a linear programming approach for the weighted graph matching problem a linear programming lp approach is proposed for the weighted graph matching problem a linear program is obtained by formulating the graph matching problem in l sub 1 norm and then transforming the resulting quadratic optimization problem to a linear one the linear program is solved using a simplex based algorithm then approximate 0 1 integer solutions are obtained by applying the hungarian method on the real solutions of the linear program the complexity of the proposed algorithm is polynomial time and it is o n sup 6 l for matching graphs of size n the developed algorithm is compared to two other algorithms one is based on an eigendecomposition approach and the other on a symmetric polynomial transform experimental results showed that the lp approach is superior in matching graphs than both other methods

global attractivity in the recursive sequence xn 1 α βxn γ xn 1 our aim in this paper is to investigate the global attractivity of the recursive sequencex n email protected bx email protected n 1 n 0 1 where a 0 b c 0 we show that one positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

boundedness analysis of finitely recursive processes ii sequential and hybrid processes part i of this paper has shown that a subclass of the finitely recursive processes frp composed without the sequential composition operator sco is bounded in this sequel it is first shown that boundedness is not guaranteed but decidable for the subclass of frp built using the sco but without the parallel composition operator pco to overcome the limitation in modeling using the sco only some bounded hybrid subclasses have been proposed where both the sco and pco can be used although in a restricted fashion finally the proposed hybrid framework is used to model a job shop and its potential in the specification and design of supervisory control systems is demonstrated

global attractivity in a rational recursive sequence our aim in this paper is to investigate the periodic character invariant intervals and the global attractivity of all positive solutions of the nonlinear difference equationx n email protected email protected email protected n 1 n 0 1 where a 0 b c 0 we show that the positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

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

scale and rotation invariant matching using linearly augmented trees we propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching the proposed method enforces pairwise matching consistency defined on trees and high order constraints on all the sites of a template the pairwise constraints admit arbitrary metrics while the high order constraints use l1 norms and therefore can be linearized such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure but different from a general loopy graph its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming the proposed method also works on continuous scale and rotation parameters we can match with a scale up to any large value with the same efficiency our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient accurate and reliable

graph matching relax at your own risk graph matching aligning a pair of graphs to minimize their edge disagreements has received wide spread attention from both theoretical and applied communities over the past several decades including combinatorics computer vision and connectomics its attention can be partially attributed to its computational difficulty although many heuristics have previously been proposed in the literature to approximately solve graph matching very few have any theoretical support for their performance a common technique is to relax the discrete problem to a continuous problem therefore enabling practitioners to bring gradient descent type algorithms to bear we prove that an indefinite relaxation when solved exactly almost always discovers the optimal permutation while a common convex relaxation almost always fails to discover the optimal permutation these theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance indeed experimental results illuminate and corroborate these theoretical findings demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches

l_p norm regularization algorithms for optimization over permutation matrices optimization problems over permutation matrices appear widely in facility layout chip design scheduling pattern recognition computer vision graph matching etc since this problem is np hard due to the combinatorial nature of permutation matrices we relax the variable to be the more tractable doubly stochastic matrices and add an l p norm 0 p 1 regularization term to the objective function the optimal solutions of the l p regularized problem are the same as the original problem if the regularization parameter is sufficiently large a lower bound estimation of the nonzero entries of the stationary points and some connections between the local minimizers and the permutation matrices are further established then we propose an l p regularization algorithm with local refinements the algorithm approximately solves a sequence of l p regularization subproblems by the projected gradient method using a nonmonotone line search with the barzilai borwein step sizes its performance can be fu

globally consistent correspondence of multiple feature sets using proximal gauss seidel relaxation feature correspondence between two or more images is a fundamental problem towards many computer vision applications the case of correspondence between two images has been intensively studied however few works so far have been concerned with multi image correspondence in this paper we address the problem of establishing a globally consistent correspondence among multiple more than two feature sets given the pairwise feature affinity information our main contribution is to propose a novel optimization framework for solving this problem based on the so called proximal gauss seidel relaxation pgsr the proposed method is distinguished from previous works mainly in three aspects 1 it is more robust to noise and outliers 2 its solution is based on convex relaxation and the principled pgsr method which in general has convergence guarantee 3 the scale of the problem in our method is linear with respect to the number of feature sets making it computationally practical to be used in real world applications experimental results both synthetic and real image datasets have demonstrated the effectiveness and superiority of the proposed method highlightswe study finding globally consistent correspondence from multiple feature sets a novel method is proposed based on proximal gauss seidel relaxation pgsr pgsr is more robust to noise outliers and deformation than competitors the optimization has general convergence guarantee the scale of our formulation is linear w r t the number of feature sets

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

gracker a graph based planar object tracker matching based algorithms have been commonly used in planar object tracking they often model a planar object as a set of keypoints and then find correspondences between keypoint sets via descriptor matching in previous work unary constraints on appearances or locations are usually used to guide the matching however these approaches rarely utilize structure information of the object and are thus suffering from various perturbation factors in this paper we proposed a graph based tracker named gracker which is able to fully explore the structure information of the object to enhance tracking performance we model a planar object as a graph instead of a simple collection of keypoints to represent its structure then we reformulate tracking as a sequential graph matching process which establishes keypoint correspondence in a geometric graph matching manner for evaluation we compare the proposed gracker with state of the art planar object trackers on three benchmark datasets two public ones and a newly collected one experimental results show that gracker achieves robust tracking results against various environmental variations and outperforms other algorithms in general on the datasets

global stability of a rational difference equation abstract in this paper we study the global stability of the difference equation x n 1 x n a a 0 x n a k x n k n 0 1 where the parameters a a i 0 for i 0 k x k x 1 0 and x 0 0 we prove that the unique positive equilibrium is globally asymptotically stable if and only if it is locally asymptotically also we provide sufficient condition for it to be globally asymptotically stable and our results solve the open problem proposed by kulenovic and ladas dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2002

an eigenspace projection clustering method for inexact graph matching in this paper we show how inexact graph matching that is the correspondence between sets of vertices of pairs of graphs can be solved using the renormalization of projections of the vertices as defined in this case by their connectivities into the joint eigenspace of a pair of graphs and a form of relational clustering an important feature of this eigenspace renormalization projection clustering epc method is its ability to match graphs with different number of vertices shock graph based shape matching is used to illustrate the model and a more objective method for evaluating the approach using random graphs is explored with encouraging results

lagrangian relaxation graph matching abstract graph matching is a fundamental problem in computer vision area graph matching problem that incorporates pair wise constraints can be formulated as an integer quadratic programming iqp problem with affine mapping constraint since it is known to be np hard approximate relaxation methods are usually required to find approximate solutions in this paper we present a new effective graph matching relaxation method called lagrangian relaxation graph matching lrgm which aims to generate a relaxation model by incorporating the affine mapping constraint into the matching objective optimization there are three main benefits of the proposed lrgm method 1 the nonnegative affine mapping constraint encoding one to one mapping is naturally incorporated in lrgm relaxation via lagrangian regularization 2 by further adding a l 1 norm constraint lrgm can generate a sparse solution empirically and thus returns a desired discrete solution for original iqp matching problem 3 an effective update algorithm is derived to solve the proposed lrgm model theoretically the converged solution can be proven to be karush kuhn tucker kkt optimal experimental results on both synthetic data and real world image datasets show the effectiveness and benefits of the proposed lrgm method

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

on the recursive sequence yn 1 p yn 1 qyn yn 1 abstract we investigate the periodic character and the global stability of solutions of the equation y n 1 p y n 1 qy n y n 1 with positive parameters and positive initial conditions

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

seeded graph matching for correlated erdos renyi graphs graph matching is an important problem in machine learning and pattern recognition herein we present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function between the vertex sets of two graphs as well as subsequent algorithmic implications when the latent alignment is partially observed in the correlated erdos renyi graph setting we prove that graph matching provides a strongly consistent estimate of the latent alignment in the presence of even modest correlation we then investigate a tractable restricted focus version of graph matching which is only concerned with adjacency involving vertices in a partial observation of the latent alignment we prove that a logarithmic number of vertices whose alignment is known is sufficient for this restricted focus version of graph matching to yield a strongly consistent estimate of the latent alignment of the remaining vertices we show how frank wolfe methodology for approximate graph matching when there is a partially observed latent alignment inherently incorporates this restricted focus graph matching lastly we illustrate the relationship between seeded graph matching and restricted focus graph matching by means of an illuminating example from human connectomics

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

robust feature point matching with sparse model feature point matching that incorporates pairwise constraints can be cast as an integer quadratic programming iqp problem since it is np hard approximate methods are required the optimal solution for iqp matching problem is discrete binary and thus sparse in nature this motivates us to use sparse model for feature point matching problem the main advantage of the proposed sparse feature point matching spm method is that it generates sparse solution and thus naturally imposes the discrete mapping constraints approximately in the optimization process therefore it can optimize the iqp matching problem in an approximate discrete domain in addition an efficient algorithm can be derived to solve spm problem promising experimental results on both synthetic points sets matching and real world image feature sets matching tasks show the effectiveness of the proposed feature point matching method

cross domain matching with squared loss mutual information the goal of cross domain matching cdm is to find correspondences between two sets of objects in different domains in an unsupervised way cdm has various interesting applications including photo album summarization where photos are automatically aligned into a designed frame expressed in the cartesian coordinate system and temporal alignment which aligns sequences such as videos that are potentially expressed using different features in this paper we propose an information theoretic cdm framework based on squared loss mutual information smi the proposed approach can directly handle non linearly related objects sequences with different dimensions with the ability that hyper parameters can be objectively optimized by cross validation we apply the proposed method to several real world problems including image matching unpaired voice conversion photo album summarization cross feature video and cross domain video to mocap alignment and kinect based action recognition and experimentally demonstrate that the proposed method is a promising alternative to state of the art cdm methods

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

an extended path following algorithm for graph matching problem the path following algorithm was proposed recently to approximately solve the matching problems on undirected graph models and exhibited a state of the art performance on matching accuracy in this paper we extend the path following algorithm to the matching problems on directed graph models by proposing a concave relaxation for the problem based on the concave and convex relaxations a series of objective functions are constructed and the frank wolfe algorithm is then utilized to minimize them several experiments on synthetic and real data witness the validity of the extended path following algorithm

global attractivity for a class of higher order nonlinear difference equations our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equationx n 1 a bx email protected k i 0b ix n i n 0 1 where a b b email protected 0 a b 0 b k email protected 0 email protected 1 2 and the initial conditions x k x 0 are arbitrary real numbers we show that one positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

global asymptotic stability of a second order nonlinear difference equation in this paper the global asymptotic stability of the nonlinear difference equationx n 1 a bx na bx n cx n 1 n 0 1 is investigated where a b a b c 0 are real numbers and the initial conditions x 1 is nonnegative real numbers and x 0 is a positive real number we show that the unique positive equilibrium of the equation is globally asymptotically stable in particular our results solve two conjectures proposed by kulenovic and ladas in their monograph m r s kulenovic g ladas dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2002 and by kulenovic et al in their paper m r s kulenovic g ladas l f martins i w rodrigues the dynamics of x n 1 a bx na bx n cx n 1 facts and conjectures comput math appl 45 2003 1087 1099 099

implementation and testing of a primal dual algorithm for the assignment problem state of the art computational results have shown that primal simplex algorithms are more efficient than primal dual algorithms for general minimum cost network flow problems there is however some controversy concerning their relative merits for solving assignment problems this paper presents a detailed development for a computationally efficient primal dual algorithm and extensive computational comparisons to primal simplex algorithms

an algorithm for finding the most similar given sized subgraphs in two weighted graphs we propose a weighted common subgraph wcs matching algorithm to find the most similar subgraphs in two labeled weighted graphs wcs matching as a natural generalization of equal sized graph matching and subgraph matching has found wide applications in many computer vision and machine learning tasks in this brief wcs matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices then it is approximately solved by a recently proposed combinatorial optimization framework graduated nonconvexity and concavity procedure experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level problem size outlier number and edge density

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

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

a sparse nonnegative matrix factorization technique for graph matching problems graph matching problem that incorporates pairwise constraints can be cast as an integer quadratic programming iqp since it is np hard approximate methods are required in this paper a new approximate method based on nonnegative matrix factorization with sparse constraints is presented firstly the graph matching is formulated as an optimization problem with nonnegative and sparse constraints followed by an efficient algorithm to solve this constrained problem then we show the strong relationship between the sparsity of the relaxation solution and its effectiveness for graph matching based on our model a key benefit of our method is that the solution is sparse and thus can approximately impose the one to one mapping constraints in the optimization process naturally therefore our method can approximate the original iqp problem more closely than other approximate methods extensive and comparative experimental results on both synthetic and real world data demonstrate the effectiveness of our graph matching method we present a graph matching method based on nmf with sparse constraints our sparse model can incorporate the mapping constraints approximately we show the link between the sparsity of the solution and its effectiveness experimental results show the effectiveness of our graph matching method

global asymptotic stability for a higher order nonlinear rational difference equations abstract in this paper we investigate the boundedness periodic character invariant intervals and the global asymptotic stability of all nonnegative solutions of the difference equation x n 1 ax n bx n k a bx n n 0 1 where a b a b are positive real numbers k 1 is a positive integer and the initial conditions x k x 1 x 0 are nonnegative real numbers it is shown that the zero equilibrium of this equation is globally asymptotically stable if b a a and the unique positive equilibrium is globally asymptotically stable if a a b a a the results obtained solve a open problem proposed by kulenovic and ladas m r s kulenovi g ladas dynamics of second order rational difference equations chapman hall crc boca raton fl 2002 p 129

correspondence matching using kernel principal components analysis and label consistency constraints this paper investigates spectral approaches to the problem of point pattern matching we make two contributions first we consider rigid point set alignment here we show how kernel principal components analysis kernel pca can be effectively used for solving the rigid point correspondence matching problem when the point sets are subject to outliers and random position jitter specifically we show how the point proximity matrix can be kernelised and spectral correspondence matching transformed into one of kernel pca second we turn our attention to the matching of articulated point sets here we show label consistency constraints can be incorporated into definition of the point proximity matrix the new methods are compared to those of shapiro and brady and scott and longuet higgins together with multidimensional scaling we provide experiments on both synthetic data and real world data

undecidability results for deterministic communicating sequential processes a study is presented of the subset of the communicating sequential processes csp formalism in which processes are described in terms of recursive equations using only constant processes deterministic choice parallel composition and sequential composition even with this limited version the formalism is powerful enough to model a turing machine so that a number of important problems such as boundedness deadlock and reachability are undecidable the subset of the csp formalism that is used is described a number of analysis problems that are common to discrete event systems are discussed the turing machine is outlined well known properties of turing machines are used to derive the undecidability results the results are compared to properties of other models

non rigid graph registration using active testing search we present a new approach for matching sets of branching curvilinear structures that form graphs embedded in mathbb r 2 or mathbb r 3 and may be subject to deformations unlike earlier methods ours does not rely on local appearance similarity nor does require a good initial alignment furthermore it can cope with non linear deformations topological differences and partial graphs to handle arbitrary non linear deformations we use gaussian process regressions to represent the geometrical mapping relating the two graphs in the absence of appearance information we iteratively establish correspondences between points update the mapping accordingly and use it to estimate where to find the most likely correspondences that will be used in the next step to make the computation tractable for large graphs the set of new potential matches considered at each iteration is not selected at random as with many ransac based algorithms instead we introduce a so called active testing search strategy that performs a priority search to favor the most likely matches and speed up the process we demonstrate the effectiveness of our approach first on synthetic cases and then on angiography data retinal fundus images and microscopy image stacks acquired at very different resolutions

fast detection of dense subgraphs with iterative shrinking and expansion in this paper we propose an efficient algorithm to detect dense subgraphs of a weighted graph the proposed algorithm called the shrinking and expansion algorithm sea iterates between two phases namely the expansion phase and the shrink phase until convergence for a current subgraph the expansion phase adds the most related vertices based on the average affinity between each vertex and the subgraph the shrink phase considers all pairwise relations in the current subgraph and filters out vertices whose average affinities to other vertices are smaller than the average affinity of the result subgraph in both phases sea operates on small subgraphs thus it is very efficient significant dense subgraphs are robustly enumerated by running sea from each vertex of the graph we evaluate sea on two different applications solving correspondence problems and cluster analysis both theoretic analysis and experimental results show that sea is very efficient and robust especially when there exists a large amount of noise in edge weights

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

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

on rational recursive sequences our goal in this chapter is to gain some understanding of the dynamics of rational recursive sequences of the form x n 1 frac a sum limits i 0 k a i x n i b sum limits i 0 k b i x n i n 0 1 3 0 1 where k is a positive integer and the coefficients a b a 0 a k b 0 b k are nonnegative real numbers

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

control of discrete event systems modeled as hierarchical state machines discrete event systems dess are systems in which state changes take place in response to events that occur discretely asynchronously and often nondeterministically a class of dess modeled as hierarchical state machines hsms a special case of the statecharts formalism introduced recently is considered an efficient algorithm is provided for solving reachability problems in the hsm framework it utilizes the hierarchical structure of hsms this efficient solution is used extensively in control applications where controllers achieving a desired behavior are synthesized online

dynamic behavior of a recursive sequence in this paper the global asymptotic stability the global attractivity the boundedness character the periodic nature and chaotic behavior of solutions of the difference equationx n 1 a x n 1x n n 0 1 are investigated where a r is a real number and the initial conditions x 1 x 0 are arbitrary real numbers as might be expected the six cases a 3 give rise to substantially different dynamic behavior

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

gnccp graduated nonconvexityand concavity procedure in this paper we propose the graduated nonconvexity and concavity procedure gnccp as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices gnccp comprises two sub procedures graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation it is proved that gnccp realizes exactly a type of convex concave relaxation procedure ccrp but with a much simpler formulation without needing convex or concave relaxation in an explicit way actually gnccp involves only the gradient of the objective function and is therefore very easy to use in practical applications two typical related np hard problems partial graph matching and quadratic assignment problem qap are employed to demonstrate its simplicity and state of the art performance

an efficient multilinear optimization framework for hypergraph matching hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows the use of higher order geometric information hypergraph matching can be formulated as a third order optimization problem subject to assignment constraints which turns out to be np hard in recent work we have proposed an algorithm for hypergraph matching which first lifts the third order problem to a fourth order problem and then solves the fourth order problem via optimization of the corresponding multilinear form this leads to a tensor block coordinate ascent scheme which has the guarantee of providing monotonic ascent in the original matching score function and leads to state of the art performance both in terms of achieved matching score and accuracy in this paper we show that the lifting step to a fourth order problem can be avoided yielding a third order scheme with the same guarantees and performance but being two times faster moreover we introduce a homotopy type method which further improves the performance

geometric graph matching using monte carlo tree search we present an efficient matching method for generalized geometric graphs such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing or vessel networks in medical imaging graph matching can be used for very fast and possibly multimodal registration of images of these structures we formulate the matching problem as a single player game solved using monte carlo tree search which automatically balances exploring new possible matches and extending existing matches our method can handle partial matches topological differences geometrical distortion does not use appearance information and does not require an initial alignment moreover our method is very efficient it can match graphs with thousands of nodes which is an order of magnitude better than the best competing method and the matching only takes a few seconds

dynamics of a rational difference equation in this paper we investigate the periodic character invariant intervals oscillation and global stability of all positive solutions of the equationx n 1 px n x n kq x n k n 0 1 where the parameters p and q and the initial conditions x k x 0 are nonnegative real numbers as might be expected the two cases p q give rise to different dynamic behaviors in particular our results solve the open problem proposed by kulenvic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2001

graph matching by simplified convex concave relaxation procedure the convex and concave relaxation procedure ccrp was recently proposed and exhibited state of the art performance on the graph matching problem however ccrp involves explicitly both convex and concave relaxations which typically are difficult to find and thus greatly limit its practical applications in this paper we propose a simplified ccrp scheme which can be proved to realize exactly ccrp but with a much simpler formulation without needing the concave relaxation in an explicit way thus significantly simplifying the process of developing ccrp algorithms the simplified ccrp can be generally applied to any optimizations over the partial permutation matrix as long as the convex relaxation can be found based on two convex relaxations we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix respectively extensive experimental results witness the simplicity as well as state of the art performance of the two simplified ccrp graph matching algorithms

a fast projected fixed point algorithm for large graph matching we propose a fast algorithm for approximate matching of large graphs previous graph matching algorithms suffer from high computational complexity and therefore do not have good scalability by using a new doubly stochastic projection for matching two weighted graphs of n nodes our algorithm has time complexity only o n 3 per iteration and space complexity o n 2 we proved that our algorithm converges at a super logarithmic rate experiments on large synthetic and real graphs over 1000 nodes were conducted to evaluate the performance of various algorithms results show that due to its fast convergence our algorithm is more than an order of magnitude faster than the previous state of the art algorithms while maintaining comparable accuracy in large graph matching highlightslow time complexity o n3 iteration for two graphs of n nodes super logarithm convergence guarantee large graph matching experiments

spectral correspondence for point pattern matching this paper investigates the correspondence matching of point sets using spectral graph analysis in particular we are interested in the problem of how the modal analysis of point sets can be rendered robust to contamination and drop out we make three contributions first we show how the modal structure of point sets can be embedded within the framework of the em algorithm second we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix third we consider alternatives to the gaussian proximity matrix we evaluate the new method on both synthetic and real world data here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50 we also provide some examples on deformed point set tracking