the set of smooth quasi periodic schrodinger cocycles with positive lyapunov exponent is not open one knows that the set of quasi periodic schrodinger cocycles with positive lyapunov exponent is open and dense in analytic topology in this paper we construct cocycles with positive lyapunov exponent which can be arbitrarily approximated by ones with zero lyapunov exponent in the space of mathcal c l 1 le l le infty smooth quasi periodic cocycles which shows that the set of quasi periodic schrodinger cocycles with positive lyapunov exponent is not open in smooth topology

a non isothermal ginzburg landau model in superconductivity existence uniqueness and asymptotic behaviour abstract in this paper we study a ginzburg landau model which describes the behaviour of a superconducting material including thermal effects we extend the traditional formulation of the problem by introducing the temperature as an additional state variable accordingly together with the gor kov eliashberg system we introduce an evolution equation for the absolute temperature we examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature neglecting the electromagnetic field for this problem existence and uniqueness of the solution are shown finally we analyze the asymptotic behaviour of the solutions proving that the system possesses a global attractor

time dependent ginzburg landau equations of superconductivity abstract we study in this article the existence uniqueness and long time behavior of the solutions of a nonstationary ginzburg landau superconductivity model we first prove the existence and uniqueness of solutions with h 1 initial data which are crucial for the study of the global attractor we also obtain for the first time the existence of global weak solutions of the model with l 2 initial data it is then proved that the ginzburg landau system admits a global attractor which represents exactly all the long time dynamics of the system the global attractor obtained consists of exactly the set of steady state solutions and its unstable manifold its hausdorff and fractal dimensions are estimated in terms of the physically relevant ginzburg landau parameter diffusion parameter and applied magnetic field we construct explicitly absorbing sets for some abstract semigroups having a lyapunov functional and consequently prove the existence of global attractors this abstract result is applied to the ginzburg landau system for which the existence of global attractor does not seem to be the direct consequence of some a priori estimates of solutions

beyond diffusion process nss is proposed to replace the role of diffusion process to capture the geometry of the underlying manifold in shape and image retrieval nss is more precise than diffusion process and more robust to noise nss is computed more efficiently than diffusion process and it no longer needs an iterative process to guarantee the retrieval precision we obtain state of the art retrieval performance on several benchmark datasets measuring the similarity between two instances reliably shape or image is a challenging problem in shape and image retrieval in this paper a simple yet effective method called neighbor set similarity nss is proposed which is superior to both traditional pairwise similarity and diffusion process nss makes full use of contextual information to capture the geometry of the underlying manifold and obtains a more precise measure than the original pairwise similarity moreover based on nss we propose a powerful fusion process to utilize the complementarity of different descriptors to further enhance the retrieval performance the experimental results on mpeg 7 shape dataset n s image dataset and orl face dataset demonstrate the effectiveness of the proposed method in addition the time complexity of nss is much lower than diffusion process which suggests that nss is more suitable for large scale image retrieval than diffusion process

shape retrieval using hierarchical total bregman soft clustering in this paper we consider the family of total bregman divergences tbds as an efficient and robust distance measure to quantify the dissimilarity between shapes we use the tbd based l1 norm center as the representative of a set of shapes and call it the t center first we briefly present and analyze the properties of the tbds and t centers following our previous work in 1 then we prove that for any tbd there exists a distribution which belongs to the lifted exponential family lef of statistical distributions further we show that finding the maximum a posteriori map estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tbd to find the t centers this leads to a new clustering technique namely the total bregman soft clustering algorithm we evaluate the tbd t center and the soft clustering algorithm on shape retrieval applications our shape retrieval framework is composed of three steps 1 extraction of the shape boundary points 2 affine alignment of the shapes and use of a gaussian mixture model gmm 2 3 4 to represent the aligned boundaries and 3 comparison of the gmms using tbd to find the best matches given a query shape to further speed up the shape retrieval algorithm we perform hierarchical clustering of the shapes using our total bregman soft clustering algorithm this enables us to compare the query with a small subset of shapes which are chosen to be the cluster t centers we evaluate our method on various public domain 2d and 3d databases and demonstrate comparable or better results than state of the art retrieval techniques

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

global solution to a singular integro differential system related to the entropy balance this paper is devoted to the mathematical analysis of a thermodynamic model describing phase transitions with thermal memory in terms of an entropy equation and a momentum balance for the microforces the initial and boundary value problem is addressed for the related integro differential system of partial differential equations pdes existence and uniqueness continuous dependence on the data and regularity results are proved for the global solution in a finite time interval

a lower bound on the lyapunov exponent for the generalized harper s model we obtain a lower bound for the lyapunov exponent of a family of discrete schrodinger operators hu n u n 1 u n 1 2a 1 cos 2 pi theta n alpha u n 2a 2 cos 4 pi theta n alpha u n that incorporates both a 1 and a 2 thus going beyond the herman s bound

hierarchical string cuts a translation rotation scale and mirror invariant descriptor for fast shape retrieval this paper presents a novel approach for both fast and accurately retrieving similar shapes a hierarchical string cuts hscs method is proposed to partition a shape into multiple level curve segments of different lengths from a point moving around the contour to describe the shape gradually and completely from the global information to the finest details at each hierarchical level the curve segments are cut by strings to extract features that characterize the geometric and distribution properties in that particular level of details the translation rotation scale and mirror invariant hsc descriptor enables a fast metric based matching to achieve the desired high accuracy encouraging experimental results on four databases demonstrated that the proposed method can consistently achieve higher or similar retrieval accuracies than the state of the art benchmarks with a more than 120 times faster speed this may suggest a new way of developing shape retrieval techniques in which a high accuracy can be achieved by a fast metric matching algorithm without using the time consuming correspondence optimization strategy

co transduction for shape retrieval in this paper we propose a new shape object retrieval algorithm namely co transduction the performance of a retrieval system is critically decided by the accuracy of adopted similarity measures distances or metrics in shape object retrieval ideally intraclass objects should have smaller distances than interclass objects however it is a difficult task to design an ideal metric to account for the large intraclass variation different types of measures may focus on different aspects of the objects for example measures computed based on contours and skeletons are often complementary to each other our goal is to develop an algorithm to fuse different similarity measures for robust shape retrieval through a semisupervised learning framework we name our method co transduction which is inspired by the co training algorithm given two similarity measures and a query shape the algorithm iteratively retrieves the most similar shapes using one measure and assigns them to a pool for the other measure to do a re ranking and vice versa using co transduction we achieved an improved result of 97 72 bull s eye measure on the mpeg 7 data set over the state of the art performance we also present an algorithm called tri transduction to fuse multiple input similarities and it achieved 99 06 on the mpeg 7 data set our algorithm is general and it can be directly applied on input similarity measures metrics it is not limited to object shape retrieval and can be applied to other tasks for ranking retrieval

on resonances and the formation of gaps in the spectrum of quasi periodic schrodinger equations we consider one dimensional difference schrodinger equations h x n n 1 n 1 v x n n e n n z x 0 1 with real analytic potential function v x if l e w o is greater than 0 for all e e e and some diophantine 0 then the integrated density of states is absolutely continuous for almost every close to 0 as shown by the authors in earlier work in this paper we establish the formation of a dense set of gaps in spec h x w e e our approach is based on an induction on scales argument and is therefore both constructive as well as quantitative resonances between eigenfunctions of one scale lead to pre gaps at a larger scale to pass to actual gaps in the spectrum we show that these pre gaps cannot be filled more than a finite and uniformly bounded number of times to accomplish this one relates a pre gap to pairs of complex zeros of the dirichlet determinants off the unit circle amongst other things we establish a nonperturbative version of the co variant parametrization of the eigenvalues and eigenfunctions via the phases in the spirit of sinai s perturbative description of the spectrum via his function a this allows us to relate the gaps in the spectrum with the graphs of the eigenvalues parametrized by the phase our infinite volume theorems hold for all diophantine frequencies up to a set of hausdorff dimension zero

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

matching images with multiple descriptors an unsupervised approach for locally adaptive descriptor selection with the aim to improve the performance of feature matching we present an unsupervised approach for adaptive description selection in the space of homographies inspired by the observation that the homographies of correct feature correspondences vary smoothly along the spatial domain our approach stands on the unsupervised nature of feature matching and can choose a good descriptor locally for matching each feature point instead of using one global descriptor to this end the homography space serves as the domain for selecting various heterogeneous descriptors correspondences obtained by any descriptors are considered as points in the space and their geometric coherence and spatial continuity are measured via computing the geodesic distances in this way mutual verification across different descriptors is allowed and correct correspondences will be highlighted with a high degree of consistency short geodesic distances here it follows that one class svm can be applied to identifying these correct correspondences and achieves adaptive descriptor selection the proposed approach is comprehensively compared with the state of the art approaches and evaluated on five benchmarks of image matching the promising results manifest its effectiveness

object matching with hierarchical skeletons the skeleton of an object provides an intuitive and effective abstraction which facilitates object matching and recognition however without any human interaction traditional skeleton based descriptors and matching algorithms are not stable for deformable objects specifically some fine grained topological and geometrical features would be discarded if the skeleton was incomplete or only represented significant visual parts of an object moreover the performance of skeleton based matching highly depends on the quality and completeness of skeletons in this paper we propose a novel object representation and matching algorithm based on hierarchical skeletons which capture the shape topology and geometry through multiple levels of skeletons for object representation we reuse the pruned skeleton branches to represent the coarse and fine grained shape topological and geometrical features moreover this can improve the stability of skeleton pruning without human interaction we also propose an object matching method which considers both global shape properties and fine grained deformations by defining singleton and pairwise potentials for similarity computation between hierarchical skeletons our experiments attest our hierarchical skeleton based method a significantly better performance than most existing shape based object matching methods on six datasets achieving a 99 21 bulls eye score on the mpeg7 shape dataset highlightsit represents the coarse and fine grained shape topological and geometrical features it improves the stability of skeleton pruning without human interaction it considers both global and fine shape properties by different potential functions it achieves a better performance than most existing methods on six datasets experiments attest our method a better performance than most related approaches we achieve a 99 21 bulls eye score on the mpeg7 shape dataset

what are lyapunov exponents and why are they interesting taking as inspiration the fields medal work of artur avila i d like to introduce you to lyapunov exponents my plan is to show how lyapunov exponents play a key role in three areas in which avila s results lie smooth ergodic theory billiards and translation surfaces and the spectral theory of 1 dimensional schrodinger operators but first what are lyapunov exponents let s begin by viewing them in one of their natural habitats the barycentric subdivision of a triangle is a collection of 6 smaller triangles obtained by joining the midpoints of the sides to opposite vertices here s what happens when you start with an equilateral triangle and repeatedly barycentrically subdivide

the lyapunov exponents of generic volume preserving and symplectic maps we show that the integrated lyapunov exponents of c1 volume preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding oseledets splitting is trivial all lyapunov exponents are equal to zero or else dominated uniform hyperbolicity in the projective bundle almost everywhere we deduce a sharp dichotomy for generic volume preserving diffeomorphisms on any compact manifold almost every orbit either is projectively hyperbolic or has all lyapunov exponents equal to zero similarly for a residual subset of all c1 symplectic diffeomorphisms on any compact manifold either the diffeomorphism is anosov or almost every point has zero as a lyapunov exponent with multiplicity at least 2 finally given any set s gl d satisfying an accessibility condition for a residual subset of all continuous s valued cocycles over any measure preserving homeomorphism of a compact space the oseledets splitting is either dominated or trivial the condition on s is satisfied for most common matrix groups and also for matrices that arise from discrete schr nodinger operators

robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching in this paper we are going to present a novel shape similarity retrieval algorithm that can be used to match and recognize 2d objects the match process uses a new multi resolution polygonal shape descriptor that is invariant to scale rotation and translation the shape descriptor equally segments the contour of any shape regardless of its complexity and captures three features around its center including the distance and slope relative to the center all parameters are normalized relative to the max values the novel shape matching algorithm uses the shape descriptor and applies it by linearly scanning a stored set of shapes and measuring the similarity using elastic comparisons of shape segments similarity measurement is achieved by the sum of differences distance measure the multi resolution segmentation provides flexibility for applications that have different time and space requirements while maintaining high accuracy results and the elastic matching adds an advantage when matching partially occluded shapes we applied our algorithms on many test databases including the mpeg 7 shape core experiment and achieved the highest result reported with a score of 84 33 for the mpeg 7 part b similarity test

second phase transition line we study the phase transion line of the almost mathieu operator that separates arithmetic regions corresponding to singular continuous and a e pure point regimes and prove that both purely singular continuous and a e pure point spectrum occur for dense sets of frequencies

shape classification using the inner distance part structure and articulation are of fundamental importance in computer and human vision we propose using the inner distance to build shape descriptors that are robust to articulation and capture part structure the inner distance is defined as the length of the shortest path between landmark points within the shape silhouette we show that it is articulation insensitive and more effective at capturing part structures than the euclidean distance this suggests that the inner distance can be used as a replacement for the euclidean distance to build more accurate descriptors for complex shapes especially for those with articulated parts in addition texture information along the shortest path can be used to further improve shape classification with this idea we propose three approaches to using the inner distance the first method combines the inner distance and multidimensional scaling mds to build articulation invariant signatures for articulated shapes the second method uses the inner distance to build a new shape descriptor based on shape contexts the third one extends the second one by considering the texture information along shortest paths the proposed approaches have been tested on a variety of shape databases including an articulated shape data set mpeg7 ce shape 1 kimia silhouettes the eth 80 data set two leaf data sets and a human motion silhouette data set in all the experiments our methods demonstrate effective performance compared with other algorithms

landmarks inside the shape in the last few decades significant advances in image matching are provided by rich local descriptors that are defined through physical measurements such as reflectance as such measurements are not naturally available for silhouettes existing arsenal of image matching tools cannot be utilized in shape matching we propose that the recently presented spem representation can be used analogous to image intensities to detect local keypoints using invariant image salient point detectors we devise a shape similarity measure based on the number of matching internal regions the performance of the similarity measure in planar shape retrieval indicates that the landmarks inside the shape silhouettes provide a strong representation of the regional characteristics of 2d planar shapes graphical abstractdisplay omitted highlightsan internal landmark based planar shape matching scheme is proposed the shape landmarks are obtained using the recently proposed spem representation properties of spem that allow the use of image descriptors inside shapes are discussed statistical evidence indicates that the number of matches can be used as a similarity measure

spectral characteristics of the unitary critical almost mathieu operator we discuss spectral characteristics of a one dimensional quantum walk whose coins are distributed quasi periodically the unitary update rule of this quantum walk shares many spectral characteristics with the critical almost mathieu operator however it possesses a feature not present in the almost mathieu operator namely singularity of the associated cocycles this feature is however present in the so called extended harper s model we show that this operator has empty absolutely continuous spectrum and that the lyapunov exponent vanishes on the spectrum hence this model exhibits cantor spectrum of zero lebesgue measure for all irrational frequencies and arbitrary phase which in physics is known as hofstadter s butterfly in fact we will show something stronger namely that all spectral parameters in the spectrum are of critical type in the language of avila s global theory of analytic quasiperiodic cocycles we further prove that it has empty point spectrum for each irrational frequency and away from a frequency dependent set of phases having lebesgue measure zero the key ingredients in our proofs are an adaptation of avila s global theory to the present setting self duality via the fourier transform and a johnson type theorem for singular dynamically defined cmv matrices which characterizes their spectra as the set of spectral parameters at which the associated cocycles fail to admit a dominated splitting

examples of discontinuity of lyapunov exponent in smooth quasiperiodic cocycles we study the regularity of the lyapunov exponent for quasiperiodic cocycles t a where t is an irrational rotation x x 2 on s1 and a cl s1 sl 2 r 0 l for any fixed l 0 1 2 and any fixed of bounded type we construct dl cl s1 sl 2 r such that the lyapunov exponent is not continuous at dl in cl topology we also construct such examples in a smaller schrodinger class

continuity of the lyapunov exponents for quasiperiodic cocycles consider the banach manifold of real analytic linear cocycles with values in the general linear group of any dimension and base dynamics given by a diophantine translation on the circle we prove a precise higher dimensional avalanche principle and use it in an inductive scheme to show that the lyapunov spectrum blocks associated to a gap pattern in the lyapunov spectrum of such a cocycle are locally holder continuous moreover we show that all lyapunov exponents are continuous everywhere in this banach manifold irrespective of any gap pattern in their spectra these results also hold for diophantine translations on higher dimensional tori albeit with a loss in the modulus of continuity of the lyapunov spectrum blocks

sharp holder continuity of the lyapunov exponent of finitely differentiable quasi periodic cocycles we show that if the base frequency is diophantine then the lyapunov exponent of a c k quasi periodic sl 2 mathbb r cocycle is 1 2 holder continuous in the almost reducible regime as a consequence we show that if the frequency is diophantine and the potential is small then the integrated density of states of the corresponding quasi periodic schrodinger operator is 1 2 holder continuous

the ten martini problem we prove the conjecture known as the ten martini problem after kac and simon that the spectrum of the almost mathieu operator is a cantor set for all nonzero values of the coupling and all irrational frequencies

similarity fusion for visual tracking multiple features integration and context structure of unlabeled data have proven their effectiveness in enhancing similarity measures in many applications of computer vision however in similarity based object tracking integration of multiple features has been rarely studied in contrast to conventional tracking approaches that utilize pairwise similarity for template matching our approach contributes in two different aspects first multiple features are integrated into a unified similarity to enhance the discriminative ability of similarity measurements second the neighborhood context of the samples in forthcoming frame are employed to further improve the measurements we utilize a diffusion process on a tensor product graph to achieve these goals the obtained approach is validated on numerous challenging video sequences and the experimental results demonstrate that it outperforms state of the art t racking methods

shape vocabulary a robust and efficient shape representation for shape matching in this paper a learning based shape descriptor for shape matching is demonstrated formulated in a bag of words like framework the proposed method summarizes the local features extracted from certain shape to generate a integrated representation it contributes to the speed up of shape matching since the distance metric in the vector space analysis can be directly applied to compare the constructed global descriptors eliminating the time consuming stage of local feature matching similar to the philosophy in spatial pyramid matching a strategy for feature division is applied in the phase of encoded feature pooling and vocabulary learning which helps to construct a more discriminative descriptor incorporating both global and local information also a local contour based feature extraction method is designed for 2d shapes while significant properties of the local contours are inspected for the design of feature division rules the designed local feature extraction method and the feature division rules manage to reduce the variances of shape representation due to the changes in rotation in addition to 2d shape we also present a simple and natural method to extend the proposed method to the scenario of 3d shape representation the proposed shape descriptor is validated on several benchmark data sets for evaluating 2d and 3d shape matching algorithms and it is observed that the investigated shape descriptor maintains superior discriminative power as well as high time efficiency

accurate image search using the contextual dissimilarity measure this paper introduces the contextual dissimilarity measure which significantly improves the accuracy of bag of features based image search our measure takes into account the local distribution of the vectors and iteratively estimates distance update terms in the spirit of sinkhorn s scaling algorithm thereby modifying the neighborhood structure experimental results show that our approach gives significantly better results than a standard distance and outperforms the state of the art in terms of accuracy on the nisteacuter steweacutenius and lola data sets this paper also evaluates the impact of a large number of parameters including the number of descriptors the clustering method the visual vocabulary size and the distance measure the optimal parameter choice is shown to be quite context dependent in particular using a large number of descriptors is interesting only when using our dissimilarity measure we have also evaluated two novel variants multiple assignment and rank aggregation they are shown to further improve accuracy at the cost of higher memory usage and lower efficiency

gauss polynomials and the rotation algebra newton s binomial theorem is extended to an interesting noncommutative setting as follows if in a ring ba ab with commuting witha andb then the generalized binomial coefficient left begin array 20 c n k end array right r arising in the expansion left a b right n sum limits k 0 n left begin array 20 c n k end array right gamma a n k b k resulting from these relations is equal to the value at of the gaussian polynomial left begin array 20 c n k end array right frac left n right left k right left n k right where m 1 x m 1 x m 1 1 x this is of course known in the case 1 from this it is deduced that in the universal c algebraa gq generated by unitariesu andv such thatvu e 2 i uv the spectrum of the self adjoint element u v u v has all the gaps that have been predicted to exist provided that either is rational or is a liouville number in the latter case the gaps are labelled in the natural way viak theory by the set of all non zero integers and the spectrum is a cantor set

analytic quasi perodic cocycles with singularities and the lyapunov exponent of extended harper s model we show how to extend and with what limitations avila s global theory of analytic sl 2 c cocycles to families of cocycles with singularities this allows us to develop a strategy to determine the lyapunov exponent for the extended harper s model for all values of parameters and all irrational frequencies in particular this includes the self dual regime for which even heuristic results did not previously exist in physics literature the extension of avila s global theory is also shown to imply continuous behavior of the le on the space of analytic m 2 mathbb c cocycles this includes rational approximation of the frequency which so far has not been available

metal insulator transition for the almost mathieu operator we prove that for diophantine and almost every the almost mathieu operator h n n 1 ni 1 cos 2 n n exhibits localization for 2 and purely absolutely continuous spectrum for 2

arithmetic spectral transitions for the maryland model we give a precise description of spectra of the maryland model h u n un 1 un 1 tan n un for all values of parameters we introduce an arithmetically defined index and show that for sc h e e and pp h e e since ac h this gives a complete description of the spectral decomposition for all values of parameters and making it the first case of a family where arithmetic spectral transition is described without any parameter exclusion the set of eigenvalues can be explicitly identified for all parameters using the quantization condition we also establish for the first time for this or any other model a quantization condition for singular continuous spectrum an arithmetically defined measure zero set that supports singular continuous measures for all parameters 2017 wiley periodicals inc

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

limit periodic schrodinger operators with a discontinuous lyapunov exponent abstract we construct a limit periodic schrodinger operator for which the lyapunov exponent has a positive measure set of discontinuities we also show that the limit periodic potentials for which the lyapunov exponent is discontinuous are dense in the space of limit periodic potentials

improving shape retrieval by spectral matching and meta similarity we propose two computational approaches for improving the retrieval of planar shapes first we suggest a geometrically motivated quadratic similarity measure that is optimized by way of spectral relaxation of a quadratic assignment by utilizing state of the art shape descriptors and a pairwise serialization constraint we derive a formulation that is resilient to boundary noise articulations and nonrigid deformations this allows both shape matching and retrieval we also introduce a shape meta similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy when applied to the mpeg 7 shape dataset in conjunction with the proposed geometric matching scheme we obtained a retrieval rate of 92 5

exploiting pairwise recommendation and clustering strategies for image re ranking in content based image retrieval cbir systems accurately ranking collection images is of great relevance users are interested in the returned images placed at the first positions which usually are the most relevant ones commonly image content descriptors are used to compute ranked lists in cbir systems in general these systems perform only pairwise image analysis that is compute similarity measures considering only pairs of images ignoring the rich information encoded in the relations among several images this paper presents a novel re ranking approach used to improve the effectiveness of cbir tasks by exploring relations among images in our approach a recommendation based strategy is combined with a clustering method both exploit contextual information encoded in ranked lists computed by cbir systems we conduct several experiments to evaluate the proposed method our experiments consider shape color and texture descriptors and comparisons with other post processing methods experimental results demonstrate the effectiveness of our method

sparse contextual activation for efficient visual re ranking in this paper we propose an extremely efficient algorithm for visual re ranking by considering the original pairwise distance in the contextual space we develop a feature vector called sparse contextual activation sca that encodes the local distribution of an image hence re ranking task can be simply accomplished by vector comparison under the generalized jaccard metric which has its theoretical meaning in the fuzzy set theory in order to improve the time efficiency of re ranking procedure inverted index is successfully introduced to speed up the computation of generalized jaccard metric as a result the average time cost of re ranking for a certain query can be controlled within 1 ms furthermore inspired by query expansion we also develop an additional method called local consistency enhancement on the proposed sca to improve the retrieval performance in an unsupervised manner on the other hand the retrieval performance using a single feature may not be satisfactory enough which inspires us to fuse multiple complementary features for accurate retrieval based on sca a robust feature fusion algorithm is exploited that also preserves the characteristic of high time efficiency we assess our proposed method in various visual re ranking tasks experimental results on princeton shape benchmark 3d object wm srhec07 3d competition yael data set b face mpeg 7 data set shape and ukbench data set image manifest the effectiveness and efficiency of sca

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

singular continuous spectrum for a class of almost periodic jacobi matrices we consider operators parametrized by a o on 2 with matrix ojy i o i fl o y with an cos 2ttcw 6 if ce is a liouville number and 2 we prove that for a e 0 the operator s spectral measures are all singular continuous we consider the operator on l2 z depending upon three parameters x a 0 1 x a 0 u n u n 1 u n 1 x cos 2iran 6 u n in this note we will sketch the proof of the following result whose detailed proof will appear elsewhere 3 theorem 1 fix a an irrational number obeying

the avalanche principle and negative curvature we use the geometric structure of the hyperbolic upper half plane to provide a new proof of the avalanche principle introduced by m goldstein and w schlag in the context of mathrm sl 2 mathbb r matrices this approach allows to interpret and extend this result to arbitrary text cat 1 metric spaces through the proof we deduce a polygonal schur theorem for these spaces

singular spectrum of lebesgue measure zero for one dimensional quasicrystals the spectrum of one dimensional discrete schrodinger operators associated to strictly ergodic dynamical systems is shown to coincide with the set of zeros of the lyapunov exponent if and only if the lyapunov exponent exists uniformly this is used to obtain the cantor spectrum of zero lebesgue measure for all aperiodic subshifts with uniform positive weights this covers in particular all aperiodic subshifts arising from primitive substitutions including new examples such as e g the rudin shapiro substitution our investigation is not based on trace maps instead it relies on an oseledec type theorem due to a furman and a uniform ergodic theorem due to the author

sharp phase transitions for the almost mathieu operator it is known that the spectral type of the almost mathieu operator amo depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency we study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place which solves jitomirskaya s conjecture together with a previous work by avila this gives the sharp description of phase transitions for the amo for the a e phase

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

operators with singular continuous spectrum iii almost periodic schrodinger operators we prove that one dimensional schrodinger operators with even almost periodic potential have no point spectrum for a dense g in the hull this implies purely singular continuous spectrum for the almost mathieu equation for coupling larger than 2 and a dense g in even if the frequency is an irrational with good diophantine properties

holder continuity of the integrated density of states for quasi periodic schrodinger equations and averages of shifts of subharmonic functions in this paper we consider various regularity results for discrete quasiperiodic schr6dinger equations n l pn 1 v 9 nw on eon with analytic potential v we prove that on intervals of positivity for the lyapunov exponent the integrated density of states is holder continuous in the energy provided w has a typical continued fraction expansion the proof is based on certain sharp large deviation theorems for the norms of the monodromy matrices and the avalanche principle the latter refers to a mechanism that allows us to write the norm of a monodromy matrix as the product of the norms of many short blocks in the multi frequency case the integrated density of states is shown to have a modulus of continuity of the form exp log tl for some 0 a 1 but currently we do not obtain holder continuity in the case of more than one frequency we also present a mechanism for proving the positivity of the lyapunov exponent for large disorders for a general class of equations the only requirement for this approach is some weak form of a large deviation theorem for the lyapunov exponents in particular we obtain an independent proof of the herman sorets spencer theorem in the multi frequency case the approach in this paper is related to the recent nonperturbative proof of anderson localization in the quasi periodic case by j bourgain and m goldstein

global theory of one frequency schrodinger operators we study schrodinger operators with a one frequency analytic potential focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials from the dynamical point of view the transition signals the emergence of non uniform hyperbolicity so the dependence of the lyapunov exponent with respect to parameters plays a central role in the analysis though often ill behaved by conventional measures we show that the lyapunov exponent is in fact remarkably regular in a stratified sense which we define the irregularity comes from the matching of nice analytic or smooth functions along sets with complicated geometry this result allows us to establish that the critical set for the transition lies within countably many codimension one subvarieties of the infinite dimensional parameter space a more refined renormalization based analysis shows that the critical set is rather thin within those subvarieties and allows us to conclude that a typical potential has no critical energies such acritical potentials also form an open set and have several interesting properties only finitely many phase transitions may happen but never at any specific point in the spectrum and the lyapunov exponent is minorated in the region of the spectrum where it is positive on the other hand we do show that the number of phase transitions can be arbitrarily large

phase transition and semi global reducibility for 1d continuous schodinger operators with large analytic quasi periodic potentials of two frequencies one knows that the spectral measure is singular at the bottom of the spectrum and purely absolutely continuous in the upper part of the spectrum so there is a phase transition when energy increases in this paper we obtain the exact power law for the phase transition in energy by the semi global reducibility theory of analytic quasi periodic linear systems

a global local affinity graph for image segmentation construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph cut based image segmentation methods in this paper we propose a novel sparse global local affinity graph over superpixels of an input image to capture both short and long range grouping cues and thereby enabling perceptual grouping laws including proximity similarity continuity and to enter in action through a suitable graph cut algorithm moreover we also evaluate three major visual features namely color texture and shape for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics which suggest combining these visual features with different emphases for perceptual grouping in particular an input image is first oversegmented into superpixels at different scales we postulate a gravitation law based on empirical observations and divide superpixels adaptively into small medium and large sized sets global grouping is achieved using medium sized superpixels through a sparse representation of superpixels features by solving a ell 0 minimization problem and thereby enabling continuity or propagation of local smoothness over long range connections small and large sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space and thus implementing perceptual laws for example similarity and proximity finally a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales extensive experiments are carried out on the berkeley segmentation database in comparison with several state of the art graph constructions the results show the effectiveness of the proposed approach which outperforms state of the art graphs using four different objective criteria namely the probabilistic rand index the variation of information the global consistency error and the boundary displacement error

reducibility or nonuniform hyperbolicity for quasiperiodic schrodinger cocycles we show that for almost every frequency r q for every c o potential v r z r and for almost every energy e the corresponding quasiperiodic schr nodinger cocycle is either reducible or nonuniformly hyperbolic this result gives very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic schr nodinger operator and allows us to complete the proof of the aubry andr le conjecture on the measure of the spectrum of the almost mathieu operator

continuity of the measure of the spectrum for quasiperiodic schrodinger operators with rough potentials we study discrete quasiperiodic schrodinger operators on ell 2 mathbb z with potentials defined by holder functions we prove a general statement that for 1 2 and under the condition of positive lyapunov exponents measure of the spectrum at irrational frequencies is the limit of measures of spectra of periodic approximants an important ingredient in our analysis is a general result on uniformity of convergence from above in the subadditive ergodic theorem for strictly ergodic cocycles

learning context sensitive shape similarity by graph transduction shape similarity and shape retrieval are very important topics in computer vision the recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes in this paper we provide a new perspective to this problem by considering the existing shapes as a group and study their similarity measures to the query shape in a graph structure our method is general and can be built on top of any existing shape similarity measure for a given similarity measure a new similarity is learned through graph transduction the new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query the basic idea here is related to pagerank ranking which forms a foundation of google web search the presented experimental results demonstrate that the proposed approach yields significant improvements over the state of art shape matching algorithms we obtained a retrieval rate of 91 61 percent on the mpeg 7 data set which is the highest ever reported in the literature moreover the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering

disconnected skeleton shape at its absolute scale we present a new skeletal representation along with a matching framework to address the deformable shape recognition problem the disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale our motivation is to rely on stable properties the shape instead of inaccurately measured secondary details the new representation does not suffer from the common instability problems of the traditional connected skeletons and the matching process gives quite successful results on a diverse database of 2d shapes an important difference of our approach from the conventional use of skeleton is that we replace the local coordinate frame with a global euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations as a result we can produce descriptions that are sensitive to any combination of changes in scale position orientation and articulation as well as invariant ones

recognize objects with three kinds of information in landmarks abstract object recognition is one of the most important tasks in computer vision domain and it has been extensively applied in many areas during the last three decades in this paper a method is proposed to recognize objects in shape spaces in which landmarks have three kinds of information i e landmarks position angle and feature vector by comparing angle and feature vector a landmark in an image can correspond with a few number of landmarks in another image then the pixel s positions of landmarks from two images are used to calculate the procrustean distance in a shape space if the value of the procrustean distance is smaller than a predefined threshold the two sets of landmarks will be considered to match each other applying the proposed method two dimensional objects including occluded objects can be recognized quickly

absolute continuity of the integrated density of states for the almost mathieu operator with non critical coupling we show that the integrated density of states of the almost mathieu operator is absolutely continuous if and only if the coupling is non critical we deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase settling the measure theoretical case of problem 6 of barry simon s list of schrodinger operator problems for the twenty first century

a condition of boshernitzan and uniform convergence in the multiplicative ergodic theorem this paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts if such a subshift satisfies a certain condition originally introduced by boshernitzan every locally constant sl 2 r valued cocycle is uniform as a consequence the corresponding schrodinger operators exhibit cantor spectrum of lebesgue measure zero an investigation of boshernitzan s condition then shows that these results cover all earlier results of this type and moreover provide various new ones in particular boshernitzan s condition is shown to hold for almost all circle maps and almost all arnoux rauzy subshifts

continuity of the lyapunov exponent for quasiperiodic operators with analytic potential we study regularity properties of the lyapunov exponent l of one frequency quasiperiodic operators with analytic potential under no assumptions on the diophantine class of the frequency we prove joint continuity of l in frequency and energy at every irrational frequency

geometry based image retrieval in binary image databases in this paper a geometry based image retrieval system is developed for multiobject images we model both shape and topology of image objects using a structured representation called curvature tree ct the hierarchy of the ct reflects the inclusion relationships between the image objects to facilitate shape based matching triangle area representation tar of each object is stored at the corresponding node in the ct the similarity between two multiobject images is measured based on the maximum similarity subtree isomorphism mssi between their cts for this purpose we adopt a recursive algorithm to solve the mssi problem and a very effective dynamic programming algorithm to measure the similarity between the attributed nodes our matching scheme agrees with many recent findings in psychology about the human perception of multiobject images experiments on a database of 13 500 real and synthesized medical images and the mpeg 7 ce 1 database of 1 400 shape images have shown the effectiveness of the proposed method

on the measure of the spectrum for the almost mathieu operator we obtain partial results on the conjecture that for the almost mathieu operator at irrational frequency the measure of the spectrum s 4 2 for 2 we show that if n is rational and alpha n to alpha irrational then s alpha n lambda theta to 4 2 lambda

uniform positivity and continuity of lyapunov exponents for a class of c 2 quasiperiodic schrodinger cocycles abstract we show that for a class of c 2 quasiperiodic potentials and for any fixed diophantine frequency the lyapunov exponent of the corresponding schrodinger cocycles as a function of energies are uniformly positive and weakly holder continuous as a corollary we obtain that the corresponding integrated density of states is weakly holder continuous as well our approach is of purely dynamical systems which depends on a detailed analysis of asymptotic stable and unstable directions we also apply it to more general sl 2 r cocycles which in turn can be applied to get uniform positivity and continuity of lyapunov exponents around unique nondegenerate extremal points of any smooth potential and to a certain class of c 2 szeg cocycles