on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

brief paper a way to stabilize linear systems with delayed state a simple method is proposed for stabilizing linear systems with delayed state using linear feedback the method requires checking the negativity of a matrix containing two free parameters and solving a matrix lyapunov equation with these parameters a known stabilizability criterion and a simple stability theorem for the open loop system are obtained as special cases of the main result

criteria for asymptotic stability of linear time delay systems several sufficient conditions which guarantee stability of linear time delay systems are derived each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness

an improved razumikhin type theorem and its applications an improved razumikhin type theorem is established and the advantage of the established theorem for reducing conservatism is discussed for a class of time delay systems a simple asymptotic stability condition is deduced as an application of the established theorem two illustrative examples are given to show the superiority of the results to those in the literature

circulant preconditioners for solving differential equations with multidelays abstract we consider the solution of differential equations with multidelays by using boundary value methods bvms these methods require the solution of some nonsymmetric large and sparse linear systems the gmres method with the strang type block circulant preconditioner is proposed to solve these linear systems if an a k 1 k 2 stable bvm is used we show that our preconditioner is invertible and the spectrum of the preconditioned matrix is clustered it follows that when the gmres method is applied to solving the preconditioned systems the method would converge fast numerical results are given to show the effectiveness of our methods

dynamical feedback compensator for uncertain time delay systems containing saturating actuator abstract the problem of the stabilization of an uncertain time delay system with a saturating actuator is discussed these uncertainties may be linear non linear and or time varying but only the upper bounds are known a linear dynamical feedback compensator is used to stabilize this uncertain saturating and time delay system the concept of matrix measure and the comparison theory are employed to investigate the robust stability condition which assures asymptotic stability one example is given to illustrate the application of the proposed design method

on delay independent stability of large scale systems with time delays a new criterion for delay independent stability of linear large scale time delay systems is deduced by employing an improved razumikhin type theorem and the m matrix properties an illustrative example is given to demonstrate the superiority of the obtained results to those in the literature

on an estimate of the decay rate for stable linear delay systems in this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

strong continuation contrast invariant inpainting with a third order optimal pde pde based image inpainting has become a very active area of research after the pioneering works of masnou and morel bertalm spl inodot spl acute o et al and ballester et al in this paper we take a different approach inspired by the excellent work of caselles et al we view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines expressing this in terms of local neighborhoods and using a taylor expansion we derive a third order pde that performs inpainting this pde is optimal in the sense that it is the most accurate third order pde which can ensure continuation of level lines the continuation is strong allowing the restoration of thin structures occluded by a wide gap the result is also contrast invariant this is a novel pde which in both its accuracy and contrast invariance outperforms the approaches cited above

annihilating filter based low rank hankel matrix approach for image inpainting in this paper we propose a patch based image inpainting method using a low rank hankel structured matrix completion approach the proposed method exploits the annihilation property between a shift invariant filter and image data observed in many existing inpainting algorithms in particular by exploiting the commutative property of the convolution the annihilation property results in a low rank block hankel structure data matrix and the image inpainting problem becomes a low rank structured matrix completion problem the block hankel structured matrices are obtained patch by patch to adapt to the local changes in the image statistics to solve the structured low rank matrix completion problem we employ an alternating direction method of multipliers with factorization matrix initialization using the low rank matrix fitting algorithm as a side product of the matrix factorization locally adaptive dictionaries can be also easily constructed despite the simplicity of the algorithm the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state of the art image inpainting methods

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

analysis of periodic schrodinger operators regularity and approximation of eigenfunctions let v be a real valued potential that is smooth everywhere on r3 except at a periodic discrete set s of points where it has singularities of the coulomb type z r we assume that the potential v is periodic with period lattice l we study the spectrum of the schrodinger operator h v acting on the space of bloch waves with arbitrary but fixed wavevector k let t r3 l let u be an eigenfunction of h with eigenvalue and let 0 be arbitrarily small we show that the classical regularity of the eigenfunction u is u h5 2 t in the usual sobolev spaces and u k3 2 m t s in the weighted sobolev spaces the regularity index m can be as large as desired which is crucial for numerical methods for any choice of the bloch wavevector k we also show that h has compact resolvent and hence a complete eigenfunction expansion the case of the hydrogen atom suggests that our regularity results are optimal we present two applications to the numerical approximation of eigenvalues using wave functions and usi

further results on the robust stability of linear systems with a single time delay abstract for linear systems with a single time varying delay time we propose a method to characterize how large the deviation of the delay time can be compared to the nominal zero value such that the system still preserves its asymptotic stability both cases of linear time delay systems with and without uncertainties are considered the criteria developed are seen to give less conservative results in simulation examples

stability of retarded delay differential systems a practical stability test for linear retarded delay differential systems is proposed based on the fact that all unstable zeros of the characteristic quasipolynomial must lie within a restricted bounded region of the complex plane the test provides a readily computable necessary and sufficient condition for asymptotic stability it also copes equally well with both cases of commensurate and non commensurate delays furthermore a method for evaluating the abscissa of stability of the quasi polynomial defined as the largest of the real parts of the zeros of the quasipolynomial is given the method is based on a known technique which makes repeated use of a stability test and thereby avoids the calculation of all the zeros the stability test and the method for computing the abscissa of stability provide useful computational tools for the design of dynamical systems with delays using the method of inequalities numerical examples are given

exemplar based inpainting technical review and new heuristics for better geometric reconstructions this paper proposes a technical review of exemplar based inpainting approaches with a particular focus on greedy methods several comparative and illustrative experiments are provided to deeply explore and enlighten these methods and to have a better understanding on the state of the art improvements of these approaches from this analysis three improvements over criminisi et al algorithm are then presented and detailed 1 a tensor based data term for a better selection of pixel candidates to fill in 2 a fast patch lookup strategy to ensure a better global coherence of the reconstruction and 3 a novel fast anisotropic spatial blending algorithm that reduces typical block artifacts using tensor models relevant comparisons with the state of the art inpainting methods are provided that exhibit the effectiveness of our contributions

adjoints of elliptic cone operators we study the adjointness problem for the closed extensions of a general b elliptic operator a x diff m b m e 0 initially defined as an unbounded operator a c c m e x l 2 b m e x l 2 b m e inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the case where a is a symmetric semibounded operator is of particular interest and we give a complete description of the domain of the friedrichs extension of such an operator

two stage image denoising by principal component analysis with local pixel grouping this paper presents an efficient image denoising scheme by using principal component analysis pca with local pixel grouping lpg for a better preservation of image local structures a pixel and its nearest neighbors are modeled as a vector variable whose training samples are selected from the local window by using block matching based lpg such an lpg procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for pca transform estimation so that the image local features can be well preserved after coefficient shrinkage in the pca domain to remove the noise the lpg pca denoising procedure is iterated one more time to further improve the denoising performance and the noise level is adaptively adjusted in the second stage experimental results on benchmark test images demonstrate that the lpg pca method achieves very competitive denoising performance especially in image fine structure preservation compared with state of the art denoising algorithms

iterative kernel principal component analysis for image modeling in recent years kernel principal component analysis kpca has been suggested for various image processing tasks requiring an image model such as e g denoising or compression the original form of kpca however can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed we therefore propose a new iterative method for performing kpca the kernel hebbian algorithm which iteratively estimates the kernel principal components with only linear order memory complexity in our experiments we compute models for complex image classes such as faces and natural images which require a large number of training examples the resulting image models are tested in single frame super resolution and denoising applications the kpca model is not specifically tailored to these tasks in fact the same model can be used in super resolution with variable input resolution or denoising with unknown noise characteristics in spite of this both super resolution and denoising performance are comparable to existing methods

stability of the radau ia and lobatto iiic methods for delay differential equations recently we have proved that the radau ia and lobatto iiic methods are p stable i e they have an analogous stability property to a stability with respect to scalar delay differential equations ddes in this paper we study stability of those methods applied to multidimensional ddes we show that they have a similar property to p stability with respect to multidimensional equations which satisfy certain conditions for asymptotic stability of the zero solutions the conditions are closely related to stability criteria for ddes considered in systems theory

on the existence and structure of ψ algebras of totally characteristic operators on compact manifolds with boundary as a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth compact manifold x with boundary a algebra a b x b 1 2 l bl2 x b 1 2 containing the algebra 0b cl x b 1 2 of totally characteristic pseudodifferential operators introduced by melrose 25 in 1981 as a dense subalgebra further there is a homomorphism b a a b x b 1 2 q b characterizing the fredholm property of a a b x b 1 2 by means of the invertibility of b a a q b where q b is an algebra of c symbols reflecting the smooth structure of the manifold x the fredholm inverses of fredholm operators in a b x b 1 2 are again in the algebra a b x r 1 2 and we have elliptic regularity corresponding to the scale bhmb x b 1 2 of b sobolev spaces naturally associated to x localized to the interior of x we recover the ordinary pseudodifferential calculus finally spectrum jacobson topology and the relationship of certain closed ideals in the algebra a b x b 1 2 are described explicitly

technical communique on delay dependent stability and decay estimate for uncertain systems with time varying delay in this note for a class of linear uncertain systems with time varying delay a delay dependent robust stability criterion which can give information on the decay rate of the systems state is presented

average consensus in multi agent systems with uncertain topologies and multiple time varying delays abstract in this paper we investigate average consensus problem in continuous time multi agent systems with uncertain topologies as well as multiple time varying communication delays the network of dynamic agents is directed and both fixed and switching topologies are considered by using the linear matrix inequality method we prove that all the nodes in the network can achieve average consensus asymptotically for appropriate delays and uncertainties if the network topology is weakly connected and balanced feasible linear matrix inequalities are established to determine the maximal allowable upper bounds of multiple delays numerical examples are presented to illustrate the availability of the theoretical results

neurocomputing with time delay analysis for solving convex quadratic programming problems this paper presents a neural network computational scheme with time delay consideration for solving convex quadratic programming problems based on some known results a delay margin is explicitly determined for the stability of the neural dynamics under which the states of the neural network does not oscillate the configuration of the proposed neural network is provided operational characteristics of the neural network are demonstrated via numerical examples

missing intensity interpolation using a kernel pca based pocs algorithm and its applications a missing intensity interpolation method using a kernel principal component analysis pca based projection onto convex sets pocs algorithm and its applications are presented in this paper in order to interpolate missing intensities within a target image the proposed method reconstructs local textures containing the missing pixels by using the pocs algorithm in this reconstruction process a nonlinear eigenspace is constructed from each kind of texture and the optimal subspace for the target local texture is introduced into the constraint of the pocs algorithm in the proposed method the optimal subspace can be selected by monitoring errors converged in the reconstruction process this approach provides a solution to the problem in conventional methods of not being able to effectively perform adaptive reconstruction of the target textures due to missing intensities and successful interpolation of the missing intensities by the proposed method can be realized furthermore since our method can restore any images including arbitrary shaped missing areas its potential in two image reconstruction tasks image enlargement and missing area restoration is also shown in this paper

the asymptotic stability of linear autonomous systems with commensurate time delays the asymptotic stability of linear systems with commensurate time delays is studied algorithms are given to check if a given system is asymptotically stable independent of delay or to determine the largest delay time the system can tolerate to preserve its asymptotic stability these algorithms are simple to apply since they require only to find the eigenvalues of two specially constructed matrices and some simple mathematical calculations

scalar criteria for exponential stability of functional differential equations abstract using a novel approach we present some scalar criteria for the exponential stability of general functional differential equations both delay independent and delay dependent stability criteria are provided a discussion of the obtained results is given

robust stability of interval time delay systems with delay dependence abstract this paper proposes a sufficient robust stability condition for interval time delay systems with delay dependence the properties of the comparison theorem and matrix measure are employed to investigate the problem the stability criteria are delay dependent and less conservative than delay independent stability criteria 5 6 12 16 and delay dependent stability criteria 1 14 15 17 when delay is small however the results of this paper indeed give us one more choice for the stability examination of the interval time delay systems simulation examples are given to demonstrate the application of our result

robust stabilization of uncertain systems with time varying multistate delay the authors deal with the problem of stabilizing a class of uncertain linear systems with time varying multi state delay and subject to norm bounded parameter uncertainty via memoryless linear state feedback some sufficient conditions for the robust stabilizability are derived fur this class of uncertain systems if there exists a positive definite symmetric solution satisfying the algebraic riccati equation or inequality a suitable memoryless state feedback law can be derived also moreover all such parametric algebraic riccati inequalities have been transformed into some linear matrix inequality problems so there is no tuning of the parameters to gain a stabilizing solution

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

the pre image problem in kernel methods in this paper we address the problem of finding the pre image of a feature vector in the feature space induced by a kernel this is of central importance in some kernel applications such as on using kernel principal component analysis pca for image denoising unlike the traditional method in which relies on nonlinear optimization our proposed method directly finds the location of the pre image based on distance constraints in the feature space it is noniterative involves only linear algebra and does not suffer from numerical instability or local minimum problems evaluations on performing kernel pca and kernel clustering on the usps data set show much improved performance

context aware patch based image inpainting using markov random field modeling in this paper we first introduce a general approach for context aware patch based image inpainting where textural descriptors are used to guide and accelerate the search for well matching candidate patches a novel top down splitting procedure divides the image into variable size blocks according to their context constraining thereby the search for candidate patches to nonlocal image regions with matching context this approach can be employed to improve the speed and performance of virtually any patch based inpainting method we apply this approach to the so called global image inpainting with the markov random field mrf prior where mrf encodes a priori knowledge about consistency of neighboring image patches we solve the resulting optimization problem with an efficient low complexity inference method experimental results demonstrate the potential of the proposed approach in inpainting applications like scratch text and object removal improvement and significant acceleration of a related global mrf based inpainting method is also evident

analytic k theory on manifolds with corners let y be a compact manifold in 1 atiyah proposed an analytic delinition of the k homology groups k y defined abstractly as the dual theory to the atiyah hirzebruch k cohomology theory these ideas were developed by kasparov 15 and brown douglas and fillmore lo cycles for this analytic k homology theory are abstract elliptic operators i e bounded linear operators between hilbert spaces satisfying additional conditions derived from the properties of elliptic pseudo differential operators in particular elliptic pseudodifferential operators between sections of vector bundles define such cycles the homology class of the cycle depends only on the principal symbol and indeed only on the k cohomology class it represents on the cotangent bundle in fact it had already been shown in essence by atiyah that the resulting map

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

bccb preconditioners for solving linear systems from delay differential equations we consider the solution of delay differential equations by using boundary value methods bvms these methods require the solution of some nonsymmetric large and sparse linear systems in this paper these systems are solved by using the gmres method a mixed type block circulant preconditioner with circulant blocks bccb preconditioner is proposed to speed up the convergence rate of the gmres method if an a ink 1 k 2 stable bvm is used and the system matrices of delay differential equations are normal then the bccb preconditioner is invertible the advantage of using such kind of preconditioner is that we can use two dimensional fast fourier transform to reduce the operation cost numerical results are given to show the effectiveness of our methods

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

color direction patch sparsity based image inpainting using multidirection features this paper proposes a color direction patch sparsity based image inpainting method to better maintain structure coherence texture clarity and neighborhood consistence of the inpainted region of an image the method uses super wavelet transform to estimate the multi direction features of a degraded image and combines with color information to construct the weighted color direction distance wcdd to measure the difference between two patches based on the wcdd the color direction structure sparsity is defined to obtain a more robust filling order and more suitable multiple candidate patches are searched then the target patches are sparsely represented by the multiple candidate patches under neighborhood consistency constraints in both the color and the multi direction spaces experimental results are presented to demonstrate the effectiveness of the proposed approach on tasks such as scratch removal text removal block removal and object removal the effects of super wavelet transforms and direction features are also investigated

singularities of solutions to semilinear boundary value problems soit p un operateur differentiel d ordre 2 strictement hyperbolique sur une region ouverte cr n a frontiere lisse non caracteristique etant donnee une solution u h s loc s n 1 2 de pu f x u on etudie la propagation des singularites microlocales h r pour s r 2n n 2 1 2 dans la situation generale ou le champ hamiltonien de p hp peut etre tangent a t o a un ordre infini ou fini arbitrairement eleve

continuous time average consensus under dynamically changing topologies and multiple time varying delays abstract the average consensus in continuous time multi agent systems with dynamically changing topologies and multiple time varying delays is studied in this paper the network topology is captured by weighted digraphs which are weakly connected and balanced some feasible linear matrix inequalities are established to determine the allowable upper bounds of multiple delays that guarantee the average consensus of the system numerical examples are provided to show the usefulness of the theoretical results

a simple criterion for global exponential stabilizability of nonlinear multiple time delay singularly perturbed systems a simple criterion for global exponential stability of a class of nonlinear multiple time delay singularly perturbed systems without the so called interconnection conditions is proposed in this paper a globally exponentially stabilizing composite feedback control is also proposed such that the chosen design manifold becomes an exact integral manifold and the trajectories of the closed loop systems starting from any initial states are steered along the integral manifold to the origin exponentially for all sufficiently small singular perturbation parameters e the composite control technique is adopted in this paper

stability tests of interval time delay systems abstract this paper presents some sufficient conditions for robust stability independent of delay and decaying rate for uncertain time delay systems the obtained robustness results are extended to cover the class of interval time delay systems sufficient conditions are also derived for checking the instability of this class of systems the results are given in terms of norm and matrix measure easy to check a comparison between the derived conditions is given numerical computations are performed to illustrate the results

normal solvability of elliptic boundary value problems on asymptotically flat manifolds abstract normal solvability is shown for a class of boundary value problems on riemannian manifolds with noncompact boundary using a concept of weighted pseudodifferential operators and weighted sobolev spaces together with lopatinski shapiro type boundary conditions an essential step is to show that the standard normal derivative defined in terms of the riemannian metric is in fact a weighted pseudodifferential operator of the considered class provided the metric is compatible with the symbols

edge based image restoration in this paper we propose a new image inpainting algorithm that relies on explicit edge information the edge information is used both for the reconstruction of a skeleton image structure in the missing areas as well as for guiding the interpolation that follows the structure reconstruction part exploits different properties of the edges such as the colors of the objects they separate an estimate of how well one edge continues into another one and the spatial order of the edges with respect to each other in order to preserve both sharp and smooth edges the areas delimited by the recovered structure are interpolated independently and the process is guided by the direction of the nearby edges the novelty of our approach lies primarily in exploiting explicitly the constraint enforced by the numerical interpretation of the sequential order of edges as well as in the pixel filling method which takes into account the proximity and direction of edges extensive experiments are carried out in order to validate and compare the algorithm both quantitatively and qualitatively they show the advantages of our algorithm and its readily application to real world cases

an analogue of the thom isomorphism for crossed products of a c algebra by an action of r abstract in this paper we show the existence and uniqueness of a natural isomorphism oj of kj a with kj 1 a r j z 2 where a r is a c dynamical r system k is the functor of topological k theory and a r is the crossed product of a by the action of r the pimsner voiculescu exact sequence is obtained as a corollary we show that given an invariant trace on a with dual trace gt one has gto 1 u 1 2 i u u for any unitary u in the domain of the derivation of a associated to the action finally we show that the crossed product of c s3 continuous functions on the 3 sphere by a minimal diffeomorphism is a simple c algebra with no nontrivial idempotent

stability of perturbed systems with time varying delays abstract this paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time delay systems subject to parametric unstructured or highly structured perturbations the criteria given in this paper are delay independent or delay dependent the considered delay may be time varying an estimation of the transient behaviour of the studied systems is also provided exponential rate of convergence scalar or vectorial inequalities involving hurwitz matrices matrix measures and norms constitute the mathematical foundations of the exposed results

stability criterion for linear systems with nonlinear delayed perturbations a stability criterion for linear systems with nonlinear time varying delayed perturbations has been derived in light of razumikhin type methods as the proposed criterion is easily applicable and independent of the delay size it provides an effective method for the stability analysis of time delay systems

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

adaptive subspace based inverse projections via division into multiple sub problems for missing image data restoration this paper presents adaptive subspace based inverse projections via division into multiple sub problems asip dimss for missing image data restoration in the proposed method a target problem for estimating missing image data is divided into multiple sub problems and each sub problem is iteratively solved with the constraints of other known image data by projection into a subspace model of image patches the solution of each sub problem is calculated where we call this procedure subspace based inverse projection for simplicity the proposed method can use higher dimensional subspaces for finding unique solutions in each sub problem and successful restoration becomes feasible since a high level of image representation performance can be preserved this is the biggest contribution of this paper furthermore the proposed method generates several subspaces from known training examples and enables derivation of a new criterion in the above framework to adaptively select the optimal subspace for each target patch in this way the proposed method realizes missing image data restoration using asip dims since our method can estimate any kind of missing image data its potential in two image restoration tasks image inpainting and super resolution based on several methods for multivariate analysis is also shown in this paper

simple stability criteria for single and composite linear systems with time delays easy ways to test the stability of systems involving time delays have been sought in this paper several stability conditions with an extremely simple form are provided first some criteria for single linear systems with time delays are presented then these results are extended to the composite linear systems with time delays which exist in each subsystem and in the interconnections between subsystems among these criteria those which are expressed by scalar inequalities also permit us to assess the transient behaviour of systems

on the index of elliptic operators on manifolds with boundary abstract an extension of the index theorem of atiyah patodi singer for dirac type operators on manifolds with boundary to general elliptic b pseudodifferential operators is given first basic results about the complex powers of these operators are established then the main formula for the index of an elliptic b pseudo differential operator acting on an r weighted sobolev space r r is proved this expresses the index as the sum of an interior contribution given in terms of regularized zeta functions and a boundary contribution generalizing the eta invariant of atiyah patodi singer this second term measures the asymmetry of the boundary spectrum of the operator a discrete set in the complex plane with respect to the line z c im z r

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

stability analysis of linear systems with time delay this paper presents asymptotic stability criteria for linear systems with time delay the results not only improve previous results but also provide a bound for the delay time such that if the system is asymptotically stable when the delay does not exist it retains the asymptotic stability when the delay time is within the bound

global dynamics of one class of nonlinear nonautonomous systems with time varying delays abstract a class of nonautonomous systems of nonlinear delay differential equations was studied via construction of matrix inequalities and comparison techniques the results for the nonautonomous systems with time varying delays are novel e g the global stability of differential equations with nonlinear casual volterra operators is considered for the first time in the literature criteria obtained for permanence and global attractivity are explicit and hence are convenient for applying verifying in practice we illustrate applications of the results obtained to the nonautonomous and asymptotically autonomous nicholson type models