a flow model based on polylinking system we introduce polylinking networks which is a flow model based on polylinking systems that generalizes the classical flow model of ford and fulkerson on acyclic networks and has applications in the context of wireless networks more precisely a flow model recently introduced by avestimehr et al proceedings of the allerton conference on communication control and computing 2007 used in the context of wireless information networks is a special case of the presented model we define a notion of source destination cut and derive a max flow min cut theorem additionally we present various properties of polylinking networks that can be seen as generalizations of properties for classical flows using submodular function minimization and submodular flow algorithms one can efficiently determine a maximum flow a minimum source destination cut as well as a minimum cost flow these algorithms lead to new efficient algorithms for the information flow model

a bound for the symmetric travelling salesman problem through matroid formulation abstract a new bound for the symmetric traveling salesman problem is proposed using a matroid theoretic formulation of the problem the resulting bound is shown to present a link between the well studied 1 tree and 2 matching bounds its potential is investigated

invariant grids for reaction kinetics abstract in this paper we construct low dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold mim mim is based on a formulation of the condition of invariance as an equation and its solution by newton iterations a grid based version of mim is developed the method of invariant grids we describe the newton method and the relaxation method for the invariant grids construction the problem of the grid correction is fully decomposed into the problems of the grid s nodes correction the edges between the nodes appear only in the calculation of the tangent spaces this fact determines high computational efficiency of the method of invariant grids the method is illustrated by two examples the simplest catalytic reaction michaelis menten mechanism and the hydrogen oxidation the algorithm of analytical continuation of the approximate invariant manifold from the discrete grid is proposed generalizations to open systems are suggested the set of methods covered makes it possible to effectively reduce description in chemical kinetics

on the existence of identifiable reparametrizations for linear compartment models the parameters of a linear compartment model are usually estimated from experimental input output data a problem arises when infinitely many parameter values can yield the same result such a model is called unidentifiable in this case one can search for an identifiable reparametrization of the model a map which reduces the number of parameters such that the reduced model is identifiable we study a specific class of models which are known to be unidentifiable using algebraic geometry and graph theory we translate a criterion given by meshkat and sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph this allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization using these constructions a large subclass of such graphs is obtained finally we present a procedure for subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization

density matrix renormalization for model reduction in nonlinear dynamics we present an approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition pod our method derived from the density matrix renormalization group provides a significant reduction in computational effort for the calculation of the reduced system compared to a pod the efficiency of the algorithm is tested on the one dimensional burgers equations and a one dimensional equation of the fisher type as nonlinear model systems

an improved algorithm for the computation of kronecker s canonical form of a singular pencil we give an 0 t algorithm for computing the kronecker structure of an arbitrary m x n pencil xe a the algorithm is shown to he numerically stable because only unitary transformations are used the improved speed over earlier unitary methods is due to the efficient use of condensed forms which are maintained throughout the recursions of the algorithm

two algorithms for weighted matroid intersection consider a finite sete a weight functionw e r and two matroidsm1 andm2 defined one the weighted matroid intersection problem consists of finding a seti e independent in both matroids that maximizes w e e ini we present an algorithm of complexity o nr r c logn for this problem wheren e r min rank m1 rank m2 c max c1 c2 and fori 1 2 ci is the complexity of finding the circuit ofi e inmi or show that none exists wheree is ine andi e is independent inm1 andm2 a related problem is to find a maximum weight set independent in both matroids and of given cardinalityk if one exists our algorithm also solves this problem in addition we present a second algorithm that given a feasible solution of cardinalityk finds an optimal one of the same cardinality a sensitivity analysis on the weights is easy to perform using this approach our two algorithms are related to existing algorithms in fact our framework provides new simple proofs of their validity other contributions of this paper are the existence of nonnegative reduced weights theorem 6 allowing the improved complexity bound and the introduction of artificial elements allowing an improved start and flexibility in the implementation of the algorithms

dynamics of predator prey system with fading memory abstract a predator prey model with fading memory for general holling type functional response is proposed the fading memory term is used with the hypothesis that the predator s growth rate at present depends on the recent past quantities of prey the effects of predator harvesting is also considered in the model the model is analysed theoretically as well as numerically two parameter bifurcation analysis are done and the existence of hopf point bifurcation is identified both supercritical and subcritical hopf bifurcations are obtained with the variation of system parameters maximum sustainable yield with respect to harvesting effort is also determined it is to be observed that the system dynamics is very rich in presence of fading memory the obtained results may be useful in the field of agriculture and fishery

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

expander graphs and their applications a major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists since expander graphs the protagonists of our story come up in numerous and often surprising contexts in both fields but perhaps we should start with a few words about graphs in general they are of course one of the prime objects of study in discrete mathematics however graphs are among the most ubiquitous models of both natural and human made structures in the natural and social sciences they model relations among species societies companies etc in computer science they represent networks of communication data organization computational devices as well as the flow of computation and more in mathematics cayley graphs are useful in group theory graphs carry a natural metric and are therefore useful in geometry and though they are just one dimensional complexes they are useful in certain parts of topology e g knot theory in statistical physics graphs can represent local connections between interacting parts of a system as well as the dynamics of a physical process on such systems the study of these models calls then for the comprehension of the significant structural properties of the relevant graphs but are there nontrivial structural properties which are universally important expansion of a graph requires that it is simultaneously sparse and highly connected expander graphs were first defined by bassalygo and pinsker and their existence first proved by pinsker in the early 70s the property of being an expander seems significant in many of these mathematical computational and physical contexts it is not surprising that expanders are useful in the design and analysis of communication networks what is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness in mathematics we will encounter e g their role in the study of metric embeddings and in particular in work around the baum connes conjecture expansion is closely related to the convergence rates of markov chains and so they play a key role in the study of monte carlo algorithms in statistical mechanics and in a host of practical computational applications the list of such interesting and fruitful connections goes on and on with so many applications we will not even

methods for dimension reduction and their application in nonlinear dynamics abstract we compare linear and nonlinear galerkin methods in their efficiency to reduce infinite dimensional systems described by partial differential equations to low dimensional systems of ordinary differential equations both concerning the effort in their application and the accuracy of the resulting reduced system important questions like the choice of the form of the ansatz functions modes the choice of the number m of modes and finally the construction of the reduced system are addressed for the latter point both the linear or standard galerkin method making use of the karhunen loeve proper orthogonal decomposition ansatz functions and the nonlinear galerkin method using approximate inertial manifold theory are used in addition also the post processing galerkin method is compared with the other approaches

algorithms and data structures for an expanded family of matroid intersection problems consider a matroid of rank n in which each element has a real valued cost and one of d 1 colors a class of matroid intersection problems is studied in which one of the matroids is a partition matroid that specifies that a base has q j elements of color j for j 1 2 cdots d relationships are characterized among the solutions to the family of problems generated when the vector q 1 q 2 cdots q d is allowed to range over all values that sum to n a fast algorithm is given for solving such matroid intersection problems when d is small a characterization is presented for how the solution changes when one element changes in cost data structures are given for updating the solution on line each time the cost of an arbitrary matroid element is modified efficient update algorithms are given for maintaining a color constrained minimum spanning tree in either a general or a planar graph an application of the techniques to the problem of finding a minimum spanning tree with several degree

an implicit explicit hybrid method for lagrangian hydrodynamics abstract we describe a new implicit explicit hybrid method for solving the equations of hydrodynamics the scheme is an extension of the explicit second order piecewise parabolic method ppm which is unconditionally stable the scheme is thus of the godunov type it is conservative accurate to second order in both space and time and makes use of a nonlinear riemann solver to obtain fluxes of the conserved quantities the hybrid character of the method provides increased accuracy and computational efficiency switching between implicit and explicit formulations occurs smoothly and in a natural way and is performed separately for each characteristic family of waves the method provides high resolution with shocks spread over only one zone and can produce accurate answers to most reasonable problems without the use of an artificial viscosity 1986 academic press inc

a novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration a novel method for analyzing the inverse problem of topological indices of graph is proposed in this paper which applies the data mining technique to classification of graphs according to topological indices differing from the way of using topological indices to categorize graphs into different isomorphic classes this method aims at dividing molecular graphs with n vertices into several compact classes according to their topological indices then the chemical and physical features of each kind of graph can be researched and new compounds can be found which has great significance on bio medical filed in the experiment three classes of simple connected graphs with 5 6 and 7 vertices respectively are investigated and analyzed using the proposed method the experimental results show the validity of it however there are still some problems needed to be researched further such as selecting the vector of topological indices for clustering selecting the distance between the vectors of topological indices choosing the aspects to analyze the properties of each kind of graph after clustering etc

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

on the kronecker canonical form of singular mixed matrix pencils consider a linear time invariant dynamical system that can be described as f dot x t a x t b u t where a b and f are mixed matrices i e matrices having two kinds of nonzero coefficients fixed constants that account for conservation laws and independent parameters that represent physical characteristics the controllable subspace of the system is closely related to the kronecker canonical form of the mixed matrix pencil begin pmatrix a sf mid b end pmatrix under a physically meaningful assumption justified by the dimensional analysis we provide a combinatorial characterization of the sums of the minimal row column indices of the kronecker canonical form of mixed matrix pencils the characterization leads to a matroid theoretic algorithm for efficiently computing the dimension of the controllable subspace for the system with nonsingular f

on matching cover of graphs a k matching cover of a graph g g is a union of k k matchings of g g which covers v g v g the matching cover number of g g denoted by mc g m c g is the minimum number k k such that g g has a k k matching cover a matching cover of g g is optimal if it consists of mc g m c g matchings of g g in this paper we present an algorithm for finding an optimal matching cover of a graph on n n vertices in o n 3 o n 3 time if use a faster maximum matching algorithm the time complexity can be reduced to o nm o n m where m e g m e g and give an upper bound on matching cover number of graphs in particular for trees a linear time algorithm is given and as a by product the matching cover number of trees is determined

an additive bounding procedure for combinatorial optimization problems we know that the effectiveness of the branch and bound algorithms proposed for the solution of combinatorial optimization problems greatly depends on the tightness of the available bounds in this paper we consider optimization problems with a linear objective function we propose an additive approach for computing lower bounds that yields an increasing sequence of values an application to the traveling salesman problem with precedence constraints is presented to exemplify the technique

solving sparse linear equations over finite fields a coordinate recurrence method for solving sparse systems of linear equations over finite fields is described the algorithms discussed all require o n 1 omega n 1 log k n 1 field operations where n 1 is the maximum dimension of the coefficient matrix omega is approximately the number of field operations required to apply the matrix to a test vector and the value of k depends on the algorithm a probabilistic algorithm is shown to exist for finding the determinant of a square matrix also probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error

aerodynamic data reconstruction and inverse design using proper orthogonal decomposition the application of proper orthogonal decomposition for incomplete gappy data for compressible external aerodynamic problems has been demonstrated successfully in this paper for the first time using this approach it is possible to construct entire aerodynamic flowfields from the knowledge of computed aerodynamic flow data or measured flow data specified on the aerodynamic surface thereby demonstrating a means to effectively combine experimental and computational data the sensitivity of flow reconstruction results to available measurements and to experimental error is analyzed another new extension of this approach allows one to cast the problem of inverse airfoil design as a gappy data problem the gappy methodology demonstrates a great simplification for the inverse airfoil design problem and is found to work well on a range of examples including both subsonic and transonic cases

improved bounds for matroid partition and intersection algorithms we give bounds on total lengths of augmenting paths in standard implementations of the matroid partition and intersection algorithms and indicate how these observations can be used to improve the running times in certain applications for example for the matroid intersection algorithm on two r by n matrices the running time is shown to be o nr 2 log r we also give improved versions of the two algorithms when running times are measured in terms of calls to an independence oracle for example there is a matroid partition algorithm on o n n element matroids using o n 2 5 independence tests

atomic routing games on maximum congestion we study atomic routing games on networks in which players choose a path with the objective of minimizing the maximum congestion along the edges of their path the social cost is the global maximum congestion over all edges in the network we show that the price of stability is 1 the price of anarchy poa is determined by topological properties of the network in particular poa o logn where is the length of the longest path in the player strategy sets and n is the size of the network further 1 poa c 2 log2n where is the length of the longest cycle in the network and c is a constant

belyakov homoclinic bifurcations in a tritrophic food chain model complex dynamics of the most frequently used tritrophic food chain model are investigated in this paper first it is shown that the model admits a sequence of pairs of belyakov bifurcations codimension two homoclinic orbits to a critical node then fold and period doubling cycle bifurcation curves associated to each pair of belyakov points are computed and analyzed the overall bifurcation scenario explains why stable limit cycles and strange attractors with different geometries can coexist the analysis is conducted by combining numerical continuation techniques with theoretical arguments

towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations we investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations the proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems we examine dynamical scaling characteristics in the short time and the long time evolution regime providing only a reduced number of degrees of freedom to the evolution process

global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting abstract this paper describes a prey predator model with stage structure for predator and selective harvesting effort on predator population the holling type ii functional response function is taken into consideration all the equilibria of the proposed system are determined and the behavior of the system is investigated near them local stability of the system is analyzed geometric approach is used to derive the sufficient conditions for global stability of the system the occurrence of hopf bifurcation of the model system in the neighborhood of the co existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource pontryagin s maximum principle is used to characterize the optimal control the optimal system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

solving ratio dependent predator prey system with constant effort harvesting using adomian decomposition method abstract in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the ratio dependent predator prey system with constant effort harvesting the convergence of the decomposition series is enhanced using pade approximation technique the qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator prey interaction some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm the decomposition method has the advantage of being more concise for numerical purposes

randomized tilde o m a randomized las vegas algorithm is given for finding the gallai edmonds decomposition of a graph let n denote the number of vertices and let m n denote the number of arithmetic operations for multiplying two n times n matrices the sequential running time i e number of bit operations is within a poly logarithmic factor of m n the parallel complexity is o log n 2 parallel time using a number of processors within a poly logarithmic factor of m n the same complexity bounds suffice for solving several other problems finding a minimum vertex cover in a bipartite graph finding a minimum x y vertex separator in a directed graph where x and y are specified sets of vertices finding the allowed edges i e edges that occur in some maximum matching of a graph finding the canonical partition of the vertex set of an elementary graph the sequential algorithms for problems i ii and iv are las vegas and the algorithm for problem iii is monte carlo the new complexity bounds are significantly better than the best previous ones e g using the best value of m n currently known the new sequential running time is o n2 38 versus the previous best o n2 5 log n or more

effects of supplying alternative food in a predator prey model with harvesting in this paper we propose a tritrophic predator prey model with harvesting where the top predator population is partially supported with alternative food we report the consequences of providing alternative food to the top predator in a top predator harvested model the extinction criterion for top predator population local stability of equilibrium points and persistence conditions are discussed theoretically pontryagins maximum principle is used to characterize the optimal control of harvesting we have derived the condition of hopf bifurcation by varying harvesting effort the bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given our analysis show that alternative food can prevent top predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species

computing the strong nash equilibrium for markov chains games present a novel method for finding the strong nash equilibriumintroduce tikhonov s regularization method to guarantee convergence to a single equilibriumprove the existence of a unique strong nash equilibriumpropose the euler method with penalty function for converging to the strong nash equilibriumpresent the convergence conditions of the step size parameter and tikhonov s regularizator in this paper we present a novel method for finding the strong nash equilibrium the approach consists on determining a scalar and the corresponding strategies d fixing specific bounds min and max that belong to the pareto front bounds correspond to restrictions imposed by the player over the pareto front that establish a specific decision area where the strategies can be selected we first exemplify the pareto front of the game in terms of a nonlinear programming problem adding a set of linear constraints for the markov chain game based on the c variable method for solving the strong nash equilibrium problem we propose to employ the euler method and a penalty function with regularization the tikhonov s regularization method is used to guarantee the convergence to a single strong equilibrium point then we established a nonlinear programming method to solve the successive single objective constrained problems that arise from taking the regularized functional of the game to achieve the goal we implement the gradient method to solve the first order optimality conditions starting from an utopia point pareto optimal point given an initial of the individual objectives the method solves an optimization problem adding linear constraints required to find the optimal strong strategy d we show that in the regularized problem the functional of the game decrease and finally converges proving the existence and uniqueness of strong nash equilibrium pareto optimal nash equilibrium in addition we present the convergence conditions and compute the estimated rate of convergence of variables and corresponding to the step size parameter of the gradient method and the tikhonov s regularization respectively moreover we provide all the details needed to implement the method in an efficient and numerically stable way the usefulness of the method is successfully demonstrated by a numerical example

optimal impulsive harvesting policies for single species populations in this paper we address an optimal impulsive control problem with the aim of optimizing the harvesting rate for a non autonomous logistic model in addressing this problem we combine bang bang and singular controls for an impulsive optimization problem in which the singular controls are blocked at certain harvesting times in our approach we first obtain the singular controls by applying a pontryagin optimal control framework for impulsive systems second we investigate and derive a number of relationships characterizing the optimal harvesting rates and present an optimization principle the optimal path lies as close as possible to the singular path finally based on this optimization principle we obtain analytical expressions for the optimal harvesting policy for our problem and use numerical simulations to demonstrate the effectiveness of our method this study develops concepts and theory related to continuous control problems and applies them to impulsive control problems and extends the related work of xiao et al 2006 and braverman and mamdani 2008

computation and efficiency of potential function minimizers of combinatorial congestion games we study the computation and efficiency of pure nash equilibria in combinatorial congestion games where the strategies of each player i are given by the binary vectors of a polytope p i our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure nash equilibria with attractive social cost approximation guarantees to this aim we identify two general properties of the underlying aggregation polytope p n sum i p i which are sufficient for our results to go through namely the integer decomposition property idp and the box totally dual integrality property box tdi our main results for polytopal congestion games satisfying idp and box tdi are as follows i we show that pure nash equilibria can be computed in polynomial time in fact we obtain this result through a general framework for separable convex function minimization which might be of independent interest ii we bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability iii we also prove that these results extend to strong equilibria for the bottleneck variant of polytopal congestion games examples of polytopal congestion games satisfying idp and box tdi include common source network congestion games symmetric totally unimodular congestion games non symmetric matroid congestion games and symmetric matroid intersection congestion games in particular r arborescences and strongly base orderable matroids

signal propagation and failure in one dimensional fitzhugh nagumo equations with periodic stimuli we analyze the effect of additive periodic stimuli in one dimensional fitzhugh nagumo equations in an excitable regime with a suitable stimulus interval the suppression of the pulse propagation occurs in some parameter regime this propagation failure comes from the formation of the death spot where successive pulses annihilate in the parameter regime where the solitary pulse cannot propagate in space stably however periodic stimuli cause a propagation of envelope of a traveling pulse under a resonance condition i e the pulse at the leading edge disappears successively however an envelope is formed and propagates with keeping its shape

model reduction for compressible flows using pod and galerkin projection abstract we present a framework for applying the method of proper orthogonal decomposition pod and galerkin projection to compressible fluids for incompressible flows only the kinematic variables are important and the techniques are well known in a compressible flow both the kinematic and thermodynamic variables are dynamically important and must be included in the configuration space we introduce an energy based inner product which may be used to obtain pod modes for this configuration space we then obtain an approximate version of the navier stokes equations valid for cold flows at moderate mach number and project these equations onto a pod basis the resulting equations of motion are quadratic and are much simpler than projections of the full compressible navier stokes equations

algebraic algorithms for matching and matroid problems we present new algebraic approaches for two well known combinatorial problems nonbipartite matching and matroid intersection our work yields new randomized algorithms that exceed or match the efficiency of existing algorithms for nonbipartite matching we obtain a simple purely algebraic algorithm with running time o n omega where n is the number of vertices and omega is the matrix multiplication exponent this resolves the central open problem of mucha and sankowski 2004 for matroid intersection our algorithm has running time o nr omega 1 for matroids with n elements and rank r that satisfy some natural conditions

the fast johnson lindenstrauss transform and approximate nearest neighbors we introduce a new low distortion embedding of ell 2 d into ell p o log n p 1 2 called the fast johnson lindenstrauss transform fjlt the fjlt is faster than standard random projections and just as easy to implement it is based upon the preconditioning of a sparse projection matrix with a randomized fourier transform sparse random projections are unsuitable for low distortion embeddings we overcome this handicap by exploiting the heisenberg principle of the fourier transform i e its local global duality the fjlt can be used to speed up search algorithms based on low distortion embeddings in ell 1 and ell 2 we consider the case of approximate nearest neighbors in ell 2 d we provide a faster algorithm using classical projections which we then speed up further by plugging in the fjlt we also give a faster algorithm for searching over the hypercube

exact and approximation algorithms for weighted matroid intersection in this paper we propose new exact and approximation algorithms for the weighted matroid intersection problem our exact algorithm is faster than previous algorithms when the largest weight is relatively small our approximation algorithm delivers a 1 epsilon approximate solution with a running time significantly faster than most known exact algorithms the core of our algorithms is a decomposition technique we decompose an instance of the weighted matroid intersection problem into a set of instances of the unweighted matroid intersection problem the computational advantage of this approach is that we can make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms more precisely we show that we can solve the weighted matroid intersection problem via solving w instances of the unweighted matroid intersection problem where w is the largest given weight assuming that all given weights are integral furthermore we can find a 1 epsilon approximate solution via solving o epsilon 1 log r instances of the unweighted matroid intersection problem where r is the smaller rank of the two given matroids our algorithms make use of the weight splitting approach of frank j algorithms 2 4 328 336 1981 and the geometric scaling scheme of duan and pettie j acm 61 1 1 2014 our algorithms are simple and flexible they can be adapted to special cases of the weighted matroid intersection problem using specialized unweighted matroid intersection algorithms in addition we give a further application of our decomposition technique we solve efficiently the rank maximal matroid intersection problem a problem motivated by matching problems under preferences

towards 3 query locally decodable codes of subexponential length a q query locally decodable code ldc encodes an n bit message x as an n bit codeword c x such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword c x even after some constant fraction of codeword bits has been corrupted we give new constructions of three query ldcs of vastly shorter length than that of previous constructions specifically given any mersenne prime p e 2t 1 we design three query ldcs of length n e exp o n1 t for every n based on the largest known mersenne prime this translates to a length of less than exp o n10 7 compared to exp o n1 2 in the previous constructions it has often been conjectured that there are infinitely many mersenne primes under this conjecture our constructions yield three query locally decodable codes of length n e exp no 1 log log n for infinitely many n we also obtain analogous improvements for private information retrieval pir schemes we give 3 server pir schemes with communication complexity of o n10 7 to access an n bit database compared to the previous best scheme with complexity o n1 5 25 assuming again that there are infinitely many mersenne primes we get 3 server pir schemes of communication complexity no 1 log logn for infinitely many n previous families of ldcs and pir schemes were based on the properties of low degree multivariate polynomials over finite fields our constructions are completely different and are obtained by constructing a large number of vectors in a small dimensional vector space whose inner products are restricted to lie in an algebraically nice set

the art of trellis decoding is fixed parameter tractable given n subspaces of a finite dimensional vector space over a fixed finite field mathbb f we wish to find a linear layout v 1 v 2 ldots v n of the subspaces such that dim v 1 v 2 cdots v i cap v i 1 cdots v n le k for all i such a linear layout is said to have width at most k when restricted to 1 dimensional subspaces this problem is equivalent to computing the trellis width or minimum trellis state complexity of a linear code in coding theory and computing the path width of an mathbb f represented matroid in matroid theory we present a fixed parameter tractable algorithm to construct a linear layout of width at most k if it exists for input subspaces of a finite dimensional vector space over mathbb f as corollaries we obtain a fixed parameter tractable algorithm to produce a path decomposition of width at most k for an input mathbb f represented matroid of path width at most k and a fixed parameter tractable algorithm to find a linear rank decomposition of width at most k for an input graph of linear rank width at most k in both corollaries no such algorithms were known previously our approach is based on dynamic programming combined with the idea developed by bodlaender and kloks 1996 for their work on path width and tree width of graphs it was previously known that a fixed parameter tractable algorithm exists for the decision version of the problem for matroid path width a theorem by geelen gerards and whittle 2002 implies that for each fixed finite field mathbb f there are finitely many forbidden mathbb f representable minors for the class of matroids of path width at most k an algorithm by hlin n 2006 can detect a minor in an input mathbb f represented matroid of bounded branch width however this indirect approach would not produce an actual path decomposition our algorithm is the first one to construct such a path decomposition and does not depend on the finiteness of forbidden minors

on the value of coordination in network design we study network design games where n self interested agents have to form a network by purchasing links from a given set of edges we consider shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge it is well known that the price of anarchy of these games is as high as n another line of research has focused on evaluating the price of stability i e the cost of the best nash equilibrium relative to the social optimum in this paper we investigate to which extent coordination among agents can improve the quality of solutions we resort to the concept of strong nash equilibria which were introduced by aumann and are resilient to deviations by coalitions of agents we analyze the price of anarchy of strong nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs these bounds are tight or nearly tight for many scenarios it shows that by using coordination the price of anarchy drops from linear to logarithmic bounds we complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria without coordination in undirected graphs more specifically we show a lower bound of omega log w log log w for weighted games where w is the total weight of all the agents this almost matches the known upper bound of o log w our results imply that for most settings the worst case performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination these settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs

on the impact of combinatorial structure on congestion games we study the impact of combinatorial structure in congestion games on the complexity of computing pure nash equilibria and the convergence time of best response sequences in particular we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time we show that if the strategy space of each player consists of the bases of a matroid over the set of resources then the lengths of all best response sequences are polynomially bounded in the number of players and resources we also prove that this result is tight that is the matroid property is a necessary and sufficient condition on the players strategy spaces for guaranteeing polynomial time convergence to a nash equilibrium in addition we present an approach that enables us to devise hardness proofs for various kinds of combinatorial games including first results about the hardness of market sharing games and congestion games for overlay network design our approach also yields a short proof for the pls completeness of network congestion games in particular we show that network congestion games are pls complete for directed and undirected networks even in case of linear latency functions

structure at infinity of structured descriptor systems and its applications the generic structure at infinity of the transfer matrix of a descriptor system is investigated under the physically reasonable assumption that the coefficients in the equations are classified into independent physical parameters and dimensionless constants for such a structured descriptor system the generic structure at infinity is characterized in terms of an independent assignment or weighted matroid intersection problem this leads to necessary and sufficient conditions for the generic solvability of the exact matching problem for a singular descriptor system and for the generic solvability of the disturbance decoupling problem for a nonsingular descriptor system the obtained conditions can be checked by efficient matroid theoretic algorithms

computing pure nash and strong equilibria in bottleneck congestion games bottleneck congestion games properly model the properties of many real world network routing applications they are known to possess strong equilibria a strengthening of nash equilibrium to resilience against coalitional deviations in this paper we study the computational complexity of pure nash and strong equilibria in these games we provide a generic centralized algorithm to compute strong equilibria which has polynomial running time for many interesting classes of games such as e g matroid or single commodity bottleneck congestion games in addition we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics using unilateral improvement dynamics in matroid games pure nash equilibria can be reached efficiently in contrast computing even a single coalitional improvement move in matroid and single commodity games is strongly np hard in addition we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics they continue to hold even for convergence to approximate equilibria

time varying linear systems and invariants of system equivalence in the paper we consider time varying systems with coefficients depending mero morphically on time in differential operator representations these systems are described by matrices over a skew polynomial ring with coefficients in the field of real meromorphic functions different kinds of indices controllability minimal geometric and dynamical are introduced and it is proved that they essentially coincide the input module and the formal transfer matrix are defined and used for an algebraic description of time varying systems a characterization of system equivalence is given in these terms and also a complete list of invariants of similarity for time varying state space systems

maximum skew symmetric flows and matchings the maximum integer skew symmetric flow problem msfp generalizes both the maximum flow and maximum matching problems it was introduced by tutte 28 in terms of self conjugate flows in antisymmetrical digraphs he showed that for these objects there are natural analogs of classical theoretical results on usual network flows such as the flow decomposition augmenting path and max flow min cut theorems we give unified and shorter proofs for those theoretical results we then extend to msfp the shortest augmenting path method of edmonds and karp 7 and the blocking flow method of dinits 4 obtaining algorithms with similar time bounds in general case moreover in the cases of unit arc capacities and unit node capacities our blocking skew symmetric flow algorithm has time bounds similar to those established in 8 21 for dinits algorithm in particular this implies an algorithm for finding a maximum matching in a nonbipartite graph in time which matches the time bound for the algorithm of micali and vazirani 25 finally extending a clique compression technique of feder and motwani 9 to particular skew symmetric graphs we speed up the implied maximum matching algorithm to run in time improving the best known bound for dense nonbipartite graphs also other theoretical and algorithmic results on skew symmetric flows and their applications are presented

efficient matrix preconditioners for black box linear algebra abstract the main idea of the black box approach in exact linear algebra is to reduce matrix problems to the computation of minimum polynomials in most cases preconditioning is necessary to obtain the desired result here good preconditioners will be used to ensure geometrical algebraic properties on matrices rather than numerical ones so we do not address a condition number we offer a review of problems for which algebraic preconditioning is used provide a bestiary of preconditioning problems and discuss several preconditioner types to solve these problems we present new conditioners including conditioners to preserve low displacement rank for toeplitz like matrices we also provide new analyses of preconditioner performance and results on the relations among preconditioning problems and with linear algebra problems thus improvements are offered for the efficiency and applicability of preconditioners the focus is on linear algebra problems over finite fields but most results are valid for entries from arbitrary fields

fast matrix rank algorithms and applications we consider the problem of computing the rank of an m n matrix a over a field we present a randomized algorithm to find a set of r rank a linearly independent columns in o vav p r field operations where vav denotes the number of nonzero entries in a and

karhunen loeve decomposition approach to analyzing complex network synchronization in this paper the approach of the karhunen lo ve decomposition known also as the proper orthogonal modes poms is taken to analyze phase synchronization of various complex networks with different topologies namely the classic kuramoto model coupled chaotic maps with gaussian delays and a chain of diffusively coupled bistable oscillators in the case of the kuramoto model the poms reveal the tendency and the level of synchronization with the increase of the coupling strength for globally coupled networks and scale free networks while periodic poms are found in nearest neighbor coupled networks furthermore for cluster networks on the kuramoto model the first leading poms based on different time intervals reveal that different sub groups of nodes synchronize gradually to different levels eventually leading to the complete phase synchronization in the case of coupled chaotic maps some properties of phase synchronization change with the coupling strength value in the case of the chain of diffusively coupled bistable oscillators several main poms not only determine the network phase synchronization but also provide good reconstruction of the network responses

control of chaos due to additional predator in the hastings powell food chain model abstract a three species hastings and powell hp food chain model involving another predator of top prey is proposed and studied the modified food web model is analyzed to obtain the different conditions for which system exhibits stability around the biological feasible equilibrium points the permanence is established and global stability of boundary equilibrium point e x is discussed it is observed through numerical simulations that four dimensional model may show stable dynamics in contrast to chaotic dynamics that occurred in three species food chain varieties of dynamical behaviors in the food web are possible depending upon the sharing of food between the two predators of the top prey the results demonstrate that the additional predator play the crucial role in reducing the complexity in the dynamical behavior of the system

cooperative regenerating codes one of the design objectives in distributed storage system is the minimization of the data traffic during the repair of failed storage nodes by repairing multiple failures simultaneously and cooperatively rather than successively and independently further reduction of repair traffic is made possible a closed form expression of the optimal tradeoff between the repair traffic and the amount of storage in each node for cooperative repair is given we show that the points on the tradeoff curve can be achieved by linear cooperative regenerating codes with an explicit bound on the required finite field size the proof relies on a max flow min cut type theorem from combinatorial optimization for submodular flows two families of explicit constructions are given

refined study on structural controllability of descriptor systems by means of matroids for a dynamical system described in the descriptor form fd bf x dt a bf x b bf u where the coefficients are classified into generic parameters and fixed constants the structural controllability is investigated under a physically reasonable assumption that can be justified by the dimensional analysis a necessary and sufficient condition for the structural controllability is given in matroid theoretic terms the condition can be tested by efficient algorithms for the matroid union intersection problem

a note on polylinking flow networks this is a supplementary note on m x goemans s iwata and r zenklusen s paper that proposes a flow model based on polylinking systems their flow model is a series or tandem connection of polylinking systems we can consider an apparently more general model of a polylinking flow network which consists of an ordinary arc capacitated network endowed with polylinking systems on the vertex set one for each vertex of the network this is a natural apparent generalization of polymatroidal flow model of e l lawler and c u martel and of generalized polymatroidal flow model of r hassin we give a max flow min cut formula for the polylinking network flow problem and discuss some acyclic flow property of polylinking flows

diseased prey predator model with general holling type interactions choice of interaction function is one of the most important parts for modelling a food chain many models have been proposed as a diseased prey predator model with holling type i or type ii or type iii interactions but there is no model with general holling type interactions in this paper we study a diseased prey predator model with general holling type interactions local stability conditions of equilibrium points are derived we obtain the permanence and impermanence conditions of the system the conditions for global stability of the system are also derived the system exhibits limit cycle period 2 higher periodic oscillations and chaotic behaviour for different values of holling parameters one parameter bifurcation analysis is done with respect to general holling parameters and infection rate we utilize the matcont package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied it is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions our results give an idea for constructing a realistic food chain model through proper choice of general holling parameters

dynamic matrix rank we consider maintaining information about the rank of a matrix under changes of the entries for nxn matrices we show an upper bound of o n 1 5 7 5 arithmetic operations and a lower bound of w n arithmetic operations per element change the upper bound is valid when changing up to o n 0 5 7 5 entries in a single column of the matrix we also give an algorithm that maintains the rank using o n 2 arithmetic operations per rank one update these bounds appear to be the first nontrivial bounds for the problem the upper bounds are valid for arbitrary fields whereas the lower bound is valid for algebraically closed fields the upper bound for element updates uses fast rectangular matrix multiplication and the lower bound involves further development of an earlier technique for proving lower bounds for dynamic computation of rational functions