clustering of tag induced subgraphs in complex networks abstract we study the behavior of the clustering coefficient in tagged networks the rich variety of tags associated with the nodes in the networks we considered provide additional relevant information about the entities represented by the nodes such specific features can be important for practical applications like searching in the networks here we examine how the clustering coefficient changes when narrowing the network to a subgraph associated with a given tag and how it correlates with various other properties of the subgraph a further question addressed in our paper is how the clustering coefficient of the individual nodes is affected by the tags on the node we argue that this kind of analysis can be useful when one is aimed at a detailed description of the structure of large complex systems

there is an equivalent norm on l1 that has the fixed point property abstract let k 8 k 1 8 k for all k n and let be the equivalent norm of l 1 defined by a n sup k n k n k a n for all x a n l 1 we prove that l 1 has the fixed point property for nonexpansive self mappings

renorming of l1 and the fixed point property abstract for any k n let p k denote the natural projections on l 1 let be an equivalent norm of l 1 that satisfies all of the following four conditions 1 there are 4 and a positive decreasing sequence n in 0 1 such that for any normalized block basis f n of l 1 and x l 1 with p k 1 x x and x k lim sup n f n x 1 x 2 there are two strictly decreasing sequences k and k with lim k k 0 and lim k k 1 such that for any normalized block basis f n of l 1 and x with i p k x x lim inf n f n x 1 k k 1 x 3 for any k n i p k 1 4 the unit ball of l 1 is l 1 c 0 closed in this article we prove that the space l 1 has the fixed point property for the nonexpansive mapping this improves a previous result of the author

near infinity concentrated norms and the fixed point property for nonexpansive maps on closed bounded convex sets abstract in this paper we define the concept of a near infinity concentrated norm on a banach space x with a boundedly complete schauder basis when is such a norm we prove that x has the fixed point property fpp that is every nonexpansive self mapping defined on a closed bounded convex subset has a fixed point in particular p k lin s norm in l 1 14 and the norm p with p p n and lim n p n 1 introduced in 3 are examples of near infinity concentrated norms when p is equivalent to the l 1 norm it was an open problem as to whether l 1 p had the fpp we prove that the norm p always generates a nonreflexive banach space x r p 1 r p 2 r p 3 satisfying the fpp regardless of whether p is equivalent to the l 1 norm we also obtain some stability results

hypergraph topological quantities for tagged social networks recent years have witnessed the emergence of a new class of social networks which require us to move beyond previously employed representations of complex graph structures a notable example is that of the folksonomy an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database in a recent paper we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest in this paper we extend our model by defining additional quantities such as edge distributions vertex similarity and correlations as well as clustering we then empirically measure these quantities on two real life folksonomies the popular online photo sharing site flickr and the bookmarking site citeulike we find that these systems share similar qualitative features with the majority of complex networks that have been previously studied we propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks

topology of correlation based minimal spanning trees in real and model markets we compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the new york stock exchange during a 12 year trading period with the one obtained from surrogated data simulated by using simple market models we find that the empirical tree has features of a complex network that cannot be reproduced even as a first approximation by a random market model and by the widespread one factor model

on super fixed point property and super weak compactness of convex subsets in banach spaces abstract for a nonempty convex set c of a banach space x a self mapping on c is said to a linear respectively affine isometry if it is the restriction of a linear respectively affine isometry defined on the whole space x by means of super weakly compact set theory established in the recent years in this paper we first show that a nonempty closed bounded convex set of a banach space has super fixed point property for affine or equivalently linear isometries if and only if it is super weakly compact and the super fixed point property and the super weak compactness coincide on every closed bounded convex subset of a banach space under equivalent renorming sense with the application of fabian montesinos zizler s renorming theorem we finally show that every strongly super weakly compact generated banach space can be renormed so that every weakly compact convex set has super fixed point property

a generalization of a renorming theorem by lin and a new nonreflexive space with the fixed point property which is nonisomorphic to l1 abstract given 1 p we construct a banach space x p hereditarily asymptotically isometric to l 1 so that for n i m k n it contains an isometric copy of i 1 k 1 m k l p n i 1 and x p contains a subspace isomorphic to c 0 where has cardinality c and use a generalization of a renorming theorem of lin to renorm x p in order to have the fixed point property also we give new renormings with the fpp in some known spaces in particular we prove that c 0 has the fixed point property where x i sup i x i i x i 2 i 0 this gives an example of a space without the fpp whose dual an isomorph of l 1 has the fpp

new families of nonreflexive banach spaces with the fixed point property abstract in this paper we define the concept of sequentially separating norm and we relate it to the fulfillment of the fixed point property for nonexpansive mappings we develop a technique to construct families of nonreflexive banach spaces with the fixed point property different examples will be exhibited we also study the geometry of the banach spaces that can be renormed with a sequentially separating norm

on the structure of the set of equivalent norms on l1 with the fixed point property abstract let a be the set of all equivalent norms on l 1 which satisfy the fpp we prove that a contains rays in fact every renorming in l 1 which verifies condition in theorem 2 1 is the starting point of a closed or open ray composed by equivalent norms on l 1 with the fpp the standard norm 1 or p k lin s norm defined in lin 2008 12 are examples of such norms moreover we study some topological properties of the set a with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to 1

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

technical communique blind identifiability of iir systems it is shown that with no prior information a necessary and sufficient condition for an nth order iir system to be blindly identifiable is that the over sampling ratio p n 1

on banach space properties that are not invariant under the banach mazur distance 1 abstract we consider which properties of banach spaces are not invariant under the banach mazur distance 1 we will say that a given property p is not invariant under the banach mazur distance 1 if there exist two banach spaces x and y such that x has property p y fails property p and the banach mazur distance d x y 1 the main results of this paper concern the case of separable lindenstrauss spaces first in the setting of preduals of l 1 we give some geometric equivalences for polyhedral properties next we show that even in the restricted framework of preduals of l 1 most of the notions of polyhedral banach spaces and their geometric equivalences fail to be invariant under the banach mazur distance 1 then in the general case of banach spaces we indicate some other geometrical properties that are invariant or not invariant under the banach mazur distance 1

distortion and stability of the fixed point property for non expansive mappings abstract let x be a banach space we say that x satisfies the fixed point property weak fixed point property if every non expansive mapping defined from a convex closed bounded convex weakly compact subset of x into itself has a fixed point we say that x satisfies the stable fixed point property stable weak fixed point property if the same is true for every equivalent norm which is close enough to the original one denote by p x the set formed by all equivalent norms with the topology of the uniform convergence on the unit ball of x we prove that the subset of p x formed by the norms failing the fixed point property is dense in p x when x is a non distortable space which fails the fixed point property in particular no renorming of l 1 can satisfy the stable fixed point property furthermore we show some examples of distortable spaces failing the weak fixed point property which can be renormed to satisfy the stable weak fixed point property as a consequence we prove that every separable banach space can be renormed to satisfy the stable weak fixed point property

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

blind identification of multi channel arma models based on second order statistics this correspondence presents a new second order statistical approach to blind identification of single input multiple output simo autoregressive and moving average arma system models the proposed approach exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block toeplitz structure of the channel convolution matrix used by classical subspace methods for the multi channel model with the same autoregressive ar polynomial sufficient conditions and an efficient identification algorithm are given such that the multi channel model can be uniquely identified up to a constant scaling factor furthermore an extension of the result to blind identification of multi channel models with different ar polynomials is presented simulation results are given to show the effectiveness of the proposed approach

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

blind multivariable arma subspace identification in this paper we study the deterministic blind identification of multiple channel state space models having a common unknown input using measured output signals that are perturbed by additive white noise sequences different from traditional blind identification problems the considered system is an autoregressive system rather than an fir system hence the concerned identification problem is more challenging but possibly having a wider scope of application two blind identification methods are presented for multi channel autoregressive systems a cross relation identification method is developed by exploiting the mutual references among different channels it requires at least three channel systems with square and stably invertible transfer matrices moreover a general subspace identification method is developed for which two channel systems are sufficient for the blind identification however it requires the additive noises to have identical variances and the transfer matrices having no transmission zeros finally numerical simulations are carried out to demonstrate the performance of the proposed identification algorithms

alignment and integration of complex networks by hypergraph based spectral clustering complex networks possess a rich multiscale structure reflecting the dynamical and functional organization of the systems they model often there is a need to analyze multiple networks simultaneously to model a system by more than one type of interaction or to go beyond simple pairwise interactions but currently there is a lack of theoretical and computational methods to address these problems here we introduce a framework for clustering and community detection in such systems using hypergraph representations our main result is a generalization of the perron frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs we illustrate our approach with applications for local and global alignment of protein protein interaction networks between multiple species for tripartite community detection in folksonomies and for detecting clusters of overlapping regulatory pathways in directed networks

exploring the random genesis of co occurrence networks using the network random generation models from gustedt 2009 we simulate and analyze several characteristics such as the number of components the degree sequence and the clustering coefficient of the generated networks this is done for a variety of distributions fixed value bernoulli poisson binomial that are used to control the parameters of generation process these parameters are in particular the size of newly appearing sets of objects the number of contexts in which new elements appear initially the number of objects that are shared with parent contexts and the time period inside which a context may serve as a parent context aging the results show that these models allow to fine tune the generation process such that the graphs adopt properties as they can be found in real world graphs