multibody grouping from motion images we want to deduce from a sequence of noisy two dimensional images of a scene of several rigid bodies moving independently in three dimensions the number of bodies and the grouping of given feature points in the images to the bodies prior processing is assumed to have identified features or points common to all frames and the images are assumed to be created by orthographic projection i e perspective effects are minimal we describe a computationally inexpensive algorithm that can determine which points or features belong to which rigid body using the fact that with exact observations in orthographic projection points on a single body lie in a three or less dimensional linear manifold of frame space if there are enough observations and independent motions these manifolds can be viewed as a set linearly independent four or less dimensional subspaces we show that the row echelon canonical form provides direct information on the grouping of points to these subspaces treatment of the noise is the most difficult part of the problem this paper uses a statistical approach to estimate the grouping of points to subspaces in the presence of noise by computing which partition has the maximum likelihood the input data is assumed to be contaminated with independent gaussian noise the algorithm can base its estimates on a user supplied standard deviation of the noise or it can estimate the noise from the data the algorithm can also be used to estimate the probability of a user specified partition so that the hypothesis can be combined with others using bayesian statistics

multiple positive radial solutions to some kirchhoff equations abstract in this paper we discuss the existence and multiplicity of positive radial solutions to some kirchhoff equations and elliptic equations by using the leggett williams three solutions theorem skillfully we obtain two positive solutions to kirchhoff equations under some appropriate conditions as a direct corollary we also obtain the same result to elliptic equations in order to facilitate the proof of main results we first establish a new simple three solutions theorems for the equation a b x x a x where a is a completely continuous operator a 0 b 0 and x k x for all x p where k is a nondecreasing nonnegative continuous function then apply it to prove the main results in addition we discover and prove a new inequality in the article in the end of the paper we present an example which makes the elliptic equation has infinite many positive radial solutions and give the approximate images of the nonlinear term

impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in banach spaces abstract in this paper we deal with the existence of impulsive mild solutions for semilinear differential inclusions with nonlocal conditions where the linear part generates an evolution system and the nonlinearity satisfies the lower scorza dragoni property our theorems extend the existence propositions proved by fan in 2010 an example is presented

unsupervised object segmentation with a hybrid graph model hgm in this work we address the problem of performing class specific unsupervised object segmentation i e automatic segmentation without annotated training images object segmentation can be regarded as a special data clustering problem where both class specific information and local texture color similarities have to be considered to this end we propose a hybrid graph model hgm that can make effective use of both symmetric and asymmetric relationship among samples the vertices of a hybrid graph represent the samples and are connected by directed edges and or undirected ones which represent the asymmetric and or symmetric relationship between them respectively when applied to object segmentation vertices are superpixels the asymmetric relationship is the conditional dependence of occurrence and the symmetric relationship is the color texture similarity by combining the markov chain formed by the directed subgraph and the minimal cut of the undirected subgraph the object boundaries can be determined for each image using the hgm we can conveniently achieve simultaneous segmentation and recognition by integrating both top down and bottom up information into a unified process experiments on 42 object classes 9 415 images in total show promising results

robust algebraic segmentation of mixed rigid body and planar motions from two views this paper studies segmentation of multiple rigid body motions in a 3 d dynamic scene under perspective camera projection we consider dynamic scenes that contain both 3 d rigid body structures and 2 d planar structures based on the well known epipolar and homography constraints between two views we propose a hybrid perspective constraint hpc to unify the representation of rigid body and planar motions given a mixture of k hybrid perspective constraints we propose an algebraic process to partition image correspondences to the individual 3 d motions called robust algebraic segmentation ras particularly we prove that the joint distribution of image correspondences is uniquely determined by a set of 2k th degree polynomials a global signature for the union of k motions of possibly mixed type the first and second derivatives of these polynomials provide a means to recover the association of the individual image samples to their respective motions finally using robust statistics we show that the polynomials can be robustly estimated in the presence of moderate image noise and outliers we conduct extensive simulations and real experiments to validate the performance of the new algorithm the results demonstrate that ras achieves notably higher accuracy than most existing robust motion segmentation methods including random sample consensus ransac and its variations the implementation of the algorithm is also two to three times faster than the existing methods the implementation of the algorithm and the benchmark scripts are available at http perception csl illinois edu ras

existence and multiplicity of non negative solutions for systems of perturbed hammerstein integral equations abstract we study the existence of positive solutions for a system of perturbed hammerstein integral equations our setting is quite general and covers a wide class of systems of boundary value problems the main ingredient in our theory is the classical fixed point index theory for compact maps

a multibody factorization method for independently moving objects the structure from motion problem has been extensively studied in the field of computer vision yet the bulk of the existing work assumes that the scene contains only a single moving object the more realistic case where an unknown number of objects move in the scene has received little attention especially for its theoretical treatment in this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images the method does not require prior knowledge of the number of objects nor is dependent on any grouping of features into an object at the image level for this purpose we introduce a mathematical construct of object shapes called the shape interaction matrix which is invariant to both the object motions and the selection of coordinate systems this invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects once the matrix is computed it allows for segmenting features into objects by the process of transforming it into a canonical form as well as recovering the shape and motion of each object the theory works under a broad set of projection models scaled orthography paraperspective and affine but they must be linear so it excludes projective cameras

solutions with a prescribed interval of positivity for differential systems with nonlocal conditions abstract based on fixed point index the paper develops a theory of existence localization and multiplicity of solutions to first order differential systems subject to linear nonlocal conditions the main features concern the role of the support of the nonlocal condition and the positivity of solutions which is only required on a prescribed subinterval several examples of problems admitting at least one two or sequences of such solutions are included and numerical solutions are obtained using the mathematica shooting program with starting initial conditions suggested by the theoretical localization results

discriminative transfer subspace learning via low rank and sparse representation in this paper we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain we use a transformation matrix to transfer both the source and target data to a common subspace where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced in this way the discrepancy of the source and target domains is reduced by imposing joint low rank and sparse constraints on the reconstruction coefficient matrix the global and local structures of data can be preserved to enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy a flexible linear classifier projection is obtained by learning a non negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and thus is more robust to different types of noise we formulate our problem as a constrained low rankness and sparsity minimization problem and solve it by the inexact augmented lagrange multiplier method extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state of the art methods the matlab code of our method will be publicly available at http www yongxu org lunwen html

existence and uniqueness results for nonlinear first order three point boundary value problems on time scales abstract in this paper we investigate the following nonlinear first order three point boundary value problem on time scale t x t p t x t f t x t t 0 t t x 0 x x t by using several well known fixed point theorems the existence of positive solutions is obtained besides the uniqueness results are obtained by imposing growth restrictions on f in particular green s function for the above boundary value problem is established

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

cross domain visual matching via generalized similarity measure and feature learning cross domain visual data matching is one of the fundamental problems in many real world vision tasks e g matching persons across id photos and surveillance videos conventional approaches to this problem usually involves two steps i projecting samples from different domains into a common space and ii computing dis similarity in this space based on a certain distance in this paper we present a novel pairwise similarity measure that advances existing models by i expanding traditional linear projections into affine transformations and ii fusing affine mahalanobis distance and cosine similarity by a data driven combination moreover we unify our similarity measure with feature representation learning via deep convolutional neural networks specifically we incorporate the similarity measure matrix into the deep architecture enabling an end to end way of model optimization we extensively evaluate our generalized similarity model in several challenging cross domain matching tasks person re identification under different views and face verification over different modalities i e faces from still images and videos older and younger faces and sketch and photo portraits the experimental results demonstrate superior performance of our model over other state of the art methods

new harnack inequalities and existence theorems for radially symmetric solutions of elliptic pdes with sign changing or vanishing green s function abstract we consider the perturbed hammerstein integral equation y t 1 t h 1 1 y 2 t h 2 2 y 0 1 g t s f s y s d s where 1 and 2 are linear functionals realized as stieltjes integrals with associated signed stieltjes measures we demonstrate that by utilizing a nonstandard order cone together with an associated nonstandard open set existence of a positive solution to the integral equation can be guaranteed under relatively mild hypotheses on the various constituent functions and functionals in the case in which the green s function t s g t s is allowed to both vanish and change sign as an example we apply our results to radially symmetric elliptic pdes of the form u h x g u x x r 1 r 2 r u x x b r 2 0 u r 1 x u r x x b 1 h u where 0 r 1 r r 2 is a linear functional and h is a continuous function as part of this analysis we demonstrate a new methodology for constructing a suitable harnack like inequality associated to the boundary value problem

estimation of subspace arrangements with applications in modeling and segmenting mixed data recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high dimensional data that have very complicated structures from both geometric and statistical points of view such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model in this paper we propose to use subspace arrangements a union of multiple subspaces for modeling mixed data each subspace in the arrangement is used to model just a homogeneous subset of the data thus multiple subspaces together can capture the heterogeneous structures within the data set in this paper we give a comprehensive introduction to a new approach for the estimation of subspace arrangements this is known as generalized principal component analysis gpca in particular we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust even when the given data are corrupted by noise or contaminated with outliers this new method in many ways improves and generalizes extant methods for modeling or clustering mixed data there have been successful applications of this new method to many real world problems in computer vision image processing and system identification in this paper we will examine several of those representative applications this paper is intended to be expository in nature however in order that this may serve as a more complete reference for both theoreticians and practitioners we take the liberty of filling in several gaps between the theory and the practice in the existing literature

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

motion segmentation in the presence of outlying incomplete or corrupted trajectories in this paper we study the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence using the affine camera model this problem can be cast as the problem of segmenting samples drawn from multiple linear subspaces in practice due to limitations of the tracker occlusions and the presence of nonrigid objects in the scene the obtained motion trajectories may contain grossly mistracked features missing entries or corrupted entries in this paper we develop a robust subspace separation scheme that deals with these practical issues in a unified mathematical framework our methods draw strong connections between lossy compression rank minimization and sparse representation we test our methods extensively on the hopkins155 motion segmentation database and other motion sequences with outliers and missing data we compare the performance of our methods to state of the art motion segmentation methods based on expectation maximization and spectral clustering for data without outliers or missing information the results of our methods are on par with the state of the art results and in many cases exceed them in addition our methods give surprisingly good performance in the presence of the three types of pathological trajectories mentioned above all code and results are publicly available at http perception csl uiuc edu coding motion

a unified existence theory for evolution equations and systems under nonlocal conditions abstract we investigate the effect of nonlocal conditions expressed by linear continuous mappings over the hypotheses which guarantee the existence of global mild solutions for functional differential equations in a banach space a progressive transition from the volterra integral operator associated to the cauchy problem to fredholm type operators appears when the support of the nonlocal condition increases from zero to the entire interval of the problem the results are extended to systems of equations in a such way that the system nonlinearities behave independently as much as possible and the support of the nonlocal condition may differ from one variable to another

multiple positive solutions of non local initial value problems for first order differential systems abstract the paper gives a new and natural method for the existence of multiple positive solutions for first order differential systems with non local initial value conditions involving linear functionals the case of higher order differential equations is also considered the results are accompanied by numerical examples confirming the theory and proving for practice the importance of the bounds in solution localization

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

existence of three solutions for a first order problem with nonlinear nonlocal boundary conditions abstract conditions for the existence of at least three positive solutions to the nonlinear first order problem with a nonlinear nonlocal boundary condition given by y t r t y t i 1 m f i t y t t 0 1 y 0 y 1 j 1 n j j y j j 0 1 are discussed for sufficiently large 1 and r 0 the leggett williams fixed point theorem is utilized

positive solutions to a system of second order nonlocal boundary value problems abstract in this paper we study the existence of positive solutions to a system of second order nonlocal boundary value problems by using fixed point index theory in a cone our hypotheses imposed on nonlinearities are those which characterize systems of nonlocal boundary value problems and our boundary value conditions are expressed in terms of possibly nonlinear functions of riemann stieltjes integrals thus generalizing and unifying the boundary value conditions in the literature therefore our results cannot be routinely deduced from the ones for single nonlocal problem in the literature

existence results for systems with coupled nonlocal initial conditions abstract in this paper an existence theory is developed for first order differential systems with coupled nonlocal conditions given by stieltjes integrals the approach is based on the fixed point theorems of perov schauder and schaefer and on a vector method for treating systems which uses matrices having spectral radius less than one when the nonlocal conditions depend on functionals restricted to a proper subinterval the nonlinear integral operator associated to the system splits into two parts one of fredholm type and another one of volterra type correspondingly the sufficient conditions for the existence results will differ in the two parts of the interval some examples are presented to illustrate the theory

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli

robust recovery of subspace structures by low rank representation in this paper we address the subspace clustering problem given a set of data samples vectors approximately drawn from a union of multiple subspaces our goal is to cluster the samples into their respective subspaces and remove possible outliers as well to this end we propose a novel objective function named low rank representation lrr which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary it is shown that the convex program associated with lrr solves the subspace clustering problem in the following sense when the data is clean we prove that lrr exactly recovers the true subspace structures when the data are contaminated by outliers we prove that under certain conditions lrr can exactly recover the row space of the original data and detect the outlier as well for data corrupted by arbitrary sparse errors lrr can also approximately recover the row space with theoretical guarantees since the subspace membership is provably determined by the row space these further imply that lrr can perform robust subspace clustering and error correction in an efficient and effective way

multitask linear discriminant analysis for view invariant action recognition robust action recognition under viewpoint changes has received considerable attention recently to this end self similarity matrices ssms have been found to be effective view invariant action descriptors to enhance the performance of ssm based methods we propose multitask linear discriminant analysis lda a novel multitask learning framework for multiview action recognition that allows for the sharing of discriminative ssm features among different views i e tasks inspired by the mathematical connection between multivariate linear regression and lda we model multitask multiclass lda as a single optimization problem by choosing an appropriate class indicator matrix in particular we propose two variants of graph guided multitask lda 1 where the graph weights specifying view dependencies are fixed a priori and 2 where graph weights are flexibly learnt from the training data we evaluate the proposed methods extensively on multiview rgb and rgbd video data sets and experimental results confirm that the proposed approaches compare favorably with the state of the art

positive solutions of nonlinear fourth order boundary value problems with local and non local boundary conditions we establish new existence results for multiple positive solutions of fourth order nonlinear equations which model deflections of an elastic beam we consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non local boundary conditions with a unified approach our method is to show that each boundary value problem can be written as the same type of perturbed integral equation in the space c 0 1 involving a linear functional u but although we seek positive solutions the functional is not assumed to be positive for all positive u the results are new even for the classic boundary conditions of clamped or hinged ends when u 0 because we obtain sharp results for the existence of one positive solution for multiple solutions we seek optimal values of some of the constants that occur in the theory which allows us to impose weaker assumptions on the nonlinear term than in previous works our non local boundary conditions contain multi point problems as special cases and for the first time in fourth order problems we allow coefficients of both signs

on the existence of mild solutions of semilinear evolution differential inclusions abstract in this paper we deal with a cauchy problem governed by the following semilinear evolution differential inclusion x t a t x t f t x t and with initial data x 0 x 0 e where a t t 0 d is a family of linear operators in the banach space e generating an evolution operator and f is a caratheodory type multifunction we prove the existence of local and global mild solutions of the problem moreover we obtain the compactness of the set of all global mild solutions in order to obtain these results we define a generalized cauchy operator our existence theorems respectively contain the analogous results provided by kamenskii obukhovskii and zecca condensing multivalued maps and semilinear differential inclusions in banach spaces de gruyter ser nonlinear anal appl vol 7 de gruyter berlin 2001 for inclusions with constant operator

decidability of zigzag codes french abstract this paper deals with zigzag factorizations and zigzag codes the language of zigzag over a regular language is represented by constructing a special family of two way automata decidability of zigzag codes previously shown for the finite languages is proved here for all regular languages by the analysis of the set of crossing sequences produced by a two way automation in the family we also obtain that it is decidable whether or not a two way automation of a certain type is non ambiguous

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

spectral curvature clustering scc this paper presents novel techniques for improving the performance of a multi way spectral clustering framework govindu in proceedings of the 2005 ieee computer society conference on computer vision and pattern recognition cvpr 05 vol 1 pp 1150 1157 2005 chen and lerman 2007 preprint in the supplementary webpage for segmenting affine subspaces specifically it suggests an iterative sampling procedure to improve the uniform sampling strategy an automatic scheme of inferring the tuning parameter from the data a precise initialization procedure for k means as well as a simple strategy for isolating outliers the resulting algorithm spectral curvature clustering scc requires only linear storage and takes linear running time in the size of the data it is supported by theory which both justifies its successful performance and guides our practical choices we compare it with other existing methods on a few artificial instances of affine subspaces application of the algorithm to several real world problems is also discussed

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

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

positive solutions to boundary value problems with nonlinear boundary conditions abstract in this paper we consider the boundary value problem y t f t y t subject to the boundary conditions y a y and y 2 b 0 in this setting c rd a 2 b t r r is a continuous functional which represents a nonlinear nonlocal boundary condition by imposing sufficient structure on and the nonlinearity f we deduce the existence of at least one positive solution to this problem the novelty in our setting lies in the fact that may be strictly nonpositive for some y 0 our results are achieved by appealing to the krasnosel ski fixed point theorem we conclude with several examples illustrating our results and the generalizations that they afford

concatention of inputs in a two way automation abstract to every input string of a two way automaton one associates a quadruple of partial functions or relations between the states this quadruple describes the behavior of the automaton on that input and can also be used to formulate acceptance or notions like the crossing sequence formulas are given that show how two such quadruples are combined multiplied as their corresponding input strings are concatenated

impulsive problems for semilinear differential equations with nonlocal conditions abstract this paper is concerned with the existence of impulsive semilinear differential equations with nonlocal conditions using the technique of fixed point theory existence results are obtained for mild solutions when the nonlocal item is lipschitz is not lipschitz and not compact respectively

daml domain adaptation metric learning the state of the art metric learning algorithms cannot perform well for domain adaptation settings such as cross domain face recognition image annotation etc because labeled data in the source domain and unlabeled ones in the target domain are drawn from different but related distributions in this paper we propose the domain adaptation metric learning daml by introducing a data dependent regularization to the conventional metric learning in the reproducing kernel hilbert space rkhs this data dependent regularization resolves the distribution difference by minimizing the empirical maximum mean discrepancy between source and target domain data in rkhs theoretically by using the empirical rademacher complexity we prove risk bounds for the nearest neighbor classifier that uses the metric learned by daml practically learning the metric in rkhs does not scale up well fortunately we can prove that learning daml in rkhs is equivalent to learning daml in the space spanned by principal components of the kernel principle component analysis kpca thus we can apply kpca to select most important principal components to significantly reduce the time cost of daml we perform extensive experiments over four well known face recognition datasets and a large scale web image annotation dataset for the cross domain face recognition and image annotation tasks under various settings and the results demonstrate the effectiveness of daml

robust transfer metric learning for image classification metric learning has attracted increasing attention due to its critical role in image analysis and classification conventional metric learning always assumes that the training and test data are sampled from the same or similar distribution however to build an effective distance metric we need abundant supervised knowledge i e side label information which is generally inaccessible in practice because of the expensive labeling cost in this paper we develop a robust transfer metric learning rtml framework to effectively assist the unlabeled target learning by transferring the knowledge from the well labeled source domain specifically rtml exploits knowledge transfer to mitigate the domain shift in two directions i e sample space and feature space in the sample space domain wise and class wise adaption schemes are adopted to bridge the gap of marginal and conditional distribution disparities across two domains in the feature space our metric is built in a marginalized denoising fashion and low rank constraint which make it more robust to tackle noisy data in reality furthermore we design an explicit rank constraint regularizer to replace the rank minimization np hard problem to guide the low rank metric learning experimental results on several standard benchmarks demonstrate the effectiveness of our proposed rtml by comparing it with the state of the art transfer learning and metric learning algorithms

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

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

on abstract differential equations with state dependent non local conditions abstract in this paper we introduce the concept of state dependent nonlocal condition and study the existence and uniqueness of solution for a general class of abstract differential equations with state dependent delay subject to this class of conditions in this type of problem the nonlocal condition can be dependent on times or time intervals determined by the unknown solution some examples on partial differential equations with state dependent delay arising in population dynamics are presented

the existence and approximation of extremal solutions to several first order discontinuous dynamic equations with nonlinear boundary value conditions abstract the goal of this paper is to give a general view of some different kinds of weak first order discontinuous boundary value problems on an arbitrary time scale with nonlinear functional boundary value conditions by assuming caratheodory s conditions and discontinuity we prove the existence of extremal solutions for all the problems in the sector formed by a lower and an upper solution to the problem considered moreover the uniform approximation by a sequence of lower and upper solutions to the problem is guaranteed

dense error correction via ell 1 minimization this paper studies the problem of recovering a sparse signal x n from highly corrupted linear measurements y ax e m where e is an unknown error vector whose nonzero entries may be unbounded motivated by an observation from face recognition in computer vision this paper proves that for highly correlated and possibly overcomplete dictionaries a any sufficiently sparse signal x can be recovered by solving an l1 minimization problem min x 1 e 1 subject to y ax e more precisely if the fraction of the support of the error e is bounded away from one and the support of a is a very small fraction of the dimension m then as m becomes large the above l1 minimization succeeds for all signals x and almost all sign and support patterns of e this result suggests that accurate recovery of sparse signals is possible and computationally feasible even with nearly 100 of the observations corrupted the proof relies on a careful characterization of the faces of a convex polytope spanned together by the standard crosspolytope and a set of independent identically distributed i i d gaussian vectors with nonzero mean and small variance dubbed the cross and bouquet cab model simulations and experiments corroborate the findings and suggest extensions to the result

regular transducer expressions for regular transformations abstract functional mso transductions deterministic two way transducers as well as streaming string transducers are all equivalent models for regular functions in this paper we show that every regular function either on finite words or on infinite words captured by a deterministic two way transducer can be described with a regular transducer expression rte for infinite words the two way transducer uses muller acceptance and regular look ahead rte s are constructed from constant functions using the combinators if then else deterministic choice hadamard product and unambiguous versions of the cauchy product the 2 chained kleene iteration and the 2 chained omega iteration our proof works for transformations of both finite and infinite words extending the result on finite words of alur et al in lics 14 the construction of an rte associated with a deterministic two way transducer is guided by a regular expression which is good wrt its transition monoid good expressions are unambiguous ensuring the functionality of the output computed moreover in good expressions iterations kleene plus or omega are restricted to subexpressions corresponding to idempotent elements of the transition monoid good expressions can be obtained with an unambiguous version of imre simon s famous forest factorization theorem to handle infinite words we introduce the notion of transition monoids for deterministic two way muller transducers with look ahead where the look ahead is captured by some backward deterministic buchi automaton this paper is an extended version of 15 presented at lics 18

learning fast low rank projection for image classification rooted in a basic hypothesis that a data matrix is strictly drawn from some independent subspaces the low rank representation lrr model and its variations have been successfully applied in various image classification tasks however this hypothesis is very strict to the lrr model as it cannot always be guaranteed in real images moreover the hypothesis also prevents the sub dictionaries of different subspaces from collaboratively representing an image fortunately in supervised image classification low rank signal can be extracted from the independent label subspaces ils instead of the independent image subspaces iis therefore this paper proposes a projective low rank representation plr model by directly training a projective function to approximate the lrr derived from the labels to the best of our knowledge plr is the first attempt to use the ils hypothesis to relax the rigorous iis hypothesis in the lrr models we further prove a low rank effect that the representations learned by plr have high intraclass similarities and large interclass differences which are beneficial to the classification tasks the effectiveness of our proposed approach is validated by the experimental results on three databases

the zig zag power series a two way version of the operator abstract this paper deals with the zig zag power series as introduced in 1 that is with a two way version of the star operator over formal languages and power series the main result is a double characterization of rationality of zig zag power series by a condition over the structure of the starting language and another over some associated two way automata for rational zig zag power series we present the construction of some one way automata recognizing them

greenʼs function for first order multipoint boundary value problems and applications to the existence of solutions with constant sign abstract we consider a first order linear differential equation subject to boundary value conditions which take into account the values of the function at multiple points in the interval of interest for this problem we calculate the green s function which allows to express in integral form the exact expression of the unique solution to the multipoint boundary value problem under the appropriate conditions from this study some results are derived concerning the existence of solutions with a constant sign that is some comparison results for first order multipoint boundary value problems

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification