a topological property of rational w languages abstract we prove that any rational subset k of a is the set of cluster points of a equipped with some ultrametric distance having some specific properties

shape retrieval using triangle area representation and dynamic space warping in this paper we present a shape retrieval method using triangle area representation for nonrigid shapes with closed contours the representation utilizes the areas of the triangles formed by the boundary points to measure the convexity concavity of each point at different scales or triangle side lengths this representation is effective in capturing both local and global characteristics of a shape invariant to translation rotation and scaling and robust against noise and moderate amounts of occlusion in the matching stage a dynamic space warping dsw algorithm is employed to search efficiently for the optimal least cost correspondence between the points of two shapes then a distance is derived based on the optimal correspondence the performance of our method is demonstrated using four standard tests on two well known shape databases the results show the superiority of our method over other recent methods in the literature

strong fairness and ultra metrics abstract we answer an open question of costa and hennessy and present a characterization of the infinite fair computations in finite labeled transition systems without any structure of the states as cluster points in metric spaces this technique is applied to reduce the logical complexity of several known fairness concepts from 03 to 02 and from 11 to 03 respectively

superstability and rigorous asymptotics in singularly perturbed state dependent delay differential equations abstract we study the singularly perturbed state dependent delay differential equation e x t x t k x t r r r x t 1 x t which is a special case of the equation e x t g x t x t r r r x t one knows that for every sufficiently small e 0 eq possesses at least one so called slowly oscillating periodic solution and moreover the graph of every such solution approaches a specific sawtooth like shape as e 0 in this paper we obtain higher order asymptotics of the sawtooth including the location of the minimum and maximum of the solution with the form of the solution near these turning points and as well an asymptotic formula for the period using these and other asymptotic formulas we further show that the solution enjoys the property of superstability namely the nontrivial characteristic multipliers are of size o e for small e this stability property implies that this solution is unique among all slowly oscillating periodic solutions again for small e

angular pattern and binary angular pattern for shape retrieval in this paper we propose two novel shape descriptors angular pattern ap and binary angular pattern bap and a multiscale integration of them for shape retrieval both ap and bap are intrinsically invariant to scale and rotation more importantly being global shape descriptors the proposed shape descriptors are computationally very efficient while possessing similar discriminability as state of the art local descriptors as a result the proposed approach is attractive for real world shape retrieval applications the experiments on the widely used mpeg 7 and tari 1000 data sets demonstrate the effectiveness of the proposed method in comparison with existing methods

sequency ordered complex hadamard transform properties computational complexity and applications in this paper the generation of sequency ordered complex hadamard transform scht based on the complex rademacher matrices is presented the exponential form of scht is also derived and the proof for the unitary property of scht is given using the sparse matrix factorization the fast and efficient algorithm to compute the scht transform is developed and its computation load is described certain properties of the scht matrices are derived and analyzed with the discussion of scht applications in spectrum analysis and image watermarking relations of scht with fast fourier transform fft and unified complex hadamard transform ucht are discussed

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

linearized stability in periodic functional differential equations with state dependent delays in this paper we study stability of periodic solutions of a class of nonlinear functional differential equations fdes with state dependent delays using the method of linearization we show that a periodic solution of the nonlinear fde is exponentially stable if the zero solution of an associated linear periodic linear homogeneous fde is exponentially stable

classification of plant leaf images with complicated background classifying plant leaves has so far been an important and difficult task especially for leaves with complicated background where some interferents and overlapping phenomena may exist in this paper an efficient classification framework for leaf images with complicated background is proposed first a so called automatic marker controlled watershed segmentation method combined with pre segmentation and morphological operation is introduced to segment leaf images with complicated background based on the prior shape information then seven hu geometric moments and sixteen zernike moments are extracted as shape features from segmented binary images after leafstalk removal in addition a moving center hypersphere mch classifier which can efficiently compress feature data is designed to address obtained mass high dimensional shape features finally experimental results on some practical plant leaves show that proposed classification framework works well while classifying leaf images with complicated background there are twenty classes of practical plant leaves successfully classified and the average correct classification rate is up to 92 6

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

differentiability of solutions with respect to parameters in neutral differential equations with state dependent delays in this paper we consider a class of nonlinear neutral differential equations with state dependent delays in both the neutral and the retarded terms we study well posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the c norm

on differentiability of solutions with respect to parameters in state dependent delay equations in this paper we study differentiability of solutions with respect to parameters in state dependent delay equations in particular we give sufficient conditions for differentiability of solutions in thew1 pnorm 1 p in establishing our main results we make use of a version of the uniform contraction principle for quasi banach spaces

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

shape matching and modeling using skeletal context shape is a significant visual clue for human perception and shape models show considerable promise as a basis for extracting objects from images this paper proposes a novel approach for shape matching and modeling using the symmetry characterization of shape interior and the spatial relationships of shape structures based on the representative skeletal features we develop a mechanism to generate a coarse segment matching between different instances of an object additionally the natural correspondence of skeletal branches to sequential segments along the shape curves is employed in the matching process to avoid false correspondences across different segments point matches within the corresponding segments are then obtained by solving a constrained assignment problem the validation of the proposed approach is illustrated on various data sets in the presence of considerable deformation and occlusion and the results are compared with those of popular approaches we also demonstrate the performance of our method on biological objects for shape modeling showing better models than those obtained by the state of the art shape modeling approaches

shape retrieval based on dynamic programming we propose a shape matching algorithm for deformed shapes based on dynamic programming our algorithm is capable of grouping together segments at finer scales in order to come up with appropriate correspondences with segments at coarser scales we illustrate the effectiveness of our algorithm in retrieval of shapes by content on two different two dimensional 2 d datasets one of static hand gesture shapes and another of marine life shapes we also demonstrate the superiority of our approach over traditional approaches to shape matching and retrieval such as fourier descriptors and geometric and sequential moments our evaluation is based on human relevance judgments following a well established methodology from the information retrieval field

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

global hopf bifurcation for differential equations with state dependent delay abstract we develop a global hopf bifurcation theory for a system of functional differential equations with state dependent delay the theory is based on an application of the homotopy invariance of s 1 equivariant degree using the formal linearization of the system at a stationary state our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state dependent delay

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

weak and strong fairness in ccs abstract we examine the issue of weak and strong fairness in the framework of milner s ccs our approach is operational we address the problem of giving sets of finite rules for generating all and only the admissible execution sequences when fairness is assumed we achieve our aims by defining two calculi one for weak and the other for strong fairness both calculi are extensions of standard ccs in neither case do we appeal to random assignment or to transformations a distinguishing feature of the weak fair calculus unlike standard approaches which appeal to random assignment is that it does not involve predictive choice

the solution manifold and c1 smoothness for differential equations with state dependent delay abstract let h 0 u c 1 h 0 r n open and f u r n continuously differentiable if f satisfies two mild additional smoothness conditions then the set x u 0 f is a c1 submanifold of codimension n in c 1 h 0 r n the maximal solutions x of the initial value problems x t f x t x 0 x define a continuous semiflow f on x and all operators f t are continuously differentiable their derivatives d2f t are given in the usual way by solutions v to the variational equation along x with segments vt in the tangent spaces tf t x the additional conditions on f are motivated by properties of differential equations with state dependent delay and are verified for an example

multiscale distance matrix for fast plant leaf recognition in this brief we propose a novel contour based shape descriptor called the multiscale distance matrix to capture the shape geometry while being invariant to translation rotation scaling and bilateral symmetry the descriptor is further combined with a dimensionality reduction to improve its discriminative power the proposed method avoids the time consuming pointwise matching encountered in most of the previously used shape recognition algorithms it is therefore fast and suitable for real time applications we applied the proposed method to the task of plan leaf recognition with experiments on two data sets the swedish leaf data set and the icl leaf data set the experimental results clearly demonstrate the effectiveness and efficiency of the proposed descriptor

c1 α strict solutions and wellposedness of abstract differential equations with state dependent delay abstract we study the existence and uniqueness of c 1 strict solutions for a general class of abstract differential equations with state dependent delay we also study the local well posedness of this type of problems on subspaces of c 1 p 0 x some examples involving partial differential equations are presented

smoothness of solutions for delay difference equations abstract for the delay difference equation x n 1 f n x n x n n satisfying x j j j belonging to an initial segment smooth dependence of a solution x n with respect to is considered

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

about fair asynchrony abstract this paper examines the joint influence of fairness and asynchrony on the semantic modelling of a c c s like language fairness is the guarantee for every agent engaged in a computation to communicate with the other asynchronous agents if such communications are infinitely often possible programs are compared according to an implementation preorder which reflects the inclusion of observable properties whenever for every context c and for every program r no computation of r experimenting upon c p allows to recognize p versus q p is considered less than q a fully abstract model of the preorder is constructed in a domain of infinitary language preferred here to classical algebraic domains the restriction to bounded parallelism is analysed in that simplified framework the model turns effective and moreover decidable

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

a robust skeletonization method for topological complex shapes in this paper we describe a skeletonization method effective and robust when applied to complex shapes even if affected by boundary perturbations this approach has been applied to binary segmented images containing bi dimensional bounded shapes generally not simply connected it has been considered an external force field derived by an anisotropic flow through the divergence we have examined the field flow at different times discovering that the field divergence satisfies an anisotropic diffusion equation as well curves of positive divergence may be thought as propagating fronts converging to a steady state formed by shocks points it has been proved that the sets of points inside the shape where divergence assumes positive values converge to the skeleton the curves with negative values of divergence remain static so they may be directly used for edge extraction this methodology has also been tested respect to boundary perturbations and disconnections

a shape recognition scheme based on relative distances of feature points from the centroid abstract in this paper a simple but efficient scheme to recognize shapes is proposed in our scheme all of the boundary points are used to calculate the centroid of an object then the distance between each feature point and the centroid is computed we have shown that the time complexity of our shape matching algorithm is o m where m is the number of feature points the most important advantage of our method is its independence to translation rotation and scaling of objects

inertial and slow manifolds for delay equations with small delays abstract yu a ryabov and r d driver proved that delay equations with small delays have lipschitz inertial manifolds we prove that these manifolds are smooth in addition we show that expansion in the small delay can be used to obtain the dynamical system on the inertial manifold this justifies post newtonian approximation for delay equations

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

boundary layer phenomena for differential delay equations with state dependent time lags iii in this paper we begin a study of the differential delay equation varepsilon x t x t f x t r r r x t

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

defining fairness in reactive and concurrent systems we define when a linear time temporal property is a fairness property with respect to a given system this captures the essence shared by most fairness assumptions that are used in the specification and verification of reactive and concurrent systems such as weak fairness strong fairness k fairness and many others we provide three characterizations of fairness a language theoretic a game theoretic and a topological characterization it turns out that the fairness properties are the sets that are large from a topological point of view that is they are the co meager sets in the natural topology of runs of a given system this insight provides a link to probability theory where a set is large when it has measure 1 while these two notions of largeness are similar they do not coincide in general however we show that they coincide for regular properties and bounded borel measures that is an regular temporal property of a finite state system has measure 1 under a bounded borel measure if and only if it is a fairness property with respect to that system the definition of fairness leads to a generic relaxation of correctness of a system in linear time semantics we define a system to be fairly correct if there exists a fairness assumption under which it satisfies its specification equivalently a system is fairly correct if the set of runs satisfying the specification is topologically large we motivate this notion of correctness and show how it can be verified in a system

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

fairness distances and degrees abstract we show the identity between sets of fair computations in recursive transition graphs sets of cluster points of finite computations for 01 ultra metrics refining the baire metrics and 03 subsets of the results are applied to recursive marked trees fairness definitions regular languages and 03 sets

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed