a generalization of the caginalp phase field system based on the cattaneo law abstract we consider in this article a generalization of the caginalp model for phase transitions based on the maxwell cattaneo law instead of the classical fourier law in particular we prove the existence and uniqueness of solutions we finally study the spatial behavior of the solutions in a semi infinite cylinder

learning multiple tasks with kernel methods we study the problem of learning many related tasks simultaneously using kernel methods and regularization the standard single task kernel methods such as support vector machines and regularization networks are extended to the case of multi task learning our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi task kernel functions we define is used these kernels model relations among the tasks and are derived from a novel form of regularizers specific kernels that can be used for multi task learning are provided and experimentally tested on two real data sets in agreement with past empirical work on multi task learning the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single task learning particularly when there are many related tasks but few data per task

convergence to equilibrium for a parabolic hyperbolic phase field system with dynamical boundary condition abstract this paper is concerned with the well posedness and the asymptotic behavior of solutions to the following parabolic hyperbolic phase field system 0 1 t 0 t t t 0 in 0 subject to the neumann boundary condition for 0 2 0 on 0 the dynamical boundary condition for 0 3 t 0 on 0 and the initial conditions 0 4 0 0 0 0 t 0 1 in where is a bounded domain in r 3 with smooth boundary is the outward normal direction to the boundary and is a real analytic function in this paper we first establish the existence and uniqueness of a global strong solution to 0 1 0 4 then we prove its convergence to an equilibrium as time goes to infinity and we provide an estimate of the convergence rate

periodic solutions of linear and quasilinear neutral functional differential equations abstract in this paper we will use the fourier expansions to generalize hale s alternative results for the existence of periodic solutions of linear retarded functional differential equations to neutral equations using some a priori estimation and the leray schauder degree theory we will obtain some existence theorems of periodic solutions for a class of quasilinear neutral equations the results also generalize the works of hatvani and krisztin on retarded equations

trace norm regularization reformulations algorithms and multi task learning we consider a recently proposed optimization formulation of multi task learning based on trace norm regularized least squares while this problem may be formulated as a semidefinite program sdp its size is beyond general sdp solvers previous solution approaches apply proximal gradient methods to solve the primal problem we derive new primal and dual reformulations of this problem including a reduced dual formulation that involves minimizing a convex quadratic function over an operator norm ball in matrix space this reduced dual problem may be solved by gradient projection methods with each projection involving a singular value decomposition the dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis

reduced rank regression via adaptive nuclear norm penalization we propose an adaptive nuclear norm penalization approach for low rank matrix approximation and use it to develop a new reduced rank estimation method for high dimensional multivariate regression the adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix and it is generally non convex under the natural restriction that the weight decreases with the singular value however we show that the proposed non convex penalized regression method has a global optimal solution obtained from an adaptively soft thresholded singular value decomposition the method is computationally efficient and the resulting solution path is continuous the rank consistency of and prediction estimation performance bounds for the estimator are established for a high dimensional asymptotic regime simulation studies and an application in genetics demonstrate its efficacy

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

robust l1 principal component analysis and its bayesian variational inference we introduce a robust probabilistic l1 pca model in which the conventional gaussian distribution for the noise in the observed data was replaced by the laplacian distribution or l1 distribution due to the heavy tail characteristics of the l1 distribution the proposed model is supposed to be more robust against data outliers in this letter we demonstrate how a variational approximation scheme enables effective inference of key parameters in the probabilistic l1 pca model as the l1 density can be expanded as a superposition of infinite number of gaussian densities we express the l1 pca model as a marginalized model over the superpositions by doing so a tractable bayesian inference can be achieved based on the variational expectation maximization type algorithm

probabilistic low rank multitask learning in this paper we consider the problem of learning multiple related tasks simultaneously with the goal of improving the generalization performance of individual tasks the key challenge is to effectively exploit the shared information across multiple tasks as well as preserve the discriminative information for each individual task to address this we propose a novel probabilistic model for multitask learning mtl that can automatically balance between low rank and sparsity constraints the former assumes a low rank structure of the underlying predictive hypothesis space to explicitly capture the relationship of different tasks and the latter learns the incoherent sparse patterns private to each task we derive and perform inference via variational bayesian methods experimental results on both regression and classification tasks on real world applications demonstrate the effectiveness of the proposed method in dealing with the mtl problems

integrated low rank based discriminative feature learning for recognition feature learning plays a central role in pattern recognition in recent years many representation based feature learning methods have been proposed and have achieved great success in many applications however these methods perform feature learning and subsequent classification in two separate steps which may not be optimal for recognition tasks in this paper we present a supervised low rank based approach for learning discriminative features by integrating latent low rank representation latlrr with a ridge regression based classifier our approach combines feature learning with classification so that the regulated classification error is minimized in this way the extracted features are more discriminative for the recognition tasks our approach benefits from a recent discovery on the closed form solutions to noiseless latlrr when there is noise a robust principal component analysis pca based denoising step can be added as preprocessing when the scale of a problem is large we utilize a fast randomized algorithm to speed up the computation of robust pca extensive experimental results demonstrate the effectiveness and robustness of our method

on a cahn hilliard allen cahn system coupled with a type iii heat equation and singular potentials abstract our aim in this article is to study the asymptotic behavior of a cahn hilliard allen cahn system coupled with a heat equation based on the type iii heat conduction law with singular potentials we also show further regularity results and we prove a strict separation property from the pure states in one space dimension

sparse coding from a bayesian perspective sparse coding is a promising theme in computer vision most of the existing sparse coding methods are based on either l0 or l1 penalty which often leads to unstable solution or biased estimation this is because of the nonconvexity and discontinuity of the l0 penalty and the over penalization on the true large coefficients of the l1 penalty in this paper sparse coding is interpreted from a novel bayesian perspective which results in a new objective function through maximum a posteriori estimation the obtained solution of the objective function can generate more stable results than the l0 penalty and smaller reconstruction errors than the l1 penalty in addition the convergence property of the proposed algorithm for sparse coding is also established the experiments on applications in single image super resolution and visual tracking demonstrate that the proposed method is more effective than other state of the art methods

analysis of a two phase field model for the solidification of an alloy abstract in this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification melting of a metallic alloy it is assumed that two different kinds of crystallization are possible consequently the unknowns are the temperature and the phase field functions u and v the time derivatives u t and v t appear in the equation for the heat equation on the other hand the equations for u and v contain nonlinear terms where we find

bayesian robust principal component analysis a hierarchical bayesian model is considered for decomposing a matrix into low rank and sparse components assuming the observed matrix is a superposition of the two the matrix is assumed noisy with unknown and possibly non stationary noise statistics the bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low rank and sparse outlier contributions the model is robust to a broad range of noise levels without having to change model hyperparameter settings in addition the bayesian framework allows exploitation of additional structure in the matrix for example in video applications each row or column corresponds to a video frame and we introduce a markov dependency between consecutive rows in the matrix corresponding to consecutive frames in the video the properties of this markov process are also inferred based on the observed matrix while simultaneously denoising and recovering the low rank and sparse components we compare the bayesian model to a state of the art optimization based implementation of robust pca considering several examples we demonstrate competitive performance of the proposed model

convergence to equilibrium for a parabolic hyperbolic phase field model with cattaneo heat flux law abstract in this paper we consider the well posedness and the asymptotic behavior of solutions to the following parabolic hyperbolic phase field system 0 1 t 3 0 t t div q 0 q t q 0 in 0 subject to the homogeneous neumann boundary condition for 0 2 n 0 on 0 and no heat flux boundary condition for q 0 3 q n 0 on 0 and the initial conditions 0 4 0 0 0 0 q 0 q 0 in where r 3 is a bounded domain with a smooth boundary and n is the outward normal direction to the boundary in this paper we first establish the existence and uniqueness of a global strong solution to 0 1 0 2 0 3 0 4 then we prove its convergence to an equilibrium as time goes to infinity

on a phase field system based on the cattaneo law abstract our aim in this paper is to study a generalization of the caginalp phase field system based on the maxwell cattaneo law for heat conduction and endowed with neumann boundary conditions in particular we obtain well posedness results and study the dissipativity of the associated solution operators we also prove when the enthalpy is conserved the existence of the global attractor we finally study the spatial behavior of solutions in a semi infinite cylinder assuming that such solutions exist and have a proper spatial decay at infinity

a generalization of the caginalp phase field system with neumann boundary conditions abstract we study a generalized caginalp phase field system based on the theory of type iii heat conduction proposed by green and naghdi and supplemented with neumann boundary conditions in contrast to the dirichlet case the system exhibits a lack of dissipation on the thermal displacement variable however minus its spatial average is dissipative and we are able to prove the existence of the global attractor with optimal regularity for the associated semigroup

stacked denoising autoencoders learning useful representations in a deep network with a local denoising criterion we explore an original strategy for building deep networks based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs the resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders it is however shown on a benchmark of classification problems to yield significantly lower classification error thus bridging the performance gap with deep belief networks dbn and in several cases surpassing it higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent svm classifiers qualitative experiments show that contrary to ordinary autoencoders denoising autoencoders are able to learn gabor like edge detectors from natural image patches and larger stroke detectors from digit images this work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations

convergence to equilibrium for the cahn hilliard equation with dynamic boundary conditions this paper is concerned with the asymptotic behavior of solution to the cahn hilliard equation 0 1 u t u u u3 x t r subject to the following dynamic boundary conditions 0 2 s u u hs gsu 1 sut t 0 x 0 t 0 x and the initial condition 0 3 u t 0 u0 x x where is a bounded domain in rn n 3 with smooth boundary and s 0 s 0 gs 0 hs are given constants is the tangential laplacian operator and is the outward normal direction to the boundary this problem has been considered in the recent paper by racke and zheng adv differential equations 8 1 2003 83 where the global existence and uniqueness were proved in a very recent manuscript by pruss racke and zheng konstanzer schrift math inform 189 2003 the results on existence of global attractor and maximal regularity of solution have been obtained in this paper convergence of solution of this problem to an equilibrium as time goes to infinity is proved

asymptotic behavior of a nonisothermal viscous cahn hilliard equation with inertial term we consider a differential model describing nonisothermal fast phase separation processes taking place in a three dimensional bounded domain this model consists of a viscous cahn hilliard equation characterized by the presence of an inertial term tt being the order parameter which is linearly coupled with an evolution equation for the relative temperature the latter can be of hyperbolic type if the cattaneo maxwell heat conduction law is assumed the state variables and the chemical potential are subject to the homogeneous neumann boundary conditions we first provide conditions which ensure the well posedness of the initial and boundary value problem then we prove that the corresponding dynamical system is dissipative and possesses a global attractor moreover assuming that the nonlinear potential is real analytic we establish that each trajectory converges to a single steady state by using a suitable version of the eojasiewicz simon inequality we also obtain an estimate of the decay rate to equilibrium

pareto path multitask multiple kernel learning a traditional and intuitively appealing multitask multiple kernel learning mt mkl method is to optimize the sum thus the average of objective functions with partially shared kernel function which allows information sharing among the tasks we point out that the obtained solution corresponds to a single point on the pareto front pf of a multiobjective optimization problem which considers the concurrent optimization of all task objectives involved in the multitask learning mtl problem motivated by this last observation and arguing that the former approach is heuristic we propose a novel support vector machine mt mkl framework that considers an implicitly defined set of conic combinations of task objectives we show that solving our framework produces solutions along a path on the aforementioned pf and that it subsumes the optimization of the average of objective functions as a special case using the algorithms we derived we demonstrate through a series of experimental results that the framework is capable of achieving a better classification performance when compared with other similar mtl approaches

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

long time behavior for a nonlinear plate equation with thermal memory abstract we consider a nonlinear plate equation with thermal memory effects due to non fourier heat flux laws first we prove the existence and uniqueness of global solutions as well as the existence of a global attractor then we use a suitable ojasiewicz simon type inequality to show the convergence of global solutions to single steady states as time goes to infinity under the assumption that the nonlinear term f is real analytic moreover we provide an estimate on the convergence rate

long time behaviour for a model of phase field type in this paper we study a model of phase field type for the kinetics of phase transitions which was considered by halperin hohenberg and ma and which includes the phase field equations we study the well posedness of the corresponding initial boundary value problem in an open bounded subset in space dimension lower than or equal to 3 and prove that under suitable conditions the long time behaviour of the solutions to this problem is described by a maximal attractor

convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity abstract we prove convergence of global bounded and smooth solutions of the wave equation with linear dissipation and analytic nonlinearity a generalization and examples of applications are given at the end of the paper

bounds for linear multi task learning we give dimension free and data dependent bounds for linear multi task learning where a common linear operator is chosen to preprocess data for a vector of task specific linear thresholding classifiers the complexity penalty of multi task learning is bounded by a simple expression involving the margins of the task specific classifiers the hilbert schmidt norm of the selected preprocessor and the hilbert schmidt norm of the covariance operator for the total mixture of all task distributions or alternatively the frobenius norm of the total gramian matrix for the data dependent version the results can be compared to state of the art results on linear single task learning