distance dissimilarity index and network community structure we address the question of finding the community structure of a complex network in an earlier effort h zhou phys rev e 67 041908 2003 the concept of network random walking is introduced and a distance measure defined here we calculate based on this distance measure the dissimilarity index between nearest neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized each community is characterized by an upper and a lower dissimilarity threshold the algorithm is applied to several artificial and real world networks and excellent results are obtained in the case of artificially generated random modular networks this method outperforms the algorithm based on the concept of edge betweenness centrality for yeast s protein protein interaction network we are able to identify many clusters that have well defined biological functions

evolutionary dynamics of spatial games abstract a lattice model of coevolution of strategies for two person 2 2 matrix games is introduced the model allows evolution in an unbounded space of strategies in particular we explore the region of parameter space corresponding to the prisoner s dilemma and classify the types of dynamical and evolutionary behavior that appear for certain restricted strategy spaces we explore the complete space of lattice games

a splitting theorem for holomorphic banach bundles this paper is motivated by grothendieck s splitting theorem in the 1960s gohberg generalized this to a class of banach bundles we consider a compact complex manifold x and a holomorphic banach bundle e x that is a compact perturbation of a trivial bundle in a sense recently introduced by lempert we prove that e splits into the sum of a finite rank bundle and a trivial bundle provided h 1 x mathcal o 0

characterization of the hilbert ball by its automorphism group let be a bounded convex domain in a separable hilbert space the authors prove a version of the theorem of bun wong which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary point then it is biholomorphic to the ball key ingredients in the proof are a new localization argument using holomorphic peaking functions and the use of new normal families arguments in the construction of the limit biholomorphism

overlapping modularity at the critical point of k clique percolation one of the most remarkable social phenomena is the formation of communities in social networks corresponding to families friendship circles work teams etc since people usually belong to several different communities at the same time the induced overlaps result in an extremely complicated web of the communities themselves thus uncovering the intricate community structure of social networks is a non trivial task with great potential for practical applications gaining a notable interest in the recent years the clique percolation method cpm is one of the earliest overlapping community finding methods which was already used in the analysis of several different social networks in this approach the communities correspond to k clique percolation clusters and the general heuristic for setting the parameters of the method is to tune the system just below the critical point of k clique percolation however this rule is based on simple physical principles and its validity was never subject to quantitative analysis here we examine the quality of the partitioning in the vicinity of the critical point using recently introduced overlapping modularity measures according to our results on real social and other networks the overlapping modularities show a maximum close to the critical point justifying the original criteria for the optimal parameter settings

inverses depending holomorphically on a parameter in a banach space abstract we show that the existence of a right inverse at each point for a holomorphic mapping from a pseudo convex domain in a banach space with an unconditional basis into a unital banach algebra implies the existence of a holomorphic right inverse variations of this result are given

clique percolation in random networks the notion of k clique percolation in random graphs is introduced where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated for the erdos renyi graph of n vertices we obtain that the percolation transition of k cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p c k k 1 n 1 k 1 at the transition point the scaling of the giant component with n is highly nontrivial and depends on k we discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks

clique percolation in random graphs as a generation of the classical percolation clique percolation focuses on the connection of cliques in a graph where the connection of two k cliques means that they share at least l 1 makes a step function like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l 1 more interesting our analysis shows that at the critical point the order parameter c for l 1 is neither 0 nor 1 but a constant depending on k and l all these theoretical findings are in agreement with the simulation results which give theoretical support and clarification for previous simulation studies of clique percolation

a dolbeault isomorphism theorem in infinite dimensions for a large class of separable banach spaces we prove the real analytic dolbeault isomorphism theorem for open subsets

evolutionary prisoner s dilemma game on hierarchical lattices an evolutionary prisoner s dilemma pd game is studied with players located on a hierarchical structure of layered square lattices the players can follow two strategies d defector and c cooperator and their income comes from pd games with the neighbors the adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference monte carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels q and by the temptation to defect according to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low q 4 for larger q however the highest frequency of cooperators occurs in the middle layers the four level hierarchical structure provides the highest average total income for the whole community

the critical point of k clique percolation in the erdős renyi graph motivated by the success of a k clique percolation method for the identification of overlapping communities in large real networks here we study the k clique percolation problem in the erd s renyi graph when the probability p of two nodes being connected is above a certain threshold pc k the complete subgraphs of size k the k cliques are organized into a giant cluster by making some assumptions that are expected to be valid below the threshold we determine the average size of the k clique percolation clusters using a generating function formalism from the divergence of this average size we then derive an analytic expression for the critical linking probability pc k

triangle percolation in mean field random graphs with pde we apply a pde based method to deduce the critical time and the size of the giant component of the triangle percolation on the erd s renyi random graph process investigated by derenyi palla and vicsek in phys rev lett 94 160202 2005 j stat phys 128 219 227 2007

phase diagrams for an evolutionary prisoner s dilemma game on two dimensional lattices the effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner s dilemma game with players located on the sites of different two dimensional lattices this system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive using monte carlo simulations and the generalized mean field approximations we have determined the phase boundaries critical points separating the two phases on the plane of the temperature noise and temptation to choose defection in the zero temperature limit the cooperation can be sustained only for those connectivity structures where three site clique percolation occurs

cohomological characterization of pseudoconvexity in a banach space let x be a banach space with a countable unconditional basis e g x l2 x open we show that is pseudoconvex if and only if for each affine complex line l in x the sheaf cohomology group h 1 i vanishes where i is the ideal sheaf of all holomorphic functions on that vanish on l we also give an example that the condition h q 0 for all q 1 unlike in finite dimensions does not imply the pseudoconvexity of lastly we prove an interpolation result

linear relations and the kronecker canonical form abstract we show that the kronecker canonical form which is a canonical decomposition for pairs of matrices is the representation of a linear relation in a finite dimensional space this provides a new geometric view upon the kronecker canonical form each of the four entries of the kronecker canonical form has a natural meaning for the linear relation which it represents these four entries represent the jordan chains at finite eigenvalues the jordan chains at infinity the so called singular chains and the multi shift part or to state it more concisely for linear relations the kronecker canonical form is the analogue of the jordan canonical form for matrices

evolutionary prisoner s dilemma game on a square lattice a simplified prisoner s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies to cooperate c or to defect d unconditionally the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference using monte carlo simulations and dynamical cluster techniques we study the density c of cooperators in the stationary state this system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect in the limits stackrel ensuremath rightarrow c 0 and 1 we have observed critical transitions belonging to the universality class of directed percolation

an embedding theorem for pseudoconvex domains in banach spaces we show that a pseudoconvex open subset of a banach space with an unconditional basis is biholomorphic to a closed direct submanifold of a banach space with an unconditional basis

holomorphic mappings on we describe the holomorphic mappings of bounded type and the arbitrary holomorphic mappings from the complex banach space 11 into a complex banach space x it is shown that these mappings have monomial expansions and the growth of the norms of the coefficients is characterized in each case this characterization is used to give new descriptions of the compact open topology and the nachbin ported topology on the space a 11 x of holomorphic mappings and to prove a lifting property for holomorphic mappings on 11 we also show that the monomials form an equicontinuous unconditional schauder basis for the space 11 so of holomorphic functions on 11 with the topology of uniform convergence on compact sets

constant coefficient differential algebraic operators and the kronecker form abstract we consider constant coefficient differential algebraic equations from an operator theoretic point of view we show that the kronecker form allows to determine the nullspace and range of the corresponding differential algebraic operators this yields simple matrix theoretic characterizations of features like closed range and fredholmness

the dolbeault complex in infinite dimensions i infinite dimensional complex analysis was a popular subject in the sixties and seventies but in the last fifteen years enjoyed much less attention oddly enough this very same period began to see the emergence of examples of infinite dimensional complex manifolds in mathematical physics representation theory and geometry thus it appears to be a worthwhile undertaking to revisit infinite dimensional complex analysis and in particular to clarify fundamental properties of infinite dimensional complex manifolds the most fundamental questions at this point seem to be related to the solvability of the inhomogeneous cauchy riemann or 0 equations and more generally to the study of the dolbeault complex as an example in le3 we use a result on the a equation to describe the virasoro group as an infinite dimensional complex manifold up to now precious little has been known about the solvability of the infinite dimensional equation the available results pertain to solving the equation in domains in or over locally convex topological vector spaces and almost exclusively on the level of 0 1 forms postponing the precise definitions to sections 1 2 below we discuss those results that are of immediate relevance to this paper see d2 for more in li ligocka observes that h6rmander s proof of ehrenpreis theorem see e hor can be extended to infinite dimensions to solve the equation

linear differential algebraic equations in spaces of integrable functions on developpe une l 2 theorie pour des equations differentielles algebriques lineaires t x t a t x t b t x t f t t a b x t r m

on the cohomology groups of holomorphic banach bundles we consider a compact complex manifold m and introduce the notion of two holomorphic banach bundles e f over m being compact perturbations of one another given two such bundles we show that if the cohomology groups h q m e are finite dimensional then so are the cohomology groups h q m f as well as a more precise result in the same spirit

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

dynamics of market correlations taxonomy and portfolio analysis the time dependence of the recently introduced minimum spanning tree description of correlations between stocks called the asset tree has been studied in order to reflect the financial market taxonomy the nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix by using the concept of a central vertex chosen as the most strongly connected node of the tree an important characteristic is defined by the mean occupation layer during crashes due to the strong global correlation in the market the tree shrinks topologically and this is shown by a low value of the mean occupation layer the tree seems to have a scale free structure where the scaling exponent of the degree distribution is different for business as usual and crash periods the basic structure of the tree topology is very robust with respect to time we also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic markowitz portfolio are always located on the outer leaves of the tree technical aspects such as the window size dependence of the investigated quantities are also discussed

intensity and coherence of motifs in weighted complex networks the local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network the clustering coefficient reflecting the local configuration of triangles can be seen as a special case of this approach in this paper we generalize this method for weighted networks we introduce subgraph intensity as the geometric mean of its link weights and coherence as the ratio of the geometric to the corresponding arithmetic mean using these measures motif scores and clustering coefficient can be generalized to weighted networks to demonstrate these concepts we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters