rich club connectivity dominates assortativity and transitivity of complex networks rich club assortativity and clustering coefficients are frequently used measures to estimate topological properties of complex networks here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network which reveals that the rich club connectivity is leveraged throughout the network our study suggests that more attention should be paid to the organization pattern of rich nodes for the structure of a complex system as a whole is determined by the associations between the most influential individuals moreover by manipulating the connectivity pattern in a very small rich club it is sufficient to produce a network with desired assortativity or transitivity conversely our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks such biases can be explained by the connectivities among the richest nodes

local langlands correspondence for mathrm gl _ n and the exterior and symmetric square varepsilon factors let f be a p adic field that is a finite extension of qp for some prime p the local langlands correspondence llc attaches to each continuous n dimensional semisimple representation of w f the weil deligne group for f f an irreducible admissible representation of gln f such that among other things the local l and e factors of pairs are preserved this correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides such as taking the exterior square or symmetric square in this article we show that this is the case for the local arithmetic and analytic symmetric square and exterior square e factors that is that e s 2 e s 2 and e s sym2 e s sym2 the agreement of the l functions also follows by our methods but this was already known by henniart the proof is a robust deformation argument combined with local global techniques which reduces the problem to the stability of the analytic factor s 2 under highly ramified twists when is supercuspidal this last step is achieved by relating the factor to a mellin transform of a partial bessel function attached to the representation and then analyzing the asymptotics of the partial bessel function inspired in part by the theory of shalika germs for bessel integrals the stability for every irreducible admissible representation then follows from those of the corresponding arithmetic factors as a corollary

rigid body considerations for non linear finite element analysis the purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element

on the local langlands conejcture mathrm gl n the cyclic case let f be a locally compact nonarchimedean field and p its residue characteristic let f be a separable algebraic closure of f wf the weil group of f over f e a character of fx of order n and e the corresponding character of wf then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of wf such that e a a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of gl n f verifying odet x 7t this map is shown to be bijective and to preserve e factors for pairs

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

a direct flexibility method we present a direct flexibility method dfm for the solution of finite element equations this method is based on a decomposition of the finite element model into substructures which may reduce to individual elements substructures are preprocessed by the direct stiffness method dsm to generate free free flexibility matrices for floating substructures the interface problem is solved for the interface forces and the solution recovered over substructure interiors the dfm shares with the dsm the advantages of being automatic maintaining locality and sparseness efficiently handling continuum elements and requiring only the availability of element stiffness libraries the new method appears to be advantageous for specific applications these include massively parallel processing inverse problems treatment of rigid members and inclusions and use of underintegrated elements without spurious mode stabilization

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

de rham factors we construct a theory of de rham epsilon factors given a smooth projective variety x over a field of characteristic 0 and a open image in new window module open image in new window we may consider the determinant of de rham cohomology open image in new window as a graded super line let s be the singular support of open image in new window u an open in x y x u and a 1 form on u x such that u s then we show the existence of a canonically defined graded super line open image in new window canonically isomorphic to open image in new window the key property is the local nature of the epsilon factor it only depends on the restriction of open image in new window and to any open neighborhood of y restricting to the case of curves gives a theory of epsilon factors for curves previously defined by beilinson bloch deligne and esnault

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

langlands parameters for epipelagic representations of hbox gl _ n let f be a non archimedean local field an irreducible cuspidal representation of mathrm gl n f is epipelagic if its swan conductor equals 1 we give a full and explicit description of the langlands parameters of such representations in terms of elementary representation theory and local class field theory

an evidential link prediction method and link predictability based on shannon entropy abstract predicting missing links is of both theoretical value and practical interest in network science in this paper we empirically investigate a new link prediction method base on similarity and compare nine well known local similarity measures on nine real networks most of the previous studies focus on the accuracy however it is crucial to consider the link predictability as an initial property of networks itself hence this paper has proposed a new link prediction approach called evidential measure em based on dempster shafer theory moreover this paper proposed a new method to measure link predictability via local information and shannon entropy

fitness networks for real world systems via modified preferential attachment complex networks are virtually ubiquitous and the barabasi and albert model baba model has became an acknowledged standard for the modelling of these systems the so called baba model is a kind of preferential attachment growth model based on the intuitive premise that popularity is attractive however preferential attachment alone is insufficient to describe the diversity of complex networks observed in the real world in this paper we first use the accuracy of a link prediction method as a metric for network fitness the link prediction method predicts the occurrence of links consistent with preferential attachment the performance of this link prediction scheme is then a natural measure of the preferential attachment likeness of a given network we then propose several modification methods and modified baba models to construct networks which more accurately describe the fitness properties of real networks we find that all features assortativity degree distribution and rich club formation can play significant roles for the network construction and eventual structure moreover link sparsity and the size of a network are key factors for network reconstruction in addition we find that the structure of the network which is limited by geographic location nodes are embedded in a euclidean space and connectivity is correlated with distances differs from other typical networks in social networks we observe that the high school contact network has similar structure as the friends network and so we speculate that the contact behaviours can reflect real friendships

the local langlands correspondence for gsp 4 over local function fields we prove the local langlands correspondence for rm gsp 4 f where f is a non archimedean local field of positive characteristic with residue characteristic 2

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

the degree related clustering coefficient and its application to link prediction abstract link prediction plays a significant role in explaining the evolution of networks however it is still a challenging problem that has been addressed only with topological information in recent years based on the belief that network nodes with a great number of common neighbors are more likely to be connected many similarity indices have achieved considerable accuracy and efficiency motivated by the natural assumption that the effect of missing links on the estimation of a node s clustering ability could be related to node degree in this paper we propose a degree related clustering coefficient index to quantify the clustering ability of nodes unlike the classical clustering coefficient our new coefficient is highly robust when the observed bias of links is considered furthermore we propose a degree related clustering ability path dcp index which applies the proposed coefficient to the link prediction problem experiments on 12 real world networks show that our proposed method is highly accurate and robust compared with four common neighbor based similarity indices common neighbors cn adamic adar aa resource allocation ra and preferential attachment pa and the recently introduced clustering ability ca index

numerically generated tangent stiffness matrices for nonlinear structural analysis accurate tangent stiffness matrices are essential for the solution of nonlinear structural problems via newton like methods the present paper presents an accurate numerical procedure for the generation of tangent stiffness matrices from the internal force generation modules the present procedure is attractive for problems that require complex constitutive relations and or kinematic nonlinearities whose models are difficult to linearize and for incorporating newton like solution strategies into vectorial based nonlinear structural analysis codes

evolving networks using past structure to predict the future abstract many previous studies on link prediction have focused on using common neighbors to predict the existence of links between pairs of nodes more broadly research into the structural properties of evolving temporal networks and temporal link prediction methods have recently attracted increasing attention in this study for the first time we examine the use of links between a pair of nodes to predict their common neighbors and analyze the relationship between the weight and the structure in static networks evolving networks and in the corresponding randomized networks we propose both new unweighted and weighted prediction methods and use six kinds of real networks to test our algorithms in unweighted networks we find that if a pair of nodes connect to each other in the current network they will have a higher probability to connect common nodes both in the current and the future networks and the probability will decrease with the increase of the number of neighbors furthermore we find that the original networks have their particular structure and statistical characteristics which benefit link prediction in weighted networks the prediction algorithm performance of networks which are dominated by human factors decrease with the decrease of weight and are in general better in static networks furthermore we find that geographical position and link weight both have significant influence on the transport network moreover the evolving financial network has the lowest predictability in addition we find that the structure of non social networks has more robustness than social networks the structure of engineering networks has both best predictability and also robustness

numerically generated tangent stiffness matrices using the complex variable derivative method for nonlinear structural analysis accurate tangent stiffness matrices are essential for solving nonlinear structural problems using newton like methods this paper presents a numerical procedure for generating accurate tangent stiffness matrices from the derivative approximation of internal force using the complex variable derivative method cvdm the present procedure is suitable for problems that require complex constitutive relations and or kinematic nonlinearities whose models are difficult to linearize as well as for the incorporation of newton like solution strategies with nonlinear structural analyses