bases axioms and circuits axioms for fuzzifying matroids abstract this paper shows that weighted graphs are examples of fuzzifying matroids axioms of bases and that of circuits are established for fuzzifying matroids

closure axioms for a class of fuzzy matroids and co towers of matroids this paper represents an attempt to define a closure operator which can determine geotschel and voxman fuzzy matroid gv fuzzy matroid for short and presents an application of the notion co tower in gv fuzzy matroids two bijections are obtained for a given finite set x one is from a x email protected 0 1 x x d is a closed singular gv fuzzy matroid or a closed proper single gv fuzzy matroid to b x the set of all triples of operators on x satisfying some fuzzy closure axioms the other is from fm x the set of all systems of gv independent fuzzy sets on x to m c x the set of all co tower structures on x the first bijection shows that a triple of operators on x satisfying some fuzzy closure axioms can determine a closed singular gv fuzzy matroid or a closed proper single gv fuzzy matroid and the second shows that a co tower structure on x can determine a gv fuzzy matroid as a result it is proved that the category fm of all gv fuzzy matroids and continuous mappings is isomorphic to the category m c of all co towers in m the category of all matroids and continuous mappings and continuous mappings

impulsive stabilization and impulsive synchronization of discrete time delayed neural networks this paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete time delayed neural networks ddnns two types of ddnns with stabilizing impulses are studied by introducing the time varying lyapunov functional to capture the dynamical characteristics of discrete time impulsive delayed neural networks didnns and by using a convex combination technique new exponential stability criteria are derived in terms of linear matrix inequalities the stability criteria for didnns are independent of the size of time delay but rely on the lengths of impulsive intervals with the newly obtained stability results sufficient conditions on the existence of linear state feedback impulsive controllers are derived moreover a novel impulsive synchronization scheme for two identical ddnns is proposed the novel impulsive synchronization scheme allows synchronizing two identical ddnns with unknown delays simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of ddnns finally an application of the obtained impulsive synchronization result for two identical chaotic ddnns to a secure communication scheme is presented

impulsive multisynchronization of coupled multistable neural networks with time varying delay this paper studies the synchronization problem of coupled delayed multistable neural networks nns with directed topology to begin with several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points then two new concepts named dynamical multisynchronization dms and static multisynchronization sms are introduced to describe the two novel kinds of synchronization manifolds using the impulsive control strategy and the razumikhin type technique some sufficient conditions for both the dms and the sms of the controlled coupled delayed multistable nns with fixed and switching topologies are derived respectively simulation examples are presented to illustrate the effectiveness of the proposed results

axioms for bases of closed regular fuzzy matroids this paper represents an attempt to define a set of bases which can determine a closed regular fuzzy matroid and to study some properties of section fuzzy matroids elementary section fuzzy matroids and elementary fuzzy matroids axioms for bases of both elementary fuzzy matroids and closed regular fuzzy matroids are presented respectively it is proved that the set of bases of all closed regular fuzzy matroids on a set equipped with a suitable order is order isomorphic to the set of systems of independent sets of all closed regular fuzzy matroids on this set equipped with the inclusion order

synchronization and desynchronization in a network of locally coupled wilson cowan oscillators a network of wilson cowan wc oscillators is constructed and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis the network is a 2d matrix where each oscillator is coupled only to its neighbors we show analytically that a chain of locally coupled oscillators the piecewise linear approximation to the wc oscillator synchronizes and we present a technique to rapidly entrain finite numbers of oscillators the coupling strengths change on a fast time scale based on a hebbian rule a global separator is introduced which receives input from and sends feedback to each oscillator in the matrix the global separator is used to desynchronize different oscillator groups unlike many other models the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding gestalt principles of feature grouping the ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure ground segregation based on oscillatory correlation

gradient flow methods for matrix completion with prescribed eigenvalues matrix completion with prescribed eigenvalues is a special type of inverse eigenvalue problem the goal is to construct a matrix subject to both the structural constraint of prescribed entries and the spectral constraint of prescribed spectrum the challenge of such a completion problem lies in the intertwining of the cardinality and the location of the prescribed entries so that the inverse problem is solvable an intriguing question is whether matrices can have arbitrary entries at arbitrary locations with arbitrary eigenvalues and how to complete such a matrix constructive proofs exist to a certain point and those proofs such as the classical schur horn theorem are amazingly elegant enough in their own right beyond which very few theories or numerical algorithms are available in this paper the completion problem is recast as one of minimizing the distance between the isospectral matrices with the prescribed eigenvalues and the affined matrices with the prescribed entries the gradient flow is proposed as a numerical means to tackle the construction this approach is general enough that it can be used to explore the existence question when the prescribed entries are at arbitrary locations with arbitrary cardinalities

a nordhaus gaddum conjecture for the minimum number of distinct eigenvalues of a graph abstract we propose a nordhaus gaddum conjecture for q g the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph g for every graph g excluding four exceptions we conjecture that q g q g c g 2 where g c is the complement of g we compute q g c for all trees and all graphs g with q g g 1 and hence we verify the conjecture for trees unicyclic graphs graphs with q g 4 and for graphs with g 7

bases of fuzzy matroids in this paper we continue our study of fuzzy matroids we define the notion of a basis for a fuzzy matroid and investigate which properties of crisp matroid bases carry over to the fuzzy case

robust neural network tracking controller using simultaneous perturbation stochastic approximation this paper considers the design of robust neural network tracking controllers for nonlinear systems the neural network is used in the closed loop system to estimate the nonlinear system function we introduce the conic sector theory to establish a robust neural control system with guaranteed boundedness for both the input output i o signals and the weights of the neural network the neural network is trained by the simultaneous perturbation stochastic approximation spsa method instead of the standard backpropagation bp algorithm the proposed neural control system guarantees closed loop stability of the estimation system and a good tracking performance the performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts fast convergence and robustness against system disturbance

the set of fuzzy rational numbers and flexible querying a fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership this notion can be viewed as a generalization of the concepts of set fuzzy set and bag the set of fuzzy integers n f provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed in the field of databases the use of fuzzy bags is motivated by their ability to manage both quantities and preferences however n f becomes too restricted a framework when dealing with queries based on difference or division operations so a more general structure based on the set of fuzzy relative integers z f in which exact differences can be performed has been first developed in this paper we carry on with this approach and we extend z f to the set of fuzzy rational numbers q f this context leads to define a closed system of multiplicative operations and allows to perform exact divisions applied to flexible querying of databases q f and the notion of division on fuzzy numbers allow to generalize the relational division they define a sound basis for queries involving ratios between quantities

unified approach fuzzy graph problems we present a taxonomy of fuzzy graphs that treats fuzziness in vertex existence edge existence edge connectivity and edge weight within that framework we formulate some standard graph theoretic problems shortest paths and minimum cut for fuzzy graphs using a unified approach distinguished by its uniform application of guiding principles such as the construction of membership grades via the ranking of fuzzy numbers the preservation of membership grade normalization and the collapsing of fuzzy sets of graphs into fuzzy graphs finally we provide algorithmic solutions to these problems with examples

average contraction and synchronization of complex switched networks this paper introduces an average contraction analysis for nonlinear switched systems and applies it to investigating the synchronization of complex networks of coupled systems with switching topology for a general nonlinear system with a time dependent switching law a basic convergence result is presented according to average contraction analysis and a special case where trajectories of a distributed switched system converge to a linear subspace is then investigated synchronization is viewed as the special case with all trajectories approaching the synchronization manifold and is thus studied for complex networks of coupled oscillators with switching topology it is shown that the synchronization of a complex switched network can be evaluated by the dynamics of an isolated node the coupling strength and the time average of the smallest eigenvalue associated with the laplacians of switching topology and the coupling fashion finally numerical simulations illustrate the effectiveness of the proposed methods

a new approach for fuzzy topology ii abstract we point out a new approach for fuzzy topology with fuzzy logic and discuss the neighborhood structure of a point and the convergence of nets and filters in this new framework

a characterization of trace zero nonnegative 5 5 matrices let 1 2 3 4 5 be a list of complex numbers with 1 2 3 4 5 0 necessary and sufficient conditions for the existence of an entry wise nonnegative 5 5 matrix a with spectrum are presented

fuzzy bases of fuzzy independent set systems abstract compactness closeness and sc are conditions to ensure the existence of fuzzy bases for polymatroids g v fuzzy matroids and h fuzzy matroids respectively in this work relations of these three conditions with different fuzzy independent systems are studied furthermore the equivalence of compactness closeness and sc for g v fuzzy matroids is proved and the existence of fuzzy bases of h fuzzy matroids is verified finally it has been pointed out that h fuzzy matroids and e fuzzy matroids induced from polymatroids are the same and the question whether an h fuzzy matroid is a fuzzy pre matroid is solved

on fuzzification of matroids in this paper we propose one possible fuzzification of matroids which entends the independence axioms of matroids from set systems to fuzzy set systemsand preserves most basic properties of matroids by representing a fuzzy subset of a finite set e as a subset of e 0 1 we obtain fuzzy matroids by fuzzifying independence spaces on e 0 1 alternatively by representing fuzzy subsets of e as functions from e into 0 1 we can obtain fuzzy matroids from polymatroids associated with real rank functions we also investigate the duality for fuzzy matroids

synchronization analysis in an array of asymmetric neural networks with time varying delays and nonlinear coupling in this paper the global exponential synchronization is investigated for an array of asymmetric neural networks with time varying delays and nonlinear coupling assuming neither the differentiability for time varying delays nor the symmetry for the inner coupling matrices by employing a new lyapunov krasovskii functional applying the theory of kronecker product of matrices and the technique of linear matrix inequality lmi a delay dependent sufficient condition in lmis form for checking global exponential synchronization is obtained the proposed result generalizes and improves the earlier publications an example with chaotic nodes is given to show the effectiveness of the obtained result

on goetschel and voxman fuzzy matroids abstract the concepts of fuzzy pre matroid and hereditary fuzzy pre matroid are introduced and investigated the property to be perfect for hereditary fuzzy pre matroids is also considered it is shown that goetschel and voxman fuzzy matroids coincide with perfect hereditary fuzzy pre matroids it is also shown that goetschel and voxman fuzzy matroids can be described via three fuzzy axioms two of which are direct fuzzy counter parts of the crisp matroid axioms in terms of elementary fuzzy sets and the third one is a decomposition axiom also in terms of elementary fuzzy sets

some properties of m fuzzifying convexities induced by m orders abstract in this paper the notions of geometric interval spaces convex geometries and base point orders in the theory of convexity spaces are generalized to m fuzzifying convexity spaces using m fuzzifying restricted hull operators the m fuzzifying convexity spaces induced by m orders are defined conveniently then it is shown that m fuzzifying convexity spaces induced by m orders are m fuzzifying jhc and arity 2 and if the m order is strongly anti symmetric then the m fuzzifying convexity space is an m fuzzifying convex geometry and its segment operator is an m fuzzifying geometric interval operator

a comment on bases of fuzzy matroids fuzzy sets and systems 31 1989 253 261 abstract in this comment two assertions concerning a regular pair of crisp matroids are presented in order to clarify an important step of the proof of lemma 2 5 of the paper by goetschel and voxman one of these assertions provides an independent proof of lemma 2 4 of the paper by goetschel and voxman as well

the maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph abstract in this paper we introduce a parameter mm g defined as the maximum over the minimal multiplicities of eigenvalues among all symmetric matrices corresponding to a graph g we develop basic properties of mm g and compute it for several families of graphs

on the polytope of non additive measures in this paper we deal with the problem of studying the structure of the polytope of non additive measures for finite referential sets we give a necessary and sufficient condition for two extreme points of this polytope to be adjacent we also show that it is possible to find out in polynomial time whether two vertices are adjacent these results can be extended to the polytope given by the convex hull of monotone boolean functions we also give some results about the facets and edges of the polytope of non additive measures we prove that the diameter of the polytope is 3 for referentials of three elements or more finally we show that the polytope is combinatorial and study the corresponding properties more concretely we show that the graph of non additive measures is hamilton connected if the cardinality of the referential set is not 2

graphs that allow all the eigenvalue multiplicities to be even abstract let g be an undirected graph on n vertices and let s g be the set of all n n real symmetric matrices whose nonzero off diagonal entries occur in exactly the positions corresponding to the edges of g the inverse eigenvalue problem for a graph g is a problem of determining all possible lists that can occur as the lists of eigenvalues of matrices in s g this question is in general hard to answer and several variations were studied most notably the minimum rank problem in this paper we introduce the problem of determining for which graphs g there exists a matrix in s g whose characteristic polynomial is a square i e the multiplicities of all its eigenvalues are even we solve this question for several families of graphs

matrix completion problems over integral domains the case with a diagonal of prescribed blocks abstract let r be an arbitrary integral domain let 1 n be a multiset of elements of r let be a permutation of 1 k let n 1 n k be positive integers such that n 1 n k n and for r 1 k let a r r n r n r we are interested in the problem of finding a block matrix q q rs r s 1 k r n n with spectrum and such that q r r a r for r 1 k cravo and silva completely characterized the existence of such a matrix when r is a field in this work we construct a solution matrix q that solves the problem when r is an integral domain with two exceptions i k 2 ii k 3 r r and n r n 2 for some r what makes this work quite unique in this area is that we consider the problem over the more general algebraic structure of integral domains which includes the important case of integers furthermore we provide an explicit and easy to implement finite step algorithm that constructs an specific solution matrix we point out that cravo and silva s proof is not constructive

a matrix completion problem over integral domains the case with 2n 3 prescribed entries abstract let 1 n n 2 be a given multiset of elements in an integral domain r and let p be a matrix of order n with at most 2 n 3 prescribed entries that belong to r under the assumption that each row each column and the diagonal of p have at least one unprescribed entry we prove that p can be completed over r to obtain a matrix a with spectrum we describe an algorithm to construct a this result is an extension to integral domains of a classical completion result by herskowitz for fields

fuzzy rank functions abstract in this paper we obtain a characterization of fuzzy matroids in terms of the fuzzy rank function defined in 1 this characterization parallels to some extent a well known characterization theorem for crisp matroids

fuzzy matroid structures abstract this paper is a continuation of our study of fuzzy matroids we examine the fuzzy counterparts of matroid sums dual and products

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

on nonnegative matrices with prescribed eigenvalues and diagonal entries abstract we consider the problem of the existence and construction of nonnegative matrices with prescribed spectrum and diagonal entries necessary and sufficient conditions have been obtained for n 3 by perfect and fiedler in the cases nonnegative and nonnegative symmetric respectively for n 4 they obtained sufficient conditions many partial results about the problem have been published by several authors mainly by smigoc this is a long standing unsolved inverse problem but also necessary to apply a perturbation result due to r rado which has played an important role in the study of nonnegative inverse eigenvalue and inverse elementary divisors problems distinct versions of rado s result have been also obtained for certain structured matrices to apply rado s result and its different versions we need to guarantee the existence of an r r r n nonnegative structured matrix with prescribed spectrum and diagonal entries this is an important motivation for this work here we prove new sufficient conditions for n 4 which extend and strictly contain the perfect and fiedler conditions our results generate an algorithmic procedure to construct a solution matrix

realizability criterion for the symmetric nonnegative inverse eigenvalue problem abstract let 1 2 n a set of real numbers the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix if there exists a nonnegative matrix a with spectrum we say that is realized by a many realizability criteria for the existence of such a matrix a are known this paper shows that a realizability criterion given by the author which contains both kellogg s realizability criterion and borobia s realizability criterion is sufficient for the existence of an n n symmetric nonnegative matrix with prescribed spectrum

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

categories of bi fuzzy pre matroids in this paper the concept of l m fuzzy weak mappings is introduced as a generalization of weak mappings matroids and weak mappings form a category which is denoted by m fuzzifying matroids and fuzzifying weak mappings form a category which is denoted by fym 0 1 pre matroids and 0 1 weak mappings form a category which is denoted by im bi fuzzy pre matroids and bi fuzzy weak mappings form a category which is denoted by iifm we study the relations among m fym im and iifm

realizable lists via the spectra of structured matrices abstract a square matrix of order n with n 2 is called a permutative matrix or permutative when all its rows up to the first one are permutations of precisely its first row in this paper the spectra of a class of permutative matrices are studied in particular spectral results for matrices partitioned into 2 by 2 symmetric blocks are presented and using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed guo perturbations on given lists are exhibited

some categorical aspects of fuzzy topology research in recent years has revealed that the construct of fuzzy topological spaces behaves quite differently from that of topological spaces with respect to certain categorical properties in this paper we discuss some of these aspects since the topological construct l fts contains nontrivial both initially and finally closed full subconstructs and each such construct gives rise to a natural autonomous theory of fuzzy topology it can be said to some extent that fuzzy topology should consist of a system of closely related topology theories including the classical topology theory as a special case with each applying to one such subconstruct therefore in the first part of this paper the theory of sobriety is established for each finally and initially closed full subconstruct of l fts to illustrate this idea the second topic of this paper is the relationship between the construct of stratified l fuzzy topological spaces and several other familiar constructs in fuzzy topology for example the constructs of sostak fuzzy topological spaces and l fuzzifying topological spaces

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

connectedness of refined goetschel voxman fuzzy matroids this paper studies connectedness of goetschel voxman fuzzy matroids briefly g v fuzzy matroids an analog of connectedness of crisp finite matroids based on the results of fuzzy circuits given by goetschel and voxman the transitivity theorem concerning fuzzy circuits of g v fuzzy matroids is established and thus the useful notion of refined g v fuzzy matroid is introduced the connectedness of refined g v fuzzy matroids is then defined by using an equivalence relation on the set of all fuzzy points on the ground set and some expected properties of these g v fuzzy matroids are presented additionally five kinds of fuzzy matroids are compared

the real nonnegative inverse eigenvalue problem is np hard abstract a list of complex numbers is realizable if it is the spectrum of a nonnegative matrix in 1949 suleimanova posed the nonnegative inverse eigenvalue problem niep the problem of determining which lists of complex numbers are realizable the version for reals of the niep rniep asks for realizable lists of real numbers in the literature there are many sufficient conditions or criteria for lists of real numbers to be realizable we will present an unified account of these criteria then we will see that the decision problem associated to the rniep is np hard and we will study the complexity for the decision problems associated to known criteria

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

on fuzzy independence set systems abstract the concept of fuzzy pre independence set system and that of fuzzy independence set system are introduced and investigated in this paper the properties to be closed to be perfect and to be strongly regular of a fuzzy independence set system are also considered several propositions concerning bases of closed perfect fuzzy independence set systems are presented an important subclass of perfect fuzzy independence set systems are fuzzy matroids introduced by goetschel and voxman fuzzy sets and systems 27 1988 291 31 1989 253

the inverse eigenvalue problem for nonnegative matrices abstract let a be a nonnegative matrix with spectrum 1 2 m and b be a nonnegative matrix with spectrum 1 2 n where 1 is the perron eigenvalue of b furthermore let a maximal diagonal element of a be greater than or equal to 1 in the article we construct a nonnegative matrix c with spectrum 1 2 m 2 n this construction enables us to obtain several results on how to determine new realizable lists from known realizable lists

exponential synchronizationlike criterion for state dependent impulsive dynamical networks this paper focuses on the problem of the exponential synchronizationlike criteria for state dependent impulsive dynamical networks sidns two types of sufficient conditions which are applied to ensure every solution intersecting each impulsive surface exactly once are derived for each type of collision conditions combining with comparison principle and inequality techniques some sufficient conditions are obtained to ensure local exponential synchronizationlike for sidn moreover a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed finally an example is given to demonstrate the effectiveness of our results

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

universal realizability of spectra with two positive eigenvalues abstract a list of eigenvalues is said to be realizable if it is the spectrum of a nonnegative matrix diagonalizably realizable dr if it is the spectrum of a diagonalizable nonnegative matrix and universally realizable ur if there is a nonnegative matrix with this spectrum and any possible jordan canonical form allowed by the spectrum the nonnegative inverse eigenvalue problem niep asks which lists are realizable it is known that there exist spectra that are realizable but not dr we raise the question of whether dr implies ur this is known in a few cases including n 4 nonnegative spectra and suleimanova spectra we add some new classes of spectra that are ur

constructing new realisable lists from old in the niep abstract given a list of complex numbers 1 2 n we say that is realisable if is the spectrum of some entrywise nonnegative matrix the nonnegative inverse eigenvalue problem or niep is the problem of characterising all realisable lists given a realisable list 2 3 m where is the perron eigenvalue and 2 is real we find families of lists 1 2 n for which 1 2 n 3 4 m is realisable in addition given a realisable list i i 4 5 m where is the perron eigenvalue and and are real we find families of lists 1 2 3 4 for which 1 2 3 4 4 5 m is realisable

global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling this paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays a novel coupling scheme is introduced in a general topological structure described by a directed or undirected graph with a linear diffusive term and discontinuous sign term several criteria are derived based on the lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme simulation results for several examples are given to substantiate the effectiveness of the theoretical results

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

nonnegative realization of spectra having negative real parts abstract the nonnegative inverse eigenvalue problem niep is the problem of determining necessary and sufficient conditions for a list of complex numbers to be the spectrum of a nonnegative matrix in this paper the problem is completely solved in the case when all numbers in the given list except for one the perron eigenvalue have real parts smaller than or equal to zero

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

synchronization of complex networks via aperiodically intermittent pinning control in this note synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller nodes dynamical behaviors in the network are described by continuous time ordinary differential equations some sufficient conditions to guarantee global synchronization are presented furthermore an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously finally numerical simulations are given to demonstrate the correctness of obtained results

l m fuzzy matroids in this paper an extension of matroids is introduced in lattice valued fuzzy set theory such a generalized matroid is a pair made of a finite set and a fuzzy subfamily of its lattice valued fuzzy subsets satisfying three axioms it uses two lattices one for membership grades of elements to fuzzy sets and another for membership degrees of fuzzy sets in a fuzzy family of fuzzy sets it is a logical generalization of the notions of matroids and fuzzifying matroids in our definition of generalized fuzzy matroids each l fuzzy subset can be regarded to be independent of other ones to some degree the relevance of generalized fuzzy matroids is shown in the setting of fuzzy vector spaces and fuzzy graphs

global mu synchronization of linearly coupled unbounded time varying delayed neural networks with unbounded delayed coupling in this brief we study the global synchronization of linearly coupled neural networks with delayed couplings where the intrinsic systems are recurrently connected neural networks with unbounded time varying delays and the couplings include instant couplings and unbounded delayed couplings the concept of mu synchronization is introduced some sufficient conditions are derived for the global mu synchronization for the underlined coupled systems

l fuzzy numbers and their properties in this paper the notions of l fuzzy convex sets and l fuzzy numbers are introduced where l is a completely distributive lattice the notions of 0 1 fuzzy convex sets and 0 1 fuzzy numbers are generalized furthermore their properties and characterizations are presented in terms of cut sets of l fuzzy sets

rough sets and matroids from a lattice theoretic viewpoint this paper studies rough sets via matroidal approaches from a lattice theoretic viewpoint we firstly give a new interpretation of definable sets of pawlak rough set model i e the set of definable sets defines uniquely a matroid in which it is the family of open and closed sets then we induce two equivalence relations on a given universe based on a matroid defined on this universe one of the equivalence relations actually is defined on the set of all atoms of a geometric lattice corresponding to the matroid another is based on the transitivity of circuits properties of these two equivalence relations are then studied besides we also investigate the connections between relation based rough sets and matroids finally we point out that a geometric lattice can induce a series of coverings of a universe on which the corresponding matroid is defined and further relations of approximations based on the induced coverings are studied

adjacency on the order polytope with applications to the theory of fuzzy measures in this paper we study the adjacency structure of the order polytope of a poset for a given poset we determine whether two vertices in the corresponding order polytope are adjacent this is done through filters in the original poset we also prove that checking adjacency between two vertices can be done in quadratic time on the number of elements of the poset as particular cases of order polytopes we recover the adjacency structure of the set of fuzzy measures and obtain it for the set of p symmetric measures for a given indifference partition moreover we show that the set of p symmetric measures can be seen as the order polytope of a quotient set of the poset leading to fuzzy measures from this property we obtain the diameter of the set of p symmetric measures finally considering the set of p symmetric measures as the order polytope of a direct product of chains we obtain some other properties of these measures as bounds on the volume and the number of vertices on certain cases

a new approach to the fuzzification of matroids in this paper the concept of closed fuzzy pre matroids is generalized to l fuzzy set theory when l is a complete lattice it is also called an l fuzzifying matroid in the definition of l fuzzifying matroids each subset can be regarded as an independent set to some degree when l is completely distributive an l fuzzifying matroid can be characterized by means of its l fuzzifying rank function an l fuzzifying matroid and its l fuzzifying rank function are one to one corresponding

on the inverse eigenvalue problem for nonnegative matrices of order two to five abstract in this paper for a given set of numbers with special conditions we construct a nonnegative matrix such that the given set is its spectrum

spanning properties for fuzzy matroids abstract in this paper we investigate the fuzzy analogs of some well known properties of the span of subsets of crisp matroids

nonnegative realizability with jordan structure abstract a general method is given for merging blocks in the jordan canonical form of a nonnegative matrix as a consequence results more general than any prior ones are given for the universal realizability of spectra that is spectra which are realizable by a nonnegative matrix for each possible jordan canonical form allowed by the spectrum in particular we generalize a classical result due to minc regarding positive diagonalizable matrices for example any spectrum that is diagonalizably realizable by a nonnegative matrix with mostly positive off diagonal entries is universally realizable

three way decision on two universes abstract rough set models on two universes are important generalizations of pawlak s classical model in most of the two universe models the upper and lower approximations are constructed based on inclusion relation we generalize inclusion relation to the general evaluation function and define the models of three way decision on two universes as an important class of evaluation functions subsethood measures are considered we compare our models with other five existing two universe models in rough set theory and point out that the model of three way decision on two universe unifies the five two universe models besides properties of the two universe model of three way decision are also given more importantly we propose an approach to computing the pair of thresholds and our approach is based on the maximum value of the accuracy measure with respect to tri partitions of a universe induced by all thresholds

on combinatorial optimization problems on matroids with uncertain weights in this paper the combinatorial optimization problem on weighted matroid is considered it is assumed that the weights in the problem are ill known and they are modeled as fuzzy intervals the optimality of solutions and the optimality of elements are characterized this characterization is performed in the setting of possibility theory a method of choosing a solution under uncertainty is also proposed

characterizations of l convex spaces via domain theory abstract we provide some new characterizations of l convex spaces by using the way below relation in domain theory for this purpose we first study the notion of domain finiteness in the lattice valued case and then introduce three kinds of spaces algebraic l closure spaces restricted l hull spaces and l entailment spaces these three spaces are shown to be categorically isomorphic to l convex spaces additionally we introduce the notion of l polytopes and prove that a subcollection of a dense l convex structure is a base if and only if it contains all l polytopes these results indicate that in the study of the theory of fuzzy convex spaces fuzzy domain theory has important applications

fuzzy matroid sums and a greedy algorithm abstract in this paper we establish a necessary and sufficient condition for a greedy algorithm to find a maximal basis for a fuzzy matroid

block matrices and guo s index for block circulant matrices with circulant blocks abstract in this paper we deal with circulant and partitioned into n by n circulant blocks matrices and introduce spectral results concerning this class of matrices the problem of finding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix the guo s index 0 of a realizable list is the minimum spectral radius such that the list up to the initial spectral radius together with 0 is realizable the guo s index of block circulant matrices with circulant blocks is obtained and in consequence necessary and sufficient conditions concerning the niep nonnegative inverse eigenvalue problem for the realizability of some spectra are given

synchronization in complex networks with stochastically switching coupling structures synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed a novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed some sufficient condition for a network with general time varying coupling structure to reach complete synchronization is provided based on the general theorem networks with stochastically switching coupling structures is investigated in particular two kinds of stochastic switching coupling networks are addressed a independent and identically distributed switching processes and b markov jump processes in both cases some sufficient condition for almost sure synchronization of the networks is given also numerical simulations are provided to illustrate the theoretical results

global synchronization of multiple recurrent neural networks with time delays via impulsive interactions in this paper new results on the global synchronization of multiple recurrent neural networks nns with time delays via impulsive interactions are presented impulsive interaction means that a number of nns communicate with each other at impulse instants only while they are independent at the remaining time the communication topology among nns is not required to be always connected and can switch on and off at different impulse instants by using the concept of sequential connectivity and the properties of stochastic matrices a set of sufficient conditions depending on time delays is derived to ascertain global synchronization of multiple continuous time recurrent nns in addition a counterpart on the global synchronization of multiple discrete time nns is also discussed finally two examples are presented to illustrate the results

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

some methods for evaluating the optimality of elements in matroids with ill known weights in this paper a class of matroidal combinatorial optimization problems with imprecise weights of elements is considered the imprecise weights are modeled by intervals and fuzzy intervals the concepts of possible and necessary optimality under imprecision are recalled some efficient methods for evaluating the possible and necessary optimality of elements in the interval valued problems are proposed some efficient algorithms for computing the exact degrees of possible and necessary optimality of elements in the fuzzy valued problems are designed

coordination of multiagents interacting under independent position and velocity topologies we consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs different algorithms are proposed and analyzed for different settings including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies as well as the case with a group velocity reference signal under switching velocity interaction it is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory matrix analysis as well as the lyapunov stability theory

fuzzy graphs in the evaluation and optimization of networks abstract referring to some predecessing models the paper introduces the concept of fuzzy vertex graphs a way is shown for modeling various quantitatively featurable functional capabilities of computer communication and similar networks it is shown that functional capability of distributed hierarchical multicomponent systems networks can be described by the directed rooted tree model according to the above fuzzy graph idea the problem of optimizing the overall functional capability with given component vertex set is introduced the fuzzy formulae based on the algebraic connectives which are to be optimized are constructed in the main part of the paper a series of results are presented concerning some special however important cases also the hypotheses founded on some computer experiments are formulated finally the application of these results and hypotheses are shown by the example of a distributed communication switching system family being in development in hungary

on universal realizability of spectra abstract a list 1 2 n of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix the list is said to be universally realizable ur if it is the spectrum of a nonnegative matrix for each possible jordan canonical form allowed by it is well known that an n n nonnegative matrix a is co spectral to a nonnegative matrix b with constant row sums in this paper we extend the co spectrality between a and b to a similarity between a and b when the perron eigenvalue is simple we also show that if 0 and 1 2 n is ur then 1 2 n is also ur we give counter examples for the cases 1 2 n is ur implies 1 2 3 n is ur and 1 2 are ur implies 1 2 is ur

consensus analysis of multiagent networks via aggregated and pinning approaches in this paper the consensus problem of multiagent nonlinear directed networks mndns is discussed in the case that a mndn does not have a spanning tree to reach the consensus of all nodes by using the lie algebra theory a linear node and node pinning method is proposed to achieve a consensus of a mndn for all nonlinear functions satisfying a given set of conditions based on some optimal algorithms large size networks are aggregated to small size ones then by applying the principle minor theory to the small size networks a sufficient condition is given to reduce the number of controlled nodes finally simulation results are given to illustrate the effectiveness of the developed criteria

nonsingular aci matrices over integral domains abstract an aci matrix is a matrix whose entries are polynomials of degree at most one in a number of indeterminates where no indeterminate appears in two different columns consider the next two problems a characterize the aci matrices of order n all of whose completions have the same nonzero constant determinant b characterize the aci matrices of order n all of whose completions are nonsingular in 2010 brualdi huang and zhan solved both problems for fields of at least n 1 elements we extend their result on problem a to integral domains and extend their result on problem b to arbitrary fields

identifying the topology of a coupled fitzhugh nagumo neurobiological network via a pinning mechanism topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology different from recent similar works in which the evolution of all the nodes in a complex network need to be received this brief presents a novel criterion to identify the topology of a coupled fitzhugh nagumo fhn neurobiological network by receiving the membrane potentials of only a fraction of the neurons meanwhile although incomplete information is received the evolution of all the neurons including membrane potentials and recovery variables are traced based on schur complement and lyapunov stability theory the exact weight configuration matrix can be estimated by a simple adaptive feedback control the effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies

spectra of principal submatrices of nonnegative matrices abstract let a be an n n nonnegative matrix with the spectrum 1 2 n and let a 1 be an m m principal submatrix of a with the spectrum 1 2 m in this paper we present some cases where the realizability of 1 2 m 1 2 s implies the realizability of 1 2 n 1 2 s and consider the question whether this holds in general in particular we show that the list 1 2 n 1 2 m is realizable

exponential stabilization of memristive neural networks with time delays in this paper a general class of memristive neural networks with time delays is formulated and studied some sufficient conditions in terms of linear matrix inequalities are obtained in order to achieve exponential stabilization the result can be applied to the closed loop control of memristive systems in particular several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks in addition a simplified and effective algorithm is considered for design of the optimal controller these conditions are the improvement and extension of the existing results in the literature two numerical examples are given to illustrate the theoretical results via computer simulations

contraction analysis of time delayed communications and group cooperation we study stability of interacting nonlinear systems with time delayed communications using contraction theory and a simplified wave variable design inspired by robotic teleoperation we show that contraction is preserved through specific time delayed feedback communications and that this property is independent of the values of the delays the approach is then applied to group cooperation with linear protocols where it is shown that synchronization can be made robust to arbitrary time delays

applications of a brauer theorem in the nonnegative inverse eigenvalue problem abstract a result by brauer which shows how to modify one single eigenvalue of a matrix without changing any of the remaining eigenvalues plays a relevant role in the study of the nonnegative inverse eigenvalue problem niep perfect in a long time ignored paper 1955 presents an extension of this result which shows how to modify r eigenvalues of a matrix of order n r n via a rank r perturbation without changing any of the n r remaining eigenvalues by using this extension perfect gives a realizability criterion for the real niep which is not contained in soto s realizability criterion in this work by extending perfect s result we give a new realizability criterion for the real niep which contains soto s criterion thus this new realizability criterion appears to be the most general sufficient condition for the real niep so far we also contribute to the solution of the symmetric niep for n 5