point set morphological filtering and semantic spatial configuration modeling application to microscopic image and bio structure analysis high level spatial relation and configuration modeling issues are gaining momentum in the image analysis and pattern recognition fields in particular it is deemed important whenever one needs to mine high content images or large scale image databases in a more expressive way than a purely statistically one continuing previous efforts to incorporate structural analysis by developing specific efficient morphological tools performing on mesh representations like delaunay triangulations we propose to formalize spatial relation modeling techniques dedicated to unorganized point sets we provide an original mesh lattice framework which is more convenient for structural representations of large image data by means of interest point sets and their morphological analysis the set of designed numerical operators is based on a specific dilation operator that makes it possible to handle concepts like between or left of over sparse representations of image data such as graphs based on this new theoretical framework for reasoning about images we are able to process high level queries over large histopathological images knowing that digitized histopathology is a new challenge in the field of bio imaging due to the high content nature and large size of these images

a shape analysis model with applications to a character recognition system a method for the recognition of multifont printed characters is proposed giving emphasis to the identification of structural descriptions of character shapes using prototypes noise and shape variations are modeled as series of transformations from groups of features in the data to features in each prototype thus the method manages systematically the relative distortion between a candidate shape and its prototype accomplishing robustness to noise with less than two prototypes per class on average the method uses a flexible matching between components and a flexible grouping of the individual components to be matched a number of shape transformations are defined including filling of gaps so that the method handles broken characters also a measure of the amount of distortion that these transformations cause is given classification of character shapes is defined as a minimization problem among the possible transformations that map an input shape into prototypical shapes some tests with hand printed numerals confirmed the method s high robustness level

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

bifurcation diagrams of coupled schrodinger equations radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations a numerical solver for initial value problems for such systems is developed based on matlab and numerical bifurcation diagrams are obtained according to the behavior of the solutions various bifurcation diagrams of coupled schrodinger equations from nonlinear physics are obtained which suggests the uniqueness of the ground state solution

hamiltonian location problems abstract exact algorithms for a series of simultaneous location and routing problems are developed problems are formulated as integer programs which are solved by a constraint relaxation procedure numerical results are reported

depth based complexity traces of graphs in this paper we aim to characterize graphs in terms of a structural measure of complexity our idea is to decompose a graph into layered substructures of increasing size and then to measure the information content of these substructures to locate dominant substructures within a graph we commence by identifying a centroid vertex which has the minimum shortest path length variance to the remaining vertices for each graph a family of centroid expansion subgraphs is derived from the centroid vertex in order to capture dominant structural characteristics of the graph since the centroid vertex is identified through a global analysis of the shortest path length distribution the expansion subgraphs provide a fine representation of a graph structure we then show how to characterize graphs using depth based complexity traces here we explore two different strategies the first strategy is to measure how the entropies on the centroid expansion subgraphs vary with the increasing size of the subgraphs the second strategy is to measure how the entropy differences vary with the increasing size of the subgraphs we perform graph classification in the principal component space of the complexity trace vectors experiments on graph datasets abstracted from some bioinformatics and computer vision databases demonstrate the effectiveness and efficiency of the proposed graph complexity traces our methods are competitive to state of the art methods highlightswe identify a centroid vertex of a graph through its shortest path matrix we establish a family of expansion subgraphs of a graph from its centroid vertex we construct depth based complexity traces of a graph on its expansion subgraphs we evaluate the performance of our complexity traces on standard graph datasets we demonstrate the effectiveness and efficiency of the graph complexity traces

optimized dissimilarity space embedding for labeled graphs this paper introduces a new general purpose classification system able to face automatically a wide range of classification problems for labeled graphs the proposed graph classifier explicitly embeds the input labeled graphs using the dissimilarity representation framework we developed a method to optimize the dissimilarity space representation estimating the quadratic renyi entropy of the underlying distribution of the generated dissimilarity values the global optimization governing the synthesis of the classifier is implemented using a genetic algorithm and it is carried out by means of two operations that perform prototype selection and extraction on the input set of graphs during the optimization step we adopted a suitable objective function which includes the classification accuracy achieved by the whole classification model on a validation set experimental evaluations have been conducted on both synthetic and well known benchmarking datasets achieving competitive test set classification accuracy results with respect to other state of the art graph embedding based classification systems

on the solutions of liouville systems for some prescribed m 0 together with the dirichlet boundary condition u 0 on 0 the liouville equation finds applications in various fields of physics and mathematics to name a few it represents the newtonian potential of a cluster of self gravitating mass distribution where a 0 1 6 36 37 the electric potential induced by charge carriers in the theory of electrolytes where a 0 31 and maximal entropy solutions of the incompressible euler equation 23 9 in the field of differential geometry it stands for the problem of finding a metric corresponding to a prescribed gaussian curvature 3 10 the system analog of l takes the form

improving vector space embedding of graphs through feature selection algorithms graph based pattern representation offers a versatile alternative to vectorial data structures therefore a growing interest in graphs can be observed in various fields however a serious limitation in the use of graphs is the lack of elementary mathematical operations in the graph domain actually required in many pattern recognition algorithms in order to overcome this limitation the present paper proposes an embedding of a given graph population in a vector space r n the key idea of this embedding approach is to interpret the distances of a graph g to a number of prototype graphs as numerical features of g in previous works the prototypes were selected beforehand with heuristic selection algorithms in the present paper we take a more fundamental approach and regard the problem of prototype selection as a feature selection or dimensionality reduction problem for which many methods are available with several experiments we show the feasibility of graph embedding based on prototypes obtained from such feature selection algorithms and demonstrate their potential to outperform previous approaches

uniqueness of ground states of some coupled nonlinear schrodinger systems and their application abstract we establish the uniqueness of ground states of some coupled nonlinear schrodinger systems in the whole space we firstly use schwartz symmetrization to obtain the existence of ground states for a more general case to prove the uniqueness of ground states we use the radial symmetry of the ground states to transform the systems into an ordinary differential system and then we use the integral forms of the system more interestingly as an application of our uniqueness results we derive a sharp vector valued gagliardo nirenberg inequality

radial symmetry results for fractional laplacian systems abstract in this paper we generalize the direct method of moving planes for the fractional laplacian to the system case considering a coupled nonlinear system with fractional laplacian we first establish a decay at infinity principle and a narrow region principle using these principles we then obtain two radial symmetry results for the decaying solutions of the fractional laplacian systems finally we apply our method to fractional schrodinger systems and fractional henon systems

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

the hamiltonian p median problem abstract this paper is concerned with a new mixed routing location problem embedding the p median and the travelling salesman problems the hamiltonian p median problem hpmp is formulated and several heuristics are proposed computational experience with a set of test problems is reported

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

feature space interpretation of svms with indefinite kernels kernel methods are becoming increasingly popular for various kinds of machine learning tasks the most famous being the support vector machine svm for classification the svm is well understood when using conditionally positive definite cpd kernel functions however in practice non cpd kernels arise and demand application in svm the procedure of plugging these indefinite kernels in svm often yields good empirical classification results however they are hard to interpret due to missing geometrical and theoretical understanding in this paper we provide a step toward the comprehension of svm classifiers in these situations we give a geometric interpretation of svm with indefinite kernel functions we show that such svm are optimal hyperplane classifiers not by margin maximization but by minimization of distances between convex hulls in pseudo euclidean spaces by this we obtain a sound framework and motivation for indefinite svm this interpretation is the basis for further theoretical analysis e g investigating uniqueness and for the derivation of practical guidelines like characterizing the suitability of indefinite svm

uniqueness of topological multi vortex solutions for a skew symmetric chern simons system in this paper we consider a skew symmetric chern simons system problem with a coupling parameter our main goal is that when the coupling parameter is small the topological type solutions to this system problem are uniquely determined by the location of their vortex points this result follows by the bubbling analysis and the non degeneracy of linearized equations

multiple bound states of nonlinear schrodinger systems this paper is concerned with existence of bound states for schrodinger systems which have appeared as several models from mathematical physics we establish multiplicity results of bound states for both small and large interactions this is done by different approaches depending upon the sizes of the interaction parameters in the systems for small interactions we give a new approach to deal with multiple bound states the novelty of our approach lies in establishing a certain type of invariant sets of the associated gradient flows for large interactions we use a minimax procedure to distinguish solutions by analyzing their morse indices

existence uniqueness and stability of positive solutions to sublinear elliptic systems reaction diffusion systems are used to model many chemical and biological phenomena in the natural world 25 26 and systems of coupled partial differential equations are also used in other physical models such as nonlinear schrodinger systems in multi component bose einstein condensates and nonlinear optics 19 23 the steady state solutions or standing wave solutions of such systems of nonlinear partial differential equations satisfy a nonlinear elliptic system with more than one equation much effort has been devoted to the existence of solutions of such systems see for example 4 8 10 11 13 15 17 24 30 33 34 but it is usually difficult to determine whether or not the solution is unique we consider the positive solutions of a semilinear elliptic system of the form

decay symmetry and existence of solutions of semilinear elliptic systems our utmost aim was originally to establish the existence of solutions of system however in this effort we got sidetracked to consider other questions in this way we come to interesting results on asymptotic behavior of solutions on symmetry properties of such solutions and the existence of ground states

symmetry results for elliptic schrodinger systems on half spaces abstract in this paper we prove some symmetry and monotonicity results for classical positive solutions for elliptic schrodinger systems on half spaces with the neumann type condition our methods employ the alexandrov serrin method of moving planes combined with hopf s lemma at a corner

automatic learning of cost functions for graph edit distance abstract graph matching and graph edit distance have become important tools in structural pattern recognition the graph edit distance concept allows us to measure the structural similarity of attributed graphs in an error tolerant way the key idea is to model graph variations by structural distortion operations as one of its main constraints however the edit distance requires the adequate definition of edit cost functions which eventually determine which graphs are considered similar in the past these cost functions were usually defined in a manual fashion which is highly prone to errors the present paper proposes a method to automatically learn cost functions from a labeled sample set of graphs to this end we formulate the graph edit process in a stochastic context and perform a maximum likelihood parameter estimation of the distribution of edit operations the underlying distortion model is learned using an expectation maximization algorithm from this model we finally derive the desired cost functions in a series of experiments we demonstrate the learning effect of the proposed method and provide a performance comparison to other models

network design using cut inequalities we study the network loading problem with and without bifurcations we use a relaxation based on the cut condition for multicommodity flows we use a solution of the bifurcated case to derive a solution to the nonbifurcated problem a standard procedure is to aggregate the problem into a backbone network we applied this method to backbone networks coming from practical instances we obtained feasible solutions and bounds for the gap from optimality

a new variant of a vehicle routing problem lower and upper bounds abstract this paper deals with a combinatorial optimization problem that arises in the design of a semi automatic system for cutting leather skins called the laser multi scanner problem lmsp the problem occurs in the first part of the cutting process the parts to be cut are placed on the cutting board by using a new technique the so called lasernest the outlines of the pieces are projected onto the board by several laser rays the optimization goal is to assign the pieces to the laser rays such that the maximum length of a laser route is minimal this can be modelled as a new variant of a vehicle routing problem due to severe time restrictions we are only interested in fast heuristic solutions we construct feasible solutions by opening heuristics namely insertion algorithms and greedy variants in a second step we improve the solutions using local search based on arc exchanges we evaluate the quality of solutions by lower bounds which are derived from combinatorial and lp relaxations thereby we examine directed q forests on a multi digraph which have matroid structure finally we present some computational results on real world data

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

symmetry properties in systems of semilinear elliptic equations abstract we investigate symmetry properties of solutions of systems of semilinear elliptic equations the two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane an application to the belousov zhabotinskii chemical reaction is given

symmetry results for semilinear elliptic systems in the whole space in this paper we obtain symmetry results of gidas ni nirenberg type for cooperative nonlinear elliptic systems in the whole space

discriminative prototype selection methods for graph embedding graphs possess a strong representational power for many types of patterns however a main limitation in their use for pattern analysis derives from their difficult mathematical treatment one way of circumventing this problem is that of transforming the graphs into a vector space by means of graph embedding such an embedding can be conveniently obtained by using a set of prototype graphs and a dissimilarity measure however when we apply this approach to a set of class labelled graphs it is challenging to select prototypes capturing both the salient structure within each class and inter class separation in this paper we introduce a novel framework for selecting a set of prototypes from a labelled graph set taking their discriminative power into account experimental results showed that such a discriminative prototype selection framework can achieve superior results in classification compared to other well established prototype selection approaches

symmetry and non existence of positive solutions for fractional p laplacian systems abstract chen and li 2018 developed maximum principles for the fractional p laplacian which carry out the direct method of moving planes to the fractional p laplacian equation in this paper we generalize their method to the system case and obtain a symmetry result for the fractional p laplacian system on the whole space we also consider the system on the upper half space and obtain a non existence result

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

exact and heuristic algorithms for the hamiltonian p median problem this paper presents an exact algorithm a constructive heuristic algorithm and a metaheuristic for the hamiltonian p median problem hpmp the exact algorithm is a branch and cut algorithm based on an enhanced p median based formulation which is proved to dominate an existing p median based formulation the constructive heuristic is a giant tour heuristic based on a dynamic programming formulation to optimally split a given sequence of vertices into cycles the metaheuristic is an iterated local search algorithm using 2 exchange and 1 opt operators computational results show that the branch and cut algorithm outperforms the existing exact solution methods