benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

regularizing effect of absorption terms in singular problems abstract we prove existence of solutions to problems whose model is p u u q f u in u 0 in u 0 on where is an open bounded subset of r n n 2 p u is the p laplacian operator for 1 p n q 0 0 and f is a nonnegative function in l m for some m 1 in particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case 1 we also study uniqueness of these solutions as well as examples which show the optimality of the results finally we find local w 1 p solutions in case 1

anisotropic model of kinetic roughening the strong coupling regime we study the strong coupling sc limit of the anisotropic kardar parisi zhang kpz model a systematic mapping of the continuum model to its lattice equivalent shows that in the sc limit anisotropic perturbations destroy all spatial correlations but retain a temporal scaling which shows a remarkable crossover along one of the two spatial directions the choice of direction depending on the relative strength of anisotropicity the results agree with exact numerics and are expected to settle the long standing sc problem of a kpz model in the infinite range limit 2007 the american physical society

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

anzellotti s pairing theory and the gauss green theorem abstract in this paper we obtain a very general gauss green formula for weakly differentiable functions and sets of finite perimeter this result is obtained by revisiting anzellotti s pairing theory and by characterizing the measure pairing a d u when a is a bounded divergence measure vector field and u is a bounded function of bounded variation

protein classification by matching and clustering surface graphs in this paper we address the problem of comparing and classifying protein surfaces with graph based methods comparison relies on matching surface graphs extracted from the surfaces by considering concave and convex patches through a kernelized version of the softassign graph matching algorithm on the other hand classification is performed by clustering the surface graphs with an em like algorithm also relying on kernelized softassign and then calculating the distance of an input surface graph to the closest prototype we present experiments showing the suitability of kernelized softassign for both comparing and classifying surface graphs

a riemannian approach to graph embedding in this paper we make use of the relationship between the laplace beltrami operator and the graph laplacian for the purposes of embedding a graph onto a riemannian manifold to embark on this study we review some of the basics of riemannian geometry and explain the relationship between the laplace beltrami operator and the graph laplacian using the properties of jacobi fields we show how to compute an edge weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths on the manifold between nodes for the particular case of a constant sectional curvature surface we use the kruskal coordinates to compute edge weights that are proportional to the geodesic distance between points we use the resulting edge weight matrix to embed the nodes of the graph onto a riemannian manifold to do this we develop a method that can be used to perform double centring on the laplacian matrix computed from the edge weights the embedding coordinates are given by the eigenvectors of the centred laplacian with the set of embedding coordinates at hand a number of graph manipulation tasks can be performed in this paper we are primarily interested in graph matching we recast the graph matching problem as that of aligning pairs of manifolds subject to a geometric transformation we show that this transformation is pro crustean in nature we illustrate the utility of the method on image matching using the coil database

divergence measure fields and hyperbolic conservation laws we analyze a class of l infty vector fields called divergence measure fields we establish the gauss green formula the normal traces over subsets of lipschitz boundaries and the product rule for this class of l infty fields then we apply this theory to analyze l infty entropy solutions of initial boundary value problems for hyperbolic conservation laws and to study the ways in which the solutions assume their initial and boundary data the examples of conservation laws include multidimensional scalar equations the system of nonlinear elasticity and a class of m x m systems with affine characteristic hypersurfaces the analysis in l infty also extends to l p

large sample theory of intrinsic and extrinsic sample means on manifolds ii this article develops nonparametric inference procedures for estimation and testing problems for means on manifolds a central limit theorem for frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on riemannian manifolds central limit theorems are also obtained for extrinsic sample means w r t an arbitrary embedding of a differentiable manifold in a euclidean space bootstrap methods particularly suitable for these problems are presented applications are given to distributions on the sphere s d directional spaces real projective space rp n 1 axial spaces complex projective space cp k 2 planar shape spaces w r t veronese whitney embeddings and a three dimensional shape space 4 3

improved pivotal methods for constructing confidence regions with directional data abstract the importance of pivoting is well established in the context of nonparametric confidence regions it ensures enhanced coverage accuracy however pivoting for directional data cannot be achieved simply by rescaling a somewhat cumbersome pivotal method which involves passing first into a space of higher dimension has been developed by fisher and hall for samples of unit vectors although that method has some advantages over nonpivotal techniques it does suffer from certain drawbacks in particular the operation of passing to a higher dimension here we suggest alternative pivotal approaches the implementation of which does not require us to increase the intrinsic dimension of the data and which in practice seem to achieve greater coverage accuracy these methods are of two types new pivotal bootstrap techniques and techniques that exploit the implicit pivotalness of the empirical likelihood algorithm unlike the method proposed by fisher and hall these methods are also applicable to axia

the gauss green theorem in stratified groups abstract we lay the foundations for a theory of divergence measure fields in noncommutative stratified nilpotent lie groups such vector fields form a new family of function spaces which generalize in a sense the bv fields they provide the most general setting to establish gauss green formulas for vector fields of low regularity on sets of finite perimeter we show several properties of divergence measure fields in stratified groups ultimately achieving the related gauss green theorem

extended divergence measure fields and the euler equations for gas dynamics a class of extended vector fields called extended divergence measure fields is analyzed these fields include vector fields in l p and vector valued radon measures whose divergences are radon measures such extended vector fields naturally arise in the study of the behavior of entropy solutions of the euler equations for gas dynamics and other nonlinear systems of conservation laws a new notion of normal traces over lipschitz deformable surfaces is developed under which a generalized gauss green theorem is established even for these extended fields an explicit formula is obtained to calculate the normal traces over any lipschitz deformable surface suitable for applications by using the neighborhood information of the fields near the surface and the level set function of the lipschitz deformation surfaces as an application we prove the uniqueness and stability of riemann solutions that may contain vacuum in the class of entropy solutions of the euler equations for gas dynamics

nonequilibrium wetting transitions with short range forces we analyze within mean field theory as well as numerically a kardar parisi zhang equation that describes nonequilibrium wetting both complete and critical wettitng transitions were found and characterized in detail for one dimensional substrates the critical weting temperature is depressed by fluctuations in addition we have investigated a region in the space of parameters temperature and chemical potential where the wet and nonwet phases coexist finite size scaling analysis of the interfacial detaching times indicates that the finite coexistence region survives in the thermodynamic limit within this region we have observed stable or very long lived structures related to spatiotemporal intermittency in other systems in the interfacial representation these structures exhibit perfect triangular pyramidal patterns in one dimension two dimensions which are characterized by their slope and size distribution

object recognition as many to many feature matching object recognition can be formulated as matching image features to model features when recognition is exemplar based feature correspondence is one to one however segmentation errors articulation scale difference and within class deformation can yield image and model features which don t match one to one but rather many to many adopting a graph based representation of a set of features we present a matching algorithm that establishes many to many correspondences between the nodes of two noisy vertex labeled weighted graphs our approach reduces the problem of many to many matching of weighted graphs to that of many to many matching of weighted point sets in a normed vector space this is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure many to many vector correspondences established by the earth mover s distance framework are mapped back into many to many correspondences between graph nodes empirical evaluation of the algorithm on an extensive set of recognition trials including a comparison with two competing graph matching approaches demonstrates both the robustness and efficacy of the overall approach

gauss green theorem for weakly differentiable vector fields sets of finite perimeter and balance laws we analyze a class of weakly differentiable vector fields f w r n r n with the property that f 2 l 1 and div f is a signed radon measure these fields are called bounded divergence measure fields the primary focus of our inves tigation is to introduce a suitable notion of the normal trace of any divergence measure field f over the boundary of an arbitrary set of finite perimeter that en sures the validity of the gauss green theorem to achieve this we first establish a fundamental approximation theorem which states that given a signed radon measurethat is absolutely continuous with respect to h n 1 on r n a ny set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure theoretic interior of the set with respect to the mea sure kk the total variation measure we employ this approximation theorem to derive the normal trace of f on the boundary of any set of finite perimeter e as the limit of the normal traces of f on the boundaries of the approximate sets with smooth boundary so that the gauss green theorem for f holds one with these results we analyze the cauchy flux that is bounded by a nonnegative radon measure over any oriented surface i e an n 1 dimensional surface that is a part of the boundary of a set of finite perimeter and thereby develop a general mathematical formulation of the physical principle of the balance law through the cauchy flux finally we apply this framework to the derivation of systems of balance laws with measure valued source terms from the formulation of the balance law this framework also allows the recovery of cauchy entropy flux through the lax entropy inequality for entropy solutions of hyperbolic con servation laws c 2008 wiley periodicals inc

toward a theory of statistical tree shape analysis to develop statistical methods for shapes with a tree structure we construct a shape space framework for tree shapes and study metrics on the shape space this shape space has singularities which correspond to topological transitions in the represented trees we study two closely related metrics on the shape space ted and qed qed is a quotient euclidean distance arising naturally from the shape space formulation while ted is the classical tree edit distance using gromov s metric geometry we gain new insight into the geometries defined by ted and qed we show that the new metric qed has nice geometric properties that are needed for statistical analysis geodesics always exist and are generically locally unique following this we can also show the existence and generic local uniqueness of average trees for qed ted while having some algorithmic advantages does not share these advantages along with the theoretical framework we provide experimental proof of concept results on synthetic data trees as well as small airway trees from pulmonary ct scans this way we illustrate that our framework has promising theoretical and qualitative properties necessary to build a theory of statistical tree shape analysis

on the chain rule formulas for divergences and applications to conservation laws abstract in this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function v x b x u x where b t is a divergence measure vector field and u is a function of bounded variation as an application we prove a uniqueness result for scalar conservation laws with discontinuous flux

heuristics for the generalized median graph problem abstract structural approaches for pattern recognition frequently make use of graphs to represent objects the concept of object similarity is of great importance in pattern recognition the graph edit distance is often used to measure the similarity between two graphs it basically consists in the amount of distortion needed to transform one graph into the other the median graph of a set s of graphs is a graph of s that minimizes the sum of its distances to all other graphs in s the generalized median graph of s is a graph that minimizes the sum of the distances to all graphs in s it is the graph that best captures the information contained in s and may be regarded as the best representative of the set exact methods for solving the generalized median graph problem are capable to handle only a few small graphs we propose two new heuristics for solving the generalized median graph problem a greedy adaptive algorithm and a grasp heuristic numerical results indicate that both heuristics can be used to obtain good approximate solutions for the generalized median graph problem significantly improving the initial solutions and the median graphs therefore the generalized median graph can be effectively computed and used as a better representation than the median graph in a number of relevant pattern recognition applications this conclusion is supported by experiments with a classification problem and comparisons with algorithm k nn

object oriented data analysis sets of trees object oriented data analysis is the statistical analysis of populations of complex objects in the special case of functional data analysis these data objects are curves where standard euclidean approaches such as principal component analysis have been very successful recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non euclidean spaces such as lie groups and symmetric spaces or of strongly non euclidean spaces such as spaces of tree structured data objects these new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics this point is illustrated through the careful development of a novel mathematical framework for statistical analysis of populations of tree structured objects

nonsmooth analysis and subgradient methods for averaging in dynamic time warping spaces abstract time series averaging in dynamic time warping dtw spaces has been successfully applied to improve pattern recognition systems this article proposes and analyzes subgradient methods for the problem of finding a sample mean in dtw spaces the class of subgradient methods generalizes existing sample mean algorithms such as dtw barycenter averaging dba we show that dba is a majorize minimize algorithm that converges to necessary conditions of optimality after finitely many iterations empirical results show that for increasing sample sizes the proposed stochastic subgradient ssg algorithm is more stable and finds better solutions in shorter time than the dba algorithm on average therefore ssg is useful in online settings and for non small sample sizes the theoretical and empirical results open new paths for devising sample mean algorithms nonsmooth optimization methods and modified variants of pairwise averaging methods

divergence measure fields sets of finite perimeter and conservation laws divergence measure fields in l over sets of finite perimeter are analyzed a notion of normal traces over boundaries of sets of finite perimeter is introduced and the gauss green formula over sets of finite perimeter is established for divergence measure fields in l the normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak star limit of the normal traces introduced in chen frid 6 over the lipschitz deformation surfaces which implies their consistency as a corollary an extension theorem of divergence measure fields in l over sets of finite perimeter is also established then we apply the theory to the initial boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

an extension of the pairing theory between divergence measure fields and bv functions abstract in this paper we introduce a nonlinear version of the notion of anzellotti s pairing between divergence measure vector fields and functions of bounded variation motivated by possible applications to evolutionary quasilinear problems as a consequence of our analysis we prove a generalized gauss green formula

the mean partition theorem in consensus clustering abstract this article presents the mean partition theorem of consensus clustering we show that the mean partition theorem is a fundamental result that connects to different but not obviously related branches such as i optimization ii statistical consistency iii optimal multiple alignment iv profiles and motifs v cluster stability vi diversity and vii condorcet s jury theorem all proofs rest on the orbit space framework the implications are twofold first the mean partition theorem plays a far reaching and central role in consensus clustering second orbit spaces constitute a convenient representation for gaining insight into partition spaces

linear stochastic dynamics with nonlinear fractal properties abstract stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we present a review of applications highlight the common physical mechanism and summarize the main known results the distribution and statistical properties of the duration of intermittent bursts are also characterized in detail

consistency driven alternating optimization for multigraph matching a unified approach the problem of graph matching gm in general is nondeterministic polynomial complete and many approximate pairwise matching techniques have been proposed for a general setting in real applications it typically requires to find the consistent matching across a batch of graphs sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence and the sequences generated in different pairwise matching orders can lead to contradictory solutions motivated by devising a robust and consistent multiple gm model we propose a unified alternating optimization framework for multi gm in addition we define and use two metrics related to graphwise and pairwise consistencies the former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure the latter defines the order in which the considered graphs in the iterations are manipulated we show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix respectively our multi gm model has two major characters 1 the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency driven mechanism and 2 the framework is flexible to incorporate various existing pairwise gm solvers in an out of box fashion and also can proceed with the output of other multi gm methods the experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state of the art

phase separation in binary systems with internal multiplicative noise abstract a study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized a mean field approach was carried out in order to obtain the stationary probability bifurcation and phase diagrams displaying reentrant phase transitions we relate our approach to entropy driven phase transitions theory

critical wetting of a class of nonequilibrium interfaces a mean field picture a self consistent mean field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing kardar parisi zhang kpz interfaces in the presence of a bounding substrate in the case of positive kpz nonlinearity a single gaussian regime is found on the contrary interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order parameter i a trivial gaussian regime ii a weak fluctuation regime with a trivially located critical point and nontrivial exponents and iii a highly nontrivial strong fluctuation regime for which we provide a full solution by finding the zeros of parabolic cylinder functions these analytical results are also verified by solving numerically the self consistent equation in each case analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed

the stampacchia maximum principle for stochastic partial differential equations and applications abstract stochastic partial differential equations spdes are considered linear and nonlinear for which we establish comparison theorems for the solutions or positivity results a e and a s for suitable data comparison theorems for spdes are available in the literature the originality of our approach is that it is based on the use of truncations following the stampacchia approach to maximum principle we believe that our method which does not rely too much on probability considerations is simpler than the existing approaches and to a certain extent more directly applicable to concrete situations among the applications boundedness results and positivity results are respectively proved for the solutions of a stochastic boussinesq temperature equation and of reaction diffusion equations perturbed by a non lipschitz nonlinear noise stabilization results to a chafee infante equation perturbed by a nonlinear noise are also derived

statistical graph space analysis the sample mean is one of the most fundamental concepts in statistics properties of the sample mean that are well defined in euclidean spaces become unclear in graph spaces this paper proposes conditions under which the following properties are valid existence uniqueness and consistency of means the midpoint property necessary conditions of optimality and convergence results of mean algorithms the theoretical results address common misconceptions about the graph mean in graph edit distance spaces serve as a first step towards a statistical analysis of graph spaces and result in a theoretically well founded mean algorithm that outperformed six other mean algorithms with respect to solution quality on different graph datasets representing images and molecules highlightsa first step towards a theory of statistical graph space analysis is proposed mmm algorithm is proposed that outperformed six other mean algorithms necessary conditions of optimality are proved convergence of mmm algorithm is shown basic statistical and geometrical properties are shown

on the entropy conditions for some flux limited diffusion equations abstract in this paper we give a characterization of the notion of entropy solutions of some flux limited diffusion equations for which we can prove that the solution is a function of bounded variation in space and time this includes the case of the so called relativistic heat equation and some generalizations for them we prove that the jump set consists of fronts that propagate at the speed given by rankine hugoniot condition and we give on it a geometric characterization of the entropy conditions since entropy solutions are functions of bounded variation in space once the initial condition is to complete the program we study the time regularity of solutions of the relativistic heat equation under some conditions on the initial datum an analogous result holds for some other related equations without additional assumptions on the initial condition

systems with multiplicative noise critical behavior from kpz equation and numerics we show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the kpz equation numerical simulations in 1d confirm this prediction and yield other exponents of the multiplicative noise problem the numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values and show that the exponent governing the divergence in this range varies continuously with control parameter

bv supersolutions to equations of 1 laplace and minimal surface type we propose notions of bv supersolutions to the dirichlet problem for the 1 laplace equation the minimal surface equation and equations of similar type we then establish some related compactness and consistency results our main technical tool is a generalized product of l divergence measure fields and gradient measures of bv functions this product crucially depends on the choice of a representative of the bv function and the proofs of its basic properties involve results on one sided approximation and fine semi continuity in the bv context

fuzzy multilevel graph embedding structural pattern recognition approaches offer the most expressive convenient powerful but computational expensive representations of underlying relational information to benefit from mature less expensive and efficient state of the art machine learning models of statistical pattern recognition they must be mapped to a low dimensional vector space our method of explicit graph embedding bridges the gap between structural and statistical pattern recognition we extract the topological structural and attribute information from a graph and encode numeric details by fuzzy histograms and symbolic details by crisp histograms the histograms are concatenated to achieve a simple and straightforward embedding of graph into a low dimensional numeric feature vector experimentation on standard public graph datasets shows that our method outperforms the state of the art methods of graph embedding for richly attributed graphs highlights we propose an explicit graph embedding method we perform multilevel analysis of graph to extract global topological structural and attribute information we use homogeneity of subgraphs in graph for extracting topological structural details we encode numeric information by fuzzy histograms and symbolic information by crisp histograms our method outperforms graph embedding methods for richly attributed graphs

mean field theory for skewed height profiles in kpz growth processes we propose a mean field theory for interfaces growing according to the kardar parisi zhang kpz equation in 1 1 dimensions the mean field equations are formulated in terms of densities at different heights taking surface tension and the influence of the nonlinear term in the kpz equation into account although spatial correlations are neglected the mean field equations still reflect the spatial dimensionality of the system in the special case of edwards wilkinson growth our mean field theory correctly reproduces all features in the presence of a nonlinear term one observes a crossover to a kpz like behaviour with the correct dynamical exponent z 3 2 in particular we compute the skewed interface profile during roughening and we study the influence of a co moving reflecting wall which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions also here the mean field approximation reproduces all qualitative features of the full kpz equation although with different values of the surface exponents

a new mathematical foundation for contact interactions in continuum physics the investigation of contact interactions such as traction and heat flux that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics however the traditional theory of stress established by cauchy and extended by noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks corner singularities and fracture this paper provides a new mathematical foundation for the treatment of contact interactions based on mild physically motivated postulates which differ essentially from those used before the existence of a corresponding interaction tensor is established while in earlier treatments contact interactions are basically defined on surfaces here contact interactions are rigorously considered as maps on pairs of subbodies this allows the action exerted on a subbody to be defined not only as usual for sets with a sufficiently regular boundary but also for borel sets which include all open and all closed sets in addition to the classical representation of such interactions by means of integrals on smooth surfaces a general representation using the distributional divergence of the tensor is derived in the case where concentrations occur this new approach allows a description of contact phenomena more precise than before

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

pattern vectors from algebraic graph theory graph structures have proven computationally cumbersome for pattern analysis the reason for this is that before graphs can be converted to pattern vectors correspondences must be established between the nodes of structures which are potentially of different size to overcome this problem in this paper we turn to the spectral decomposition of the laplacian matrix we show how the elements of the spectral matrix for the laplacian can be used to construct symmetric polynomials that are permutation invariants the coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner we extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a hermitian property matrix that can be viewed as a complex analogue of the laplacian to embed the graphs in a pattern space we explore whether the vectors of invariants can be embedded in a low dimensional space using a number of alternative strategies including principal components analysis pca multidimensional scaling mds and locality preserving projection lpp experimentally we demonstrate that the embeddings result in well defined graph clusters our experiments with the spectral representation involve both synthetic and real world data the experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure the real world experiments show that the method can be used to locate clusters of graphs

relationship between directed percolation and the synchronization transition in spatially extended systems we study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model an analytic argument is put forward showing that in the limit of discontinuous processes the transition belongs to the directed percolation dp universality class the analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold we find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena as a result of this analysis we conclude that the synchronization transition belongs to the dp class also in continuous models the conclusions are supported by numerical checks on coupled map lattices too

cauchy fluxes associated with tensor fields having divergence measure cauchy fluxes induced by locally summable tensor fields with divergence measure are characterized the equivalence between integral formulations involving subsets of finite perimeter and much more restricted classes of subsets is proved

generalized median graph computation by means of graph embedding in vector spaces the median graph has been presented as a useful tool to represent a set of graphs nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data in this paper we propose a new approach for the computation of the median graph based on graph embedding graphs are embedded into a vector space and the median is computed in the vector domain we have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph we have also applied the median graph to perform some basic classification tasks achieving reasonable good results these experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

population extinction on a random fitness seascape we explore the role of stochasticity and noise in the statistical outcomes of commonly studied population dynamics models within a space independent mean field perspective specifically we consider a distributed population with logistic growth at each location subject to seascape noise wherein the population s fitness randomly varies with location and time despite its simplicity the model actually incorporates variants of directed percolation and directed polymers in random media within a mean field perspective probability distributions of the population can be computed self consistently and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes the results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction

topology of strings median string is np complete given a set of strings the problem of finding a string that minimises its distance to the set is directly related with problems frequently encountered in areas involving pattern recognition or computational biology based on the levenshtein or edit distance different definitions of distances between a string and a set of strings can be adopted in particular if this definition is the sum of the distances to each string of the set the string that minimises this distance is the generalised median string finding this string corresponds in speech recognition to giving a model for a set of acoustic sequences and in computational biology to constructing an optimal evolutionary tree when the given phylogeny is a star only efficient algorithms are known for finding approximate solutions the results in this paper are combinatorial and negative we prove that computing the median string corresponds to a np complete decision problems thus proving that this problem is np hard

the complex bingham distribution and shape analysis summary a complex version of the bingham distribution is defined on the unit complex sphere in ck various statistical properties including asymptotic normality under high concentration are derived symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions strengths and weaknesses of this approach are investigated links and contrasts with bookstein co ordinates are discussed a hybrid approach to principal component analysis based on complex and real co ordinates is suggested

an median graphs properties algorithms and applications in object prototype learning and similar tasks median computation is an important technique for capturing the essential information of a given set of patterns we extend the median concept to the domain of graphs in terms of graph distance we introduce the novel concepts of set median and generalized median of a set of graphs we study properties of both types of median graphs for the more complex task of computing generalized median graphs a genetic search algorithm is developed experiments conducted on randomly generated graphs demonstrate the advantage of generalized median graphs compared to set median graphs and the ability of our genetic algorithm to find approximate generalized median graphs in reasonable time application examples with both synthetic and nonsynthetic data are shown to illustrate the practical usefulness of the concept of median graphs

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

ensemble clustering by means of clustering embedding in vector spaces ensemble clustering is a recently evolving research direction in cluster analysis and has found several different application domains in this work the complex ensemble clustering problem is reduced to the well known euclidean median problem by clustering embedding in vector spaces the euclidean median problem is solved by the weiszfeld algorithm and an inverse transformation maps the euclidean median back into the clustering domain in the experiment study different evaluation strategies are considered the proposed embedding strategy is compared to several state of art ensemble clustering algorithms and demonstrates superior performance highlightsthis paper presents a novel approach to solving the ensemble clustering problem an embedding method successful for strings and graphs is adapted to clusterings an extensive experiment study is presented the proposed method is superior to several state of the art related algorithms

fuzzy generalized median graphs computation application to content based document retrieval abstract fuzzy median graph is an important new concept that can represent a set of fuzzy graphs by a representative fuzzy graph prototype however the computation of a fuzzy median graph remains a computationally expensive task in this paper we propose a new approximate algorithm for the computation of the fuzzy generalized median graph fgmg based on fuzzy attributed relational graph farg embedding in a suitable vector space in order to capture the maximum information in graphs and to improve the accuracy and speed of document image retrieval processing in this study we focus on the application of fgmgs to the content based document retrieval cbdr problem experiments on real and synthetic databases containing a large number of fargs with large sizes show that a cbdr using the fgmg as a dataset representative yields better results than an exhaustive and sequential retrieval in terms of gains in accuracy and time processing

erratum to existence and strong pre compactness properties for entropy solutions of a first order quasilinear equation with discontinuous flux sequences of entropy solutions of a non degenerate first order quasilinear equation are shown to be strongly pre compact in the general case of a caratheodory flux vector existence of the weak and entropy solution to the cauchy problem for such an evolutionary equation is also established the proofs are based on the general localization principle for h measures corresponding to sequences of measure valued functions