minimal representation of directed hypergraphs in this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed various concepts of minimal representations of directed hypergraphs called minimal equivalent hypergraphs are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs in particular we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph number of hyperarcs number of adjacency lists required for the representation length of the overall description etc the relationships among the various concepts of minimality are discussed and their computational properties are analyzed in order to derive such results a graph representation of hypergraphs is introduced

yosida approximations for multivalued stochastic partial differential equations driven by levy noise on a gelfand triple abstract we prove the existence and uniqueness of solutions for a class of multivalued stochastic partial differential equations with maximal monotone drift on banach space driven by multiplicative levy noise we also establish the strong convergence result for solutions of the approximating equations where the maximal monotone drift operator is replaced by its yosida approximation as an application the existence and uniqueness of solutions for multivalued stochastic porous medium equations is obtained

skorohod problems with nonsmooth boundary conditions abstract the classical skorohod problem deals with a path by path construction of a diffusion process in a region with oblique reflection at the boundary starting from a standard brownian motion we show an existence of a weak solution to this problem if the boundary and the reflection vector field satisfy the uniform interior cone condition

a splitting step algorithm for reflected stochastic differential equations in r 1 a new algorithm which is based on the splitting step idea and the penalization method for reflected stochastic differential equation rsde in the upper half space r 1 is presented in this paper after some important estimates about rsdes and penalization odes are obtained the local pathwise error of the suggested algorithm are considered and an estimate of local error in the 2pth moment is proved under the assumptions of lipschitz continuity and linear growth some numerical experiments based on matlab programs are given to support the suggested algorithm

reflected diffusion processes with jumps a stochastic differential equation of wiener poisson type is considered in a d dimensional bounded region by using a penalization argument on the domain we are able to prove the existence and uniqueness of solutions in the strong sense the main assumptions are lipschitzian coefficients either convex or smooth domains and a regular outward reflecting direction as a direct consequence it is verified that the reflected diffusion process with jumps depends on the initial date in a lipschitz fashion

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

stochastic variational inequalities on non convex domains abstract the objective of this work is to prove in a first step the existence and the uniqueness of a solution of the following multivalued deterministic differential equation d x t x t d t d m t t 0 x 0 x 0 where m r r d is a continuous function and is the frechet subdifferential of a semiconvex function the domain of can be non convex but some regularities of the boundary are required the continuity of the map m x c 0 t r d c 0 t r d associating to the input function m the solution x of the above equation as well as tightness criteria allows to pass from the above deterministic case to the following stochastic variational inequality driven by a multi dimensional brownian motion x t k t 0 t f s x s d s 0 t g s x s d b s t 0 d k t x t d t

second order multivalued stochastic differential equations on riemannian manifolds the existence and uniqueness of solutions to multivalued stochastic differential equations of the second order on riemannian manifolds are proved the class of problem is motivated by rigid body and multibody dynamics with friction and an application to the spherical pendulum with friction is presented

stochastic approximation and large deviations upper bounds and w p 1 convergence with probability one convergence results are obtained for stochastic recursive approximation algorithms under very general conditions the gain sequence a n can go to zero very slowly and state dependent noise discontinuous dynamical equations and the projected or constrained algorithm are all treated the basic technique is the theory of large deviations prior results obtained via this theory are extended in many directions let dot x bar b x denote the mean equation for the algorithm let delta 0 be given and let g theta be a neighborhood of a stable point theta of that ordinary differential equation then asymptotic upper bounds to a n log p x n notin g theta n geqq n mid x n theta leqq delta are obtained these are often more informative than the usual classical rate of convergence results that use a local linearization and furthermore are obtained for the constrained and nonsmooth cases for which there are no rate of convergence

the probabilistic solution of the third boundary value problem for second order elliptic equations using standard reflected brownian motion srbm and martingales we define in the spirit of stroock and varadhan see s v the probabilistic solution of the boundary value problem begin gathered frac 1 2 delta u qu 0 in d hfill frac partial u partial n cu f on partial d hfill end gathered whered is a bounded domain withc3 boundary andn is the inward unit oormal vector on d the assumptions forq c andf are quite general

succinctness and tractability of closure operator representations it is widely known that closure operators on finite sets can be represented by sets of implications also known as inclusion dependencies as well as by formal contexts in this article we consider these two representation types as well as generalizations of them extended implication sets and context families we discuss the mutual succinctness of these four representations and the tractability of certain operations used to compare and modify closure operators

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

an optimal tree search method for the manufacturing systems cell formation problem abstract a solution methodology producting exact solutions to the manufacturing systems cell formation problem is presented a distance matrix representing the closeness between pairs of machines with regard to the parts they process is taken into account the proposed approach is an optimal tree search method which empoys two different bounds a classical bound for the quadratic assignment problem and a recently proposed one for the quadratic transportation problem as well as a new heuristic for the cell formation problem a special tree search was designed in order to reduce the size of the tree minimize the computational effort required in time consuming calculations and exploit symmetries of the problem computational results indicate that the proposed algorithm is very efficient in generating optimal solutions at low computational cost

the equipartition polytope i formulations dimension and basic facets the following basic clustering problem arises in different domains ranging from physics statistics and boolean function minimization given a graphg v e and edge weightsce partition the setv into two sets of 1 2 v and 1 2 v nodes in such a way that the sum of the weights of edges not having both endnodes in the same set is maximized or minimized anequicut is a feasible solution of the above problem and theequicut polytope q g is the convex hull of the incidence vectors of equicuts ing in this paper we give some integer programming formulations of the equicut problem study the dimension of the equicut polytope and describe some basic classes of facet inducing inequalities forq g

second order hamilton jacobi bellman equations with an unbounded operator abstract this work is devoted to the study of a class of hamilton jacobi bellman equations associated to an optimal control problem where the state equation is a stochastic differential inclusion with a maximal monotone operator we show that the value function minimizing a bolza type cost functional is a viscosity solution of the hjb equation the proof is based on the perturbation of the initial problem by approximating the unbounded operator finally by providing a comparison principle we are able to show that the solution of the equation is unique

a decomposition method for cnf minimality proofs a cnf is minimal if no shorter cnf representing the same function exists where by cnf length we mean either the number of clauses or the total number of literals sum of clause lengths in this paper we develop a decomposition approach that can be in certain situations applied to a cnf formula when proving its minimality we give two examples in which this decomposition approach is used both examples deal with pure horn minimization a problem defined as follows given a pure horn cnf construct a logically equivalent pure horn cnf which is the shortest possible either w r t the number of clauses or w r t the total number of literals both presented examples give alternative proofs of known complexity results for pure horn minimization

a non convex setup for multivalued differential equations driven by oblique subgradients abstract the paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients considered in a non convex domain x t h t x t x t g t x t t 0 x 0 x 0 where stands for the frechet subdifferential of the semiconvex function and the matrix application x h x is a lipschitz mapping the presence of the oblique reflection brought by the term h leads to the use of different techniques comparing to the cases of standard reflection in non convex domains or oblique reflection in convex domains the last section of the article is focused on the qualitative analysis of a non convex skorohod problem with generalized reflection and as applications stochastic variational inequalities driven by oblique frechet subgradients are addressed

the stochastic reflection problem with multiplicative noise abstract this paper addresses the existence and uniqueness of strong solutions to the stochastic variational inequality d x x d t f t x d t x d t k 1 m x k d k t f t d t in a bounded domain o r d with dirichlet homogeneous conditions here r 0 for r 0 0 0 r 0 for r 0 an application to the one phase stefan problem with a stochastic heat source is given one studies also the corresponding stochastic parabolic equation with signorini boundary conditions x x 0 on o

probabilistic approach for nonlinear partial differential equations and stochastic partial differential equations with neumann boundary conditions abstract in this study we consider nonlinear partial differential equations pdes and stochastic pdes spdes with neumann boundary conditions on domains that satisfy the lions sznitmann saisho conditions using the convergence result based on the penalization approximation for stochastic differential equations with normal reflections on nonsmooth and nonconvex domains we establish the existence and comparison principle for the viscosity solutions of nonlinear pdes with the neumann conditions associated with the optimal control problem we also obtain for nonlinear spdes and backward spdes with neumann condition the representations of the stochastic viscosity solutions

a version of the bundle idea for minimizing a nonsmooth function conceptual idea convergence analysis numerical results during recent years various proposals for the minimization of a nonsmooth functional have been made amongst these the bundle concept turned out to be an especially fruitful idea based on this concept a number of authors have developed codes that can successfully deal with nonsmooth problems the aim of the paper is to show that by adding some features of the trust region philosophy to the bundle concept the end result is a distinguished member of the bundle family with a more stable behaviour than some other bundle versions the reliability and efficiency of this code is demonstrated on the standard academic test examples and on some real life problems

the equipartition polytope ii valid inequalities and facets theequipartition problem is defined as follows given a graphg v e and edge weightsce partition the setv into two sets of 1 2 v and 1 2 v nodes in such a way that the sum of the weights of edges not having both endnodes in the same set is maximized or minimized anequicut is a feasible solution of the above problem and theequicut polytope q g is the convex hull of the incidence vectors of equicuts ing in this paper we describe some facet inducing inequalities of this polytope

semidefinite programming and eigenvalue bounds for the graph partition problem the graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized in this paper we simplify a known matrix lifting semidefinite programming relaxation of the graph partition problem for several classes of graphs and also show how to aggregate additional triangle and independent set constraints for graphs with symmetry we present an eigenvalue bound for the graph partition problem of a strongly regular graph extending a similar result for the equipartition problem we also derive a linear programming bound of the graph partition problem for certain johnson and kneser graphs using what we call the laplacian algebra of a graph we derive an eigenvalue bound for the graph partition problem that is the first known closed form bound that is applicable to any graph thereby extending a well known result in spectral graph theory finally we strengthen a known semidefinite programming relaxation of a specific quadratic assignment problem and the above mentioned matrix lifting semidefinite programming relaxation by adding two constraints that correspond to assigning two vertices of the graph to different parts of the partition this strengthening performs well on highly symmetric graphs when other relaxations provide weak or trivial bounds

bsdes with terminal conditions that have bounded malliavin derivative abstract we show existence and uniqueness of solutions to bsdes of the form y t t t f s y s z s d s t t z s d w s in the case where the terminal condition has bounded malliavin derivative the driver f s y z is assumed to be lipschitz continuous in y but only locally lipschitz continuous in z in particular it can grow arbitrarily fast in z if in addition to having bounded malliavin derivative is bounded the driver needs only be locally lipschitz continuous in y in the special case where the bsde is markovian we obtain existence and uniqueness results for semilinear parabolic pdes with non lipschitz nonlinearities we discuss the case where there is no lateral boundary as well as lateral boundary conditions of dirichlet and neumann type

the skorohod oblique reflection problem in domains with corners and application to stochastic differential equations the skorohod oblique reflection problem for d w d a general domain in d x x d a convex cone of directions of reflection w a function ind d is considered it is first proved under a condition on d corresponding to x not being simultaneously too large and too much skewed with respect to d that given a sequence wn of functions converging in the skorohod topology tow any sequence xn n of solutions to the skorohod problem for d wn is relatively compact and any of its limit points is a solution to the skorohod problem for d w next it is shown that if d satisfies the uniform exterior sphere condition and another requirement then solutions to the skorohod problem for d w exist for everyw d d with small enough jump size the requirement is met in the case when d is piecewisecb1 is generated by continuous vector fields on the faces ofd and x makes and angle in a suitable sense of less than 2 with the cone of inward normals atd for everyx d existence of obliquely reflecting brownian motion and of weak solutions to stochastic differential equations with oblique reflection boundary conditions is derived

a system of infinitely many mutually reflecting brownian balls in ℝd an infinite system of skorohod type equations is studied the unique solution of the system is obtained from a finite case by passing to the limit it is a diffusion process describing a system of infinitely many brownian hard balls and has a gibbs state associated with the hard core pair potential as a reversible measure

ultraboundedness for parabolic equations in convex domains without boundary conditions abstract we consider the operator a u 1 2 u d u d u where u is a convex real function defined in a convex open set o r n and lim x u x lim x o u x we prove that the associated markov semigroup is ultrabounded with respect to the gibbs measure e 2 u x d x

stochastic recursive optimal control problem of reflected stochastic differential systems in this paper we study one kind of stochastic recursive optimal control problem in which the control system is stochastic differential equations reflected in a domain and the cost functional is de

large deviations of max weight scheduling policies on convex rate regions we consider a single server discrete time system with a fixed number of users where the server picks operating points from a compact convex and coordinate convex set for this system we analyse the performance of a stabilising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rates where the weights depend on the work loads of the users assuming a large deviations principle ldp for the arrival processes in the skorohod space of functions that are right continuous with left hand limits we establish an ldp for the work load process using a generalised version of the contraction principle to derive the corresponding rate function with the ldp result available we then analyse the tail probabilities of the work loads under different buffering scenarios

white noise driven spdes with reflection we study reflected solutions of a nonlinear heat equation on the spatial interval 0 1 with dirichlet boundary conditions driven by space time white noise the nonlinearity appears both in the drift and in the diffusion coefficient roughly speaking at any point t x where the solutionu t x is strictly positive it obeys the equation and at a point t x whereu t x is zero we add a force in order to prevent it from becoming negative this can be viewed as an extension both of one dimensional sdes reflected at 0 and of deterministic variational inequalities existence of a minimal solution is proved the construction uses a penalization argument a new existence theorem for spdes whose coefficients depend on the past of the solution and a comparison theorem for solutions of white noise driven spdes

on the number of databases and closure operations abstract closure operations are considered as models of databases estimates on the number of closure operations on n elements or equivalently on the number of databases with n attributes are given

the optimal control problem associated with multi valued stochastic differential equations with jumps abstract this work concerns the optimal control problem associated with multi valued stochastic differential equations with levy jumps through the yosida approximation technique we prove that the value function of the control problem is the unique viscosity solution of a second order parabolic integro differential equation involving a multi valued maximal monotone operator the dynamic programming principle and the comparison theorem are also proved

solving large scale sparse semidefinite programs for combinatorial optimization we present a dual scaling interior point algorithm and show how it exploits the structure and sparsity of some large scale problems we solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints we report the first computational results of interior point algorithms for approximating maximum cut semidefinite programs with dimension up to 3 000

deterministic and stochastic differential inclusions with multiple surfaces of discontinuity we consider a class of deterministic and stochastic dynamical systems with discontinuous drift f and solutions that are constrained to live in a given closed domain g in mathbb r n according to a constraint vector field d specified on the boundary partial g of the domain specifically we consider equations of the form phi theta eta u quad dot theta t in f phi t quad mbox a e t for u in an appropriate class of functions where is the constraining term in the skorokhod problem specified by g d and f is the set valued upper semicontinuous envelope of f the case g mathbb r n when there is no constraining mechanism and u is absolutely continuous corresponds to the well known setting of differential inclusions di we provide a general sufficient condition for uniqueness of solutions and lipschitz continuity of the solution map in the form of existence of a lyapunov set here we assume i g is convex and admits the representation g cup i overline c i where c i i in mathbb i is a finite collection of disjoint open convex polyhedral cones in mathbb r n each having its vertex at the origin ii f b f c is a vector field defined on g such that b assumes a constant value on each of the given cones and f c is lipschitz continuous on g and iii d is an upper semicontinuous cone valued vector field that is constant on each face of g we also provide existence results under much weaker conditions where no lyapunov set condition is imposed for stochastic differential equations sde possibly reflected that have drift coefficient f and a lipschitz continuous possibly degenerate diffusion coefficient we establish strong existence and pathwise uniqueness under appropriate conditions our approach yields new existence and uniqueness results for both di and sde even in the case g mathbb r n the work has applications in the study of scaling limits of stochastic networks

a computational study of graph partitioning letg n e be an edge weighted undirected graph the graph partitioning problem is the problem of partitioning the node setn intok disjoint subsets of specified sizes so as to minimize the total weight of the edges connecting nodes in distinct subsets of the partition we present a numerical study on the use of eigenvalue based techniques to find upper and lower bounds for this problem results for bisecting graphs with up to several thousand nodes are given and for small graphs some trisection results are presented we show that the techniques are very robust and consistently produce upper and lower bounds having a relative gap of typically a few percentage points

reaction diffusion on metric graphs from 3d to 1d abstract we provide stochastic foundations for the analysis of a class of reaction diffusion systems using as an example the known temporal analysis of products tap experiments showing how to effectively obtain explicit solutions to the associated equations by approximating the 3 dimensional domain of diffusion u the reactor by 1 dimensional network models in a typical tap experiment a pulse of reactant gas of species a is injected into u which is filled with chemically inert material permeable to gas diffusion particles of catalyst are placed amid this inert medium forming active sites where the reaction a b may occur on part of the boundary of u designated as the exit a mixture of a and b can escape we study the problem of determining the molar fraction of product gas in the mixture after u is fully evacuated this fraction is identified with the reaction probability that is the probability of a single diffusing molecule reacting before leaving u specifically we are interested in how this probability depends on the reaction rate constant k after giving a stochastic formulation of the problem and the boundary value problem whose solution is this probability we study a class of domains called fat graphs comprising a network of thin tubes with active sites at junctures the main result of the paper is that in the limit as the thin tubes approach curves in 3 dimensional space reaction probability converges to functions of the point of gas injection that can be computed explicitly in terms of a rescaled parameter k by this 3d to 1d reduction the simpler processes on metric graphs can be used as model systems for more realistic 3 dimensional configurations this is illustrated with analytic and numerical examples one example in particular illustrates an important application of our method finding the catalyst configuration that maximizes reaction probability at a given reaction rate constant

probleme de skorohod multivoque on prouve un resultat d existence et d unicite pour une generalisation par introduction d un operateur maximal monotone multivoque du probleme de skorohod avec reflexion normale deterministe associe a un convexe ferme d de r d la formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine cette approche multivoque clarifie la connexion entre probleme de skorohod et semigroupes nonlineaires en guise d application on considere ensuite le cas stochastique les equations differentielles stochastiques multivoques sont ainsi revisitees par consequent cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu explosif

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

lifschitz tail on hyperbolic space neumann conditions on considere un espace hyperbolique h de dimension n et l operateur laplacien hyperbolique h etant donne une distribution aleatoire de points a l aide d un processus ponctuel de poisson tel que chaque point se situe dans une boule hyperbolique de rayons on etudie la question suivante si est un petit nombre reel combien y a t il de valeurs propres inferieures a pour l operateur 1 2 h dans une boule b de centre o avec des conditions de neumann sur la frontiere et avec des conditions aux limites de dirichlet sur les boules aleatoires formant des intersections avec b si le rayon de b est suffisamment grand

stabilities of shape identification inverse problems in a bayesian framework abstract a general shape identification inverse problem is studied in a bayesian framework this problem requires the determination of the unknown shape of a domain in the euclidean space from finite dimensional observation data with some gaussian random noise then the stability of posterior is studied for observation data for each point of the space the conditional probability that the point is included in the unknown domain given the observation data is considered the stability is also studied for this probability distribution as a model problem for our inverse problem a heat inverse problem is considered this problem requires the determination of the unknown shape of cavities in a heat conductor from temperature data of some portion of the surface of the heat conductor to apply the above stability results to this model problem one needs the measurability and some boundedness of the forward operator these properties are shown

a low dimensional semidefinite relaxation for the quadratic assignment problem the quadratic assignment problem qap is arguably one of the hardest np hard discrete optimization problems problems of dimension greater than 25 are still considered to be large scale current successful solution techniques use branch and bound methods which rely on obtaining strong and inexpensive bounds in this paper we introduce a new semidefinite programming sdp relaxation for generating bounds for the qap in the trace formulation we apply majorization to obtain a relaxation of the orthogonal similarity set of the quadratic part of the objective function this exploits the matrix structure of qap and results in a relaxation with much smaller dimension than other current sdp relaxations we compare the resulting bounds with several other computationally inexpensive bounds such as the convex quadratic programming relaxation qpb we find that our method provides stronger bounds on average and is adaptable for branch and bound methods

multi valued stochastic differential equations driven by g brownian motion and related stochastic control problems abstractin this paper we prove the existence and uniqueness of a solution for a class of multi valued stochastic differential equations driven by g brownian motion msdeg by means of the yosida approximation method moreover we set up an optimality principle of stochastic control problem and prove the value function of the control problem is the unique viscosity solution of a class of nonlinear partial differential variational inequalities

stochastic differential equations for multi dimensional domain with reflecting boundary in this paper we prove that there exists a unique solution of the skorohod equation for a domain inr d with a reflecting boundary condition we remove the admissibility condition of the domain which is assumed in the work 4 of lions and sznitman we first consider a deterministic case and then discuss a stochastic case

on the oblique derivative problem for diffusion processes and diffusion equations with holder continuous coefficients on a c2 domain in a euclidean space we consider the oblique derivative problem for a diffusion equation and assume the coefficients of the diffusion and boundary operators are holder continuous we then prove the uniqueness of diffusion processes and fundamental solutions corresponding to the problem for the purpose obtaining a stochastic representation of some so lutions to the problem plays a key role in our situation a difficulty arises from the absence of a fundamental solution with c2 smoothness up to the boundary it is overcome by showing some stability of a fundamental solution and a dif fusion process respectively under approximation of the domain in particular the stability of the fundamental solution is verified through construction it is done by applying the parametrix method twice to a parametrix with explicit expression

the submartingal problem for brownian motion in a cone with non constant oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties 1 the state space is a cone ind dimensions d 3 and the process behaves in the interior of the cone like ordinary brownian motion 2 the process reflects instantaneously at the boundary of the cone the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial line emanating from the vertex 3 the amount of time that the process spends at the vertex of the cone is zero i e the set of times for which the process is at the vertex has zero lebesgue measure

an exact algorithm for graph partitioning an exact algorithm is presented for solving edge weighted graph partitioning problems the algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine underestimate it is shown that the best affine underestimate can be expressed in terms of the center and the radius of the smallest sphere containing the feasible set the concave term is obtained either by a constant diagonal shift associated with the smallest eigenvalue of the objective function hessian or by a diagonal shift obtained by solving a semidefinite programming problem numerical results show that the proposed algorithm is competitive with state of the art graph partitioning codes

set estimation from reflected brownian motion we study the problem of estimating a compact set s rd from a trajectory of a reflected brownian motion in s with reflections on the boundary of s this problem has relevant applications in ecology in estimating the home range of an animal based on tracking data

numerical simulation of multi dimensional reflecting geometrical brownian motion and its application to mathematical finance abstract we investigate the mean square error of the euler maruyama type approximate solution of the multi dimensional reflecting geometrical brownian motion using the penalty method furthermore we show some examples of it with several boundaries

algorithms for graph partitioning problems by means of eigenspace relaxations abstract graph partitioning problems are np hard problems and very important in vlsi design we study relations among several eigenvalue bounds and algorithms for graph partitioning problems also we design an algorithm for the problems which performs the following first it computes the k largest eigenvalues of the affine symmetric matrix function to attain donath hoffman bound then it calculates a relaxed partition which is an array constant factor of an eigenspace associated with k eigenvalues finally it generates an actual partition from the relaxed solution of a method similar to boppana s algorithm to compute optimal eigenvalue bounds one needs to solve eigenvalue optimization problems which minimize the sum of the k largest eigenvalues of the nonsmooth functions we use a subgradient method to compute the donath hoffman eigenvalue bound numerical results indicate that although the donath hoffman bound is not tight for graph partitioning problems our algorithm can generate optimal partitions

rubber bands pursuit games and shy couplings in this paper we consider pursuit evasion and probabilistic consequences of some geometric notions for bounded and suitably regular domains in euclidean space that are cat for some 0 these geometric notions are useful for analysing the related problems of a existence non existence of successful evasion strategies for the man in lion and man problems and b existence non existence of shy couplings for reflected brownian motions they involve properties of rubber bands and the extent to which a loop in the domain in question can be deformed to a point without in between increasing its loop length the existence of a stable rubber band will imply the existence of a successful evasion strategy but if all loops in the domain are well contractible then no successful evasion strategy will exist and there can be no co adapted shy coupling for example there can be no shy couplings in bounded and suitably regular star shaped domains and so in this setting any two reflected brownian motions must almost surely make arbitrarily close encounters as t

evolution problems in spaces of probability measures abstract this is a short survey paper on the application of monge s theory of optimal mass transportation to evolution problems of a gradient type in the case when the natural state space is the space of probability measures this occurs for instance for fokker planck equations and optimal mass transportation methods provide in this setting very general existence and stability results

the joy of implications aka pure horn formulas pure horn clauses have also been called among others functional dependencies strong association rules or simply implications we survey the mathematical theory of implications with an emphasis on the progress made in the last 30 years