uses the 3d lark to compute the space time motion saliency of foreground which is combined with the l 1 norm and improves the robustness of foreground extraction finally we solve the proposed model with globally optimal guarantee extensive experiments on challenging well known data sets demonstrate that our method significantly outperforms the state of the art approaches and works effectively on a wide range of complex scenarios

tensor n tubal rank and its convex relaxation for low rank tensor recovery abstract the recent popular tensor tubal rank defined based on tensor singular value decomposition t svd yields promising results however its framework is applicable only to three way tensors and lacks the flexibility necessary tohandle different correlations along different modes to tackle these two issues we define a new tensor unfolding operator named mode k 1 k 2 tensor unfolding as the process of lexicographically stacking all mode k 1 k 2 slices of an n way tensor into a three way tensor which is a three way extension of the well known mode k tensor matricization on this basis we define a novel tensor rank named the tensor n tubal rank as a vector consisting of the tubal ranks of all mode k 1 k 2 unfolding tensors to depict the correlations along different modes to efficiently minimize the proposed n tubal rank we establish its convex relaxation the weighted sum of the tensor nuclear norm wstnn then we apply the wstnn to low rank tensor completion lrtc and tensor robust principal component analysis trpca the corresponding wstnn based lrtc and trpca models are proposed and two efficient alternating direction method of multipliers admm based algorithms are developed to solve the proposed models numerical experiments demonstrate that the proposed models significantly outperform the compared ones

oscillating epidemics a discrete time model abstract we study a model of an epidemic where the individuals which are cured from the infection are not permanently immunised but have a finite probability of becoming reinfected we show that the epidemic does not follow the usual pattern of growth and decay but rather oscillates towards an endemic fixed point where a certain number of infectives may persist we present a discrete time version of the model which may also serve as an integrator of the continuous time one an appropriate choice of the discrete system allows the derivation of a cellular automaton version which incorporates the essential dynamical behaviour of the model

stationary states and spatial patterning in an sis epidemiology model with implicit mobility abstract by means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an s i s model in which the individuals are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size q here we consider the following cases q is fixed at certain value and q is taken at random at each step and for each individual the obtained numerical data are then mapped onto the solution of its version corresponding to the limit q this allows for deducing an explicit form of the dependence of the fraction of infected individuals on the curing rate a detailed analysis of the appearance of spatial patterns of infected individuals in the stationary state is performed

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

the twist tensor nuclear norm for video completion in this paper we propose a new low rank tensor model based on the circulant algebra namely twist tensor nuclear norm t tnn the twist tensor denotes a three way tensor representation to laterally store 2 d data slices in order on one hand t tnn convexly relaxes the tensor multirank of the twist tensor in the fourier domain which allows an efficient computation using fast fourier transform on the other t tnn is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain which extends the traditional matrix nuclear norm in a block circulant way we test the t tnn model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness especially when dealing with video recorded by a nonstationary panning camera the block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance this representation after transformation exploits the horizontal translation relationship between the frames in a video and endows the t tnn model with a more powerful ability to reconstruct panning videos than the existing state of the art low rank models

simultaneous tensor decomposition and completion using factor priors the success of research on matrix completion is evident in a variety of real world applications tensor completion which is a high order extension of matrix completion has also generated a great deal of research interest in recent years given a tensor with incomplete entries existing methods use either factorization or completion schemes to recover the missing parts however as the number of missing entries increases factorization schemes may overfit the model because of incorrectly predefined ranks while completion schemes may fail to interpret the model factors in this paper we introduce a novel concept complete the missing entries and simultaneously capture the underlying model structure to this end we propose a method called simultaneous tensor decomposition and completion stdc that combines a rank minimization technique with tucker model decomposition moreover as the model structure is implicitly included in the tucker model we use factor priors which are usually known a priori in real world tensor objects to characterize the underlying joint manifold drawn from the model factors by exploiting this auxiliary information our method leverages two classic schemes and accurately estimates the model factors and missing entries we conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real world data the results demonstrate the efficacy of the proposed method and its potential usage in tensor based applications it also outperforms state of the art methods on multilinear model analysis and visual data completion tasks

existence of traveling wave solutions for hyperbolic systems of balance laws this paper is concerned with traveling wave solutions for hyperbolic systems of balance laws satisfying a stability condition and a kawashima like condition we are interested in the case where the traveling wave equations have a singularity which is absent for 2 2 systems satisfying the two conditions to deal with the singularity we reduce the problem to a parametrized one without singularity by using the center manifold theorem for the parametrized problem we prove the existence of solutions by modifying an existing argument in the literature in this way we show the existence of traveling wave solutions

multi view intact space learning it is practical to assume that an individual view is unlikely to be sufficient for effective multi view learning therefore integration of multi view information is both valuable and necessary in this paper we propose the multi view intact space learning misl algorithm which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data even though each view on its own is insufficient we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning employing the cauchy loss a technique used in statistical learning as the error measurement strengthens robustness to outliers we propose a new definition of multi view stability and then derive the generalization error bound based on multi view stability and rademacher complexity and show that the complementarity between multiple views is beneficial for the stability and generalization misl is efficiently optimized using a novel iteratively reweight residuals irr technique whose convergence is theoretically analyzed experiments on synthetic data and real world datasets demonstrate that misl is an effective and promising algorithm for practical applications

an order p tensor factorization with applications in imaging operations with tensors or multiway arrays are increasingly prevalent in many applications involving multiway data analysis this paper extends a third order factorization strategy and tensor operations defined in a recent paper m e kilmer and c d martin linear algebra appl 435 2011 pp 641 658 to order p tensors the extension to order p tensors is explained in a recursive way but for computational speed is implemented directly using the fast fourier transform a major motivation for considering factorization strategies for order p tensors is to devise new types of algorithms for general order p tensors which can be used in applications we conclude with two applications in imaging the first application is image deblurring and the second application is video facial recognition both applications involve order 4 tensors

robust low rank tensor minimization via a new tensor spectral k support norm recently based on a new tensor algebraic framework for third order tensors the tensor singular value decomposition t svd and its associated tubal rank definition have shed new light on low rank tensor modeling its applications to robust image video recovery and background modeling show promising performance due to its superior capability in modeling cross channel frame information under the t svd framework we propose a new tensor norm called tensor spectral k support norm tsp k by an alternative convex relaxation as an interpolation between the existing tensor nuclear norm tnn and tensor frobenius norm tfn it is able to simultaneously drive minor singular values to zero to induce low rankness and to capture more global information for better preserving intrinsic structure we provide the proximal operator and the polar operator for the tsp k norm as key optimization blocks along with two showcase optimization algorithms for medium and large size tensors experiments on synthetic image and video datasets in medium and large sizes all verify the superiority of the tsp k norm and the effectiveness of both optimization methods in comparison with the existing counterparts

existence of relaxation shock profiles for hyperbolic conservation laws in this paper we prove that like viscosity relaxation can also smooth weak shocks for strict hyperbolic conservation laws as equilibium systems of hyperbolic relaxation systems under some natural structural conditions these conditions were derived previously by yong from stability considerations and hence are entirely analogous to the majda pego criterion of the viscous case the proof involves a new parametrization of hugoniot curves and a delicate analysis of the algebraic structure of relaxation systems as well as construction of an appropriate center manifold

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

dissipative structure and entropy for hyperbolic systems of balance laws in this paper we introduce an entropy condition for hyperbolic systems of balance laws under this condition we use the chapman enskog expansion to derive the corresponding viscous conservation laws further structural conditions are discussed in order to develop local and global existence theories for the balance laws and viscous conservation laws

validity of the chapman enskog expansion for a class of hyperbolic relaxation systems this paper presents a validity proof of the chapman enskog expansion for a class of hyperbolic relaxation systems this class is characterized with a set of conservation dissipation structural conditions and contains many classical models from mathematical physics our main result confirms that the hyperbolic relaxation systems can be well approximated in the time interval where the corresponding conservation laws have smooth solutions with the corresponding viscous systems derived by using the chapman enskog expansion

an interesting class of partial differential equations this paper presents an observation that under reasonable conditions many partial differential equations from mathematical physics possess three structural properties one of them can be understand as a variant of the celebrated onsager reciprocal relation in modern thermodynamics it displays a direct relation of irreversible processes to the entropy change we show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems as an application of the observation we propose an approximation method to solve relaxation problems moreover the observation is interpreted physically and verified with eight sets of systems from different fields

generalized unitarily invariant gauge regularization for fast low rank matrix recovery spectral regularization is a widely used approach for low rank matrix recovery lrmr by regularizing matrix singular values most of the existing lrmr solvers iteratively compute the singular values via applying singular value decomposition svd on a dense matrix which is computationally expensive and severely limits their applications to large scale problems to address this issue we present a generalized unitarily invariant gauge guig function for lrmr the proposed guig function does not act on the singular values however we show that it generalizes the well known spectral functions including the rank function the schatten p quasi norm and logsum of singular values the proposed guig regularization model can be formulated as a bilinear variational problem which can be efficiently solved without computing svd such a property makes it well suited for large scale lrmr problems we apply the proposed guig model to matrix completion and robust principal component analysis and prove the convergence of the algorithms experimental results demonstrate that the proposed guig method is not only more accurate but also much faster than the state of the art algorithms especially on large scale problems

robust low rank tensor recovery with regularized redescending m estimator this paper addresses the robust low rank tensor recovery problems tensor recovery aims at reconstructing a low rank tensor from some linear measurements which finds applications in image processing pattern recognition multitask learning and so on in real world applications data might be contaminated by sparse gross errors however the existing approaches may not be very robust to outliers to resolve this problem this paper proposes approaches based on the regularized redescending m estimators which have been introduced in robust statistics the robustness of the proposed approaches is achieved by the regularized redescending m estimators however the nonconvexity also leads to a computational difficulty to handle this problem we develop algorithms based on proximal and linearized block coordinate descent methods by explicitly deriving the lipschitz constant of the gradient of the data fitting risk the descent property of the algorithms is present moreover we verify that the objective functions of the proposed approaches satisfy the kurdyka ojasiewicz property which establishes the global convergence of the algorithms the numerical experiments on synthetic data as well as real data verify that our approaches are robust in the presence of outliers and still effective in the absence of outliers

generalized tensor function via the tensor singular value decomposition based on the t product abstract in this paper we present the definition of generalized tensor function according to the tensor singular value decomposition t svd based on the tensor t product also we introduce the compact singular value decomposition t csvd of tensors from which the projection operators and moore penrose inverse of tensors are obtained we establish the cauchy integral formula for tensors by using the partial isometry tensors and apply it into the solution of tensor equations then we establish the generalized tensor power and the taylor expansion of tensors explicit generalized tensor functions are listed we define the tensor bilinear and sesquilinear forms and propose theorems on structures preserved by generalized tensor functions for complex tensors we established an isomorphism between complex tensors and real tensors in the last part of our paper we find that the block circulant operator establishes an isomorphism between tensors and matrices this isomorphism is used to prove the f stochastic structure is invariant under generalized tensor functions the concept of invariant tensor cones is raised

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

tensor based formulation and nuclear norm regularization for multienergy computed tomography the development of energy selective photon counting x ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation under the assumption of perfect energy resolution here we propose a tensor based iterative algorithm that simultaneously reconstructs the x ray attenuation distribution for each energy we use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor based regularizers in particular we model the multispectral unknown as a three way tensor where the first two dimensions are space and the third dimension is energy this approach allows for the design of tensor nuclear norm regularizers which like its 2d counterpart is a convex function of the multispectral unknown the solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective spectral computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent

correlation metric for generalized feature extraction beyond linear and kernel based feature extraction we propose in this paper the generalized feature extraction formulation based on the so called graph embedding framework two novel correlation metric based algorithms are presented based on this formulation correlation embedding analysis cea which incorporates both correlational mapping and discriminating analysis boosts the discriminating power by mapping data from a high dimensional hypersphere onto another low dimensional hypersphere and preserving the intrinsic neighbor relations with local graph modeling correlational principal component analysis cpca generalizes the conventional principal component analysis pca algorithm to the case with data distributed on a high dimensional hypersphere their advantages stem from two facts 1 tailored to normalized data which are often the outputs from the data preprocessing step and 2 directly designed with correlation metric which shows to be generally better than euclidean distance for classification purpose extensive comparisons with existing algorithms on visual classification experiments demonstrate the effectiveness of the proposed algorithms

a second order phase transition in the complete graph stochastic epidemic model abstract a stochastic model for epidemic spread in a set of individuals placed upon the sites of a complete graph of relations is investigated the model is defined by three parameters the number of individuals or sites n the probability that an infected site transmits the disease to a susceptible site and the probability of recovery of infected sites both referred to the unit of time we show that this system evolves towards a approximately gaussian stationary distribution of infected sites whose mean and variance can be analytically estimated also we find that the average fraction of infected sites x is zero for transmission probabilities below the critical value c 1 e n and grows linearly with for 0 c 1 a sharp peak observed in monte carlo simulations of the variance of the number of infected sites as a function of allows us to classify this dynamical phase transition as second order with x playing the role of an order parameter some consequences of this model to the dynamics of highly connected complex systems such as the brain cortex are also discussed

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

large margin multi viewinformation bottleneck in this paper we extend the theory of the information bottleneck ib to learning from examples represented by multi view features we formulate the problem as one of encoding a communication system with multiple senders each of which represents one view of the data based on the precise components filtered out from multiple information sources through a bottleneck a margin maximization approach is then used to strengthen the discrimination of the encoder by improving the code distance within the frame of coding theory the resulting algorithm therefore inherits all the merits of the ib principle and coding theory it has two distinct advantages over existing algorithms namely that our method finds a tradeoff between the accuracy and complexity of the multi view model and that the encoded multi view data retains sufficient discrimination for classification we also derive the robustness and generalization error bound of the proposed algorithm and reveal the specific properties of multi view learning first the complementarity of multi view features guarantees the robustness of the algorithm second the consensus of multi view features reduces the empirical rademacher complexity of the objective function enhances the accuracy of the solution and improves the generalization error bound of the algorithm the resulting objective function is solved efficiently using the alternating direction method experimental results on annotation classification and recognition tasks demonstrate that the proposed algorithm is promising for practical applications

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws

twist tensor total variation regularized reweighted nuclear norm based tensor completion for video missing area recovery abstract this paper focuses on recovering multi dimensional signal called tensor which is corrupted by random missing areas the performance of the conventional tensor completion techniques deteriorate when the tensor multi rank is large and or large missing areas moreover these techniques are weak in preserving the edges in the signals like images videos this paper proposes an efficient method to overcome these problems by simultaneously combining novel twist tensor total variation norm to exploit spatio temporal correlation and tensor singular value decomposition t svd based reweighted nuclear norm to improve low multi rank tensor recovery the twist tensor total variation norm takes care of edges in the recovered data and aids the recovery of missing areas by utilising the similarities in the adjacent samples the reweighted nuclear norm handles corrupted large rank tensors by sparsity enhancement via reweighting its singular values the effectiveness of the proposed method is established by applying to video completion problem and experimental results reveal that the algorithm outperforms its counterparts

on modeling epidemics including latency incubation and variable susceptibility abstract a cellular automata model for an epidemic is given it includes inhomogeneous mixing latency incubation andvariable suscepibility to the disease these features are shown to be extremely difficult to be studied using differential equations

population dynamics models based on the transmission mechanism of mcr 1 abstract antimicrobial resistance is now considered as one of the most serious global threats to human health in the 21st century recently the discovery of a plasmid borne colistin resistance gene mcr 1 in china heralds the emergence of truly pan drug resistant bacteria the gene has been found primarily in escherichia coli but has also been identified in other members of the enterobacteriaceae in animal food human and environmental samples on every continent until now the articles published have appeared to fairly use and interpret experimental studies the aim of our work is to develop mathematic models that quantitatively describe the dynamic of the population of domestic animals and humans we propose two ordinary differential equation models for the transmission dynamic of mcr 1 gene the models are analyzed using stability theory of differential equations positive equilibrium points of the system are investigated and their stability analyses are carried out moreover the numerical simulations of the proposed model are also represented our results show that the fraction of animals used for human consumption is the most effective parameters of controlling the spread of mcr 1 gene in comparison with other parameters

global classical solutions for partially dissipative hyperbolic system of balance laws the basic existence theory of kato and majda enables us to obtain local in time classical solutions to generally quasilinear hyperbolic systems in the framework of sobolev spaces in x with higher regularity however it remains a challenging open problem whether classical solutions still preserve well posedness in the case of critical regularity this paper is concerned with partially dissipative hyperbolic system of balance laws under the entropy dissipative assumption we establish the local well posedness and blow up criterion of classical solutions in the framework of besov spaces with critical regularity with the aid of the standard iteration argument and friedrichs regularization method then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous chemin lerner spaces mixed space time besov spaces this fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well posedness and stability by assuming at all times the shizuta kawashima algebraic condition as a direct application the corresponding well posedness and stability of classical solutions to the compressible euler equations with damping are also obtained

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

third order tensors as linear operators on a space of matrices abstract a recently proposed tensor tensor multiplication m e kilmer c d martin l perrone a third order generalization of the matrix svd as a product of third order tensors tech rep tr 2008 4 tufts university october 2008 opens up new avenues to understanding the action of n n n tensors on a space of n n matrices in particular it emphasizes the need to understand the space of objects upon which tensors act this paper defines a free module and shows that every linear transformation on that module can be represented by tensor multiplication in addition it presents a generalization of ideas of eigenvalue and eigenvector to the space of n n n tensors

a fused cp factorization method for incomplete tensors low rank tensor completion methods have been advanced recently for modeling sparsely observed data with a multimode structure however low rank priors may fail to interpret the model factors of general tensor objects the most common method to address this drawback is to use regularizations together with the low rank priors however due to the complex nature and diverse characteristics of real world multiway data the use of a single or a few regularizations remains far from efficient and there are limited systematic experimental reports on the advantages of these regularizations for tensor completion to fill these gaps we propose a modified cp tensor factorization framework that fuses the l 2 norm constraint sparseness l 1 norm manifold and smooth information simultaneously the factorization problem is addressed through a combination of nesterov s optimal gradient descent method and block coordinate descent here we construct a smooth approximation to the l 1 norm and tv norm regularizations and then the tensor factor is updated using the projected gradient method where the step size is determined by the lipschitz constant extensive experiments on simulation data visual data completion intelligent transportation systems and gps data of user involvement are conducted and the efficiency of our method is confirmed by the results moreover the obtained results reveal the characteristics of these commonly used regularizations for tensor completion in a certain sense and give experimental guidance concerning how to use them

structural stability of a 1d compressible viscoelastic fluid model abstract this paper is concerned with a compressible viscoelastic fluid model proposed by ottinger although the model has a convex entropy the hessian matrix of the entropy does not symmetrize the system of first order partial differential equations due to the non conservative terms in the constitutive equation we show that the corresponding 1d model is symmetrizable hyperbolic and dissipative and satisfies the kawashima condition based on these we prove the global existence of smooth solutions near equilibrium and justify the compatibility of the model with the navier stokes equations

materials with internal variables and relaxation to conservation laws the theory of materials with internal state variables of coleman gurtin cg provides a natural framework to investigate the structure of relaxation approximations of conservation laws from the viewpoint of continuum thermomechanics after reviewing the requirements imposed on constitutive theories by the principle of consistency with the clausius duhem inequality we pursue two specific theories pertaining to stress relaxation and relaxation of internal energy they each lead to a relaxation framework for the theory of thermoelastic non conductors of heat equipped with globally defined entropy functions for the associated relaxation process next we consider a semilinear model problem of stress relaxation we discuss uniform stability and compactness for solutions of the relaxation system in the zero relaxation limit and establish convergence to the system of isothermal elastodynamics by using compensated compactness finally we prove a strong dissipation estimate for the relaxation approximations proposed in jin xin jx when the limit system is equipped with a strictly convex entropy