a complex networks approach for data clustering abstract this work proposes a method for data clustering based on complex networks theory a data set is represented as a network by considering different metrics to establish the connection between each pair of objects the clusters are obtained by taking into account five community detection algorithms the network based clustering approach is applied in two real world databases and two sets of artificially generated data the obtained results suggest that the exponential of the minkowski distance is the most suitable metric to quantify the similarities between pairs of objects in addition the community identification method based on the greedy optimization provides the best cluster solution we compare the network based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate

binary spatial partitioning of the central difference time integration scheme for explicit fast transient dynamics this paper proposes a generalization of the explicit central difference time integration scheme using a time step variable not only in time but also in space the solution at each element node is advanced in time following local rather than global stability limitations this allows substantial saving of computer time in realistic applications with non uniform meshes especially in multi field problems like fluid structure interactions a binary scheme in space is used time steps are not completely arbitrary but stay in a constant ratio of two when passing from one partition level to the next one this choice greatly facilitates implementation via an integer based logic ensures inherent synchronization and avoids any interpolations necessary in other partitioning schemes in the literature but which may reduce numerical stability the mesh partition is automatically built up and continuously updated by simple spatial adjacency considerations the resulting algorithm deals automatically with large variations in time of stability limits the paper introduces the core spatial partitioning technique in the lagrangian formulation some academic numerical examples allow a detailed comparison with the standard spatially uniform algorithm a final more realistic example shows the application of partitioning in simulations with arbitrary lagrangian eulerian formulation and fully coupled boundary conditions fluid structure interaction copyright 2008 john wiley sons ltd

projective varieties admitting an embedding with gauss map of rank zero abstract we introduce an intrinsic property for a projective variety as follows there exists an embedding into some projective space such that the gauss map is of rank zero which we call gmrz for short it turns out that gmrz imposes strong restrictions on rational curves on projective varieties in fact using gmrz we show that contrary to the characteristic zero case the existence of free rational curves does not imply that of minimal free rational curves in positive characteristic case we also focus attention on segre varieties grassmann varieties and hypersurfaces of low degree in particular we give a characterisation of fermat cubic hypersurfaces in terms of gmrz and show that a general hypersurface of low degree does not satisfy gmrz

a framework for detecting communities of unbalanced sizes in networks abstract community detection in large networks has been a focus of recent research in many of fields including biology physics social sciences and computer science most community detection methods partition the entire network into communities groups of nodes that have many connections within communities and few connections between them and do not identify different roles that nodes can have in communities we propose a community detection model that integrates more different measures that can fast identify communities of different sizes and densities we use node degree centrality strong similarity with one node from community maximal similarity of node to community compactness of communities and separation between communities each measure has its own strength and weakness thus combining different measures can benefit from the strengths of each one and eliminate encountered problems of using an individual measure we present a fast local expansion algorithm for uncovering communities of different sizes and densities and reveals rich information on input networks experimental results show that the proposed algorithm is better or as effective as the other community detection algorithms for both real world and synthetic networks while it requires less time

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

the separability of the gauss map and the reflexivity for a projective surface it is known that if a projective variety x in p n is reflexive with respect to the projective dual then the gauss map of x defined by embedded tangent spaces is separable and moreover that the converse is not true in general we prove that the converse holds under the assumption that x is of dimension two explaining the subtleness of the problem we present an example of smooth projective surfaces in arbitrary positive characteristic which gives a negative answer to a question raised by s kleiman and r piene on the inseparability of the gauss map

community extraction for social networks analysis of networks and in particular discovering communities within networks has been a focus of recent work in several fields and has diverse applications most community detection methods focus on partitioning the entire network into communities with the expectation of many ties within communities and few ties between however many networks contain nodes that do not fit in with any of the communities and forcing every node into a community can distort results here we propose a new framework that extracts one community at a time allowing for arbitrary structure in the remainder of the network which can include weakly connected nodes the main idea is that the strength of a community should depend on ties between its members and ties to the outside world but not on ties between nonmembers the proposed extraction criterion has a natural probabilistic interpretation in a wide class of models and performs well on simulated and real networks for the case of the block model we establish asymptotic consistency of estimated node labels and propose a hypothesis test for determining the number of communities

a numerical scheme to couple subdomains with different time steps for predominantly linear transient analysis abstract this paper generalizes the explicit implicit time integration algorithms pioneered by belytschko hughes and their respective co workers and the feti domain decomposition methods introduced by farhat and his co workers to the case where the same newmark scheme but different and coefficients and different time steps are specified in each subdomain building upon the work of farhat crivelli and geradin it considers various interface boundary constraints and performs a stability analysis of the proposed time integration algorithms

algorithms by design a new normalized time weighted residual methodology and design of a family of energy momentum conserving algorithms for non linear structural dynamics a new approach termed as the hybrid displacement strain based normalized time weighted residual approach is presented to accurately model non linear structural dynamic problems the focus here is restricted to all possible algorithmic designs within the class of linear multi step methods that fall under the umbrella of the generalized single solve single step linear dynamic framework originally developed via the classical time weighted residual approach involving a single solve within each time step as such designs are the most predominant in research and commercial software int j numer meth engng 2004 59 597 668 int j numer meth engng 2006 66 1738 1790 however traditional practices via classical time weighted residual approaches fail to preserve the underlying physics and stability and do not serve the purposes of extensions to non linear dynamic situations in contrast a new normalized time weighted residual approach is proposed that naturally enables such extensions leading to the design of a family of conserving time operators for unconstrained conservative dynamic systems without resorting to enforcing energy constraints as in past practices consequently the algorithmic stability in the sense of energy stability via this approach for non linear dynamic problems is also preserved for linear dynamic situations it reverts to the classical paradigm only simple numerical illustrations are purposely presented to demonstrate the basic concepts copyright 2009 john wiley sons ltd

local modal reduction in explicit dynamics with domain decomposition part 1 extension to subdomains undergoing finite rigid rotations we present an extension of the dual schur multidomain method with local linear modal reduction previously introduced by gravouil combescure herry and faucher to the case of modal reduction on geometrically non linear vibrating subdomains this first part of a two part paper describes a new formalism based on an original set of parameters to represent a subdomain s finite rigid body motion special attention is paid to the stability issues with time integration using the central difference scheme the method is validated on an academic example and its efficiency is demonstrated on a large scale example copyright 2004 john wiley sons ltd

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 role of geometric stiffness in momentum and energy conserving time integration a momentum and energy conserving time integration algorithm is developed for the motion of elastic bodies described in terms of the quadratic green strain momentum conserving algorithms are formulated from an integral of the equations of motion and energy conservation has traditionally been obtained by evaluating the contribution from the internal forces by use of a combined mean value of stresses and virtual strains on the element level it is here demonstrated that momentum and energy conservation can be obtained from the classic central difference formulation by including an extra global term in the form of the increment of the geometric stiffness matrix over the current time step usually directly available in global form in existing finite element programmes the theory is derived by the use of a state space formulation where this extra term is located in the same position as the viscous damping matrix indicating that the effect of the extra incremental geometric stiffness term in the non linear algorithm is equivalent to a variable damping term depending on the change of the state of stress over a time increment in the actual numerical algorithm the new value of the velocity vector is eliminated leaving a non linear equation for the displacement increment alone followed by an explicit vector update of the velocity increment copyright 2006 john wiley sons ltd

extended state space time integration with high frequency energy dissipation the introduction of algorithmic dissipation into conservative time integration algorithms is addressed in two steps the problem is formulated in state space and it is demonstrated that the use of two balanced dissipation terms one in the equation of motion and the other in the relation between the state space variables can produce dissipation that increases monotonically with the modal frequency this formulation is only partially satisfactory because it leads to dissipation also in the low frequency range a substantially improved form of algorithmic dissipation is then developed by representing the two balanced dissipation terms via auxiliary state space variables related to the displacement and velocity increments by a first order filter the filter technique retains the high frequency behavior of the original balanced algorithm but reduces the low frequency dissipation from first order in the frequency to third order energy balance equations are derived and the behavior of the two algorithms is described by detailed spectral analysis with explicit asymptotic results directly in terms of the damping parameter of the algorithms both algorithms satisfy full symmetry of displacement and normalized velocity variables for the free algorithmically damped vibration of any single mode and therefore exhibit monotonic transients without overshoot effects it is also demonstrated how the algorithm can be arranged in single solve format where only the displacement update requires a matrix equation solution while the velocity and the auxiliary state space variables are updated subsequently in each time step by simple vector relations with scalar coefficients copyright 2007 john wiley sons ltd

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

detecting communities in clustered networks based on group action on set abstract in this paper we propose a well targeted algorithm gas algorithm for detecting communities in high clustered networks by presenting group action technology on community division during the processing of this algorithm the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved as the derivation of the orbit partition an algebraic structure r cycle can be considered as the origin of the community to be a priori estimation for the community structure of the algorithm the community separability is introduced to indicate whether a network has distinct community structure by executing the algorithm on several typical networks and the lfr benchmark it shows that this gas algorithm can detect communities accurately and effectively in high clustered networks furthermore we compare the gas algorithm and the clique percolation algorithm on the lfr benchmark it is shown that the gas algorithm is more accurate at detecting non overlapping communities in clustered networks it is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks

the reflexivity of a segre product of projective varieties we study the reflexivity of a segre product of a projective space mathbb p m and a projective variety y and give a criterion for mathbb p m times y to be reflexive in terms of m the dimension of y the rank of the general hessian of y and the characteristic of the ground field our study is closely related to a question raised by kleiman and piene on the relationship between the conormal map and the gauss map

stability of explicit subcycling time integration with linear interpolation for first order finite element semidiscretizations an explicit subcycling time integration algorithm based on an element partition is presented for first order finite element systems this method uses linear interpolation to compute intermediate values at nodes in the subdomains integrated with the larger time steps stability of the algorithm for the two partition cases is analyzed by showing that the eigenvalues of the amplification matrix for the total integration cycle are not greater than one in absolute value using this stability criterion critical time steps for the element subdomains are derived in terms of element eigenvalues several numerical examples are considered to compare the accuracy of the method with previously developed subcycling algorithms to numerically verify the stability analysis

arlequin framework for multi model multi time scale and heterogeneous time integrators for structural transient dynamics this paper presents a general framework for performing spatio temporal multi scale multi model coupling based on displacement continuity this approach guarantees a global energy balance of the system in the context of the arlequin method it introduces specific interpolation of the lagrange multipliers and parameters of time integration operators in the overlapping zone a dual schur implementation is then used to illustrate the efficiency and robustness of the method convergence analysis with numerical experiments is performed finally 1d 1d and 2d 1d coupling applications are presented in which each subdomain is integrated in time using different time steps and different schemes this approach gives the user more ways of controlling computational behaviour via newmark parameters time steps and sizing the overlapping zones

on a multiscale computational strategy with time and space homogenization for structural mechanics a new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale this strategy which involves homogenization in space as well as in time could replace in several domains of application the standard homogenization techniques which are generally limited to the space domain it is an iterative strategy which calls for the resolution of problems on both a micro fine scale and a macro homogenized scale in this paper we review the bases of this approach and present improved approximation techniques to solve the micro and macro problems

overview of metrics and their correlation patterns for multiple metric topology analysis on heterogeneous graph ensembles this study is an overview of network topology metrics and a computational approach to analyzing graph topology via multiple metric analysis on graph ensembles the paper cautions against studying single metrics or combining disparate graph ensembles from different domains to extract global patterns this is because there often exists considerable diversity among graphs that share any given topology metric patterns vary depending on the underlying graph construction model and many real data sets are not actual statistical ensembles as real data examples we present five airline ensembles comprising temporal snapshots of networks of similar topology wikipedia language networks are shown as an example of a nontemporal ensemble general patterns in metric correlations as well as exceptions are discussed by representing the data sets via hierarchically clustered correlation heat maps most topology metrics are not independent and their correlation patterns vary across ensembles in general density related metrics and graph distance based metrics cluster and the two groups are orthogonal to each other metrics based on degree degree correlations have the highest variance across ensembles and cluster the different data sets on par with principal component analysis namely the degree correlation the s metric their elasticities and the rich club moments appear to be most useful in distinguishing topologies

duality with expanding maps and shrinking maps and its applications to gauss maps we study expanding maps and shrinking maps of subvarieties of grassmann varieties in arbitrary characteristic the shrinking map was studied independently by landsberg and piontkowski in order to characterize gauss images to develop their method we introduce the expanding map which is a dual notion of the shrinking map and is a generalization of the gauss map then we give a characterization of separable gauss maps and their images which yields results for the following topics 1 linearity of general fibers of separable gauss maps 2 generalization of the characterization of gauss images 3 duality on one dimensional parameter spaces of linear subvarieties lying in developable varieties

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

analysis and implementation of a new constant acceleration subcycling algorithm an algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps with integer time step ratios the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle the algorithm is shown to have good accuracy and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms the implementation of a generalised form of the algorithm with non integer time step ratios is presented c 1997 by john wiley sons ltd

a feti based multi time step coupling method for newmark schemes in structural dynamics we present an efficient and accurate multi time step coupling method using feti domain decomposition for structural dynamics using this method one can divide a large structural mesh into a number of smaller subdomains solve the individual subdomains separately and couple the solutions together to obtain the solution to the original problem the various subdomains can be integrated in time using different time steps and or different newmark schemes this approach will be most effective for very large scale simulations on complex geometries our coupling method builds upon a method previously proposed by gravouil and combescure gc method we show that for the simplest case when the same time step is used in all subdomains of the mesh our method reduces to the gc method and is unconditionally stable and energy preserving in addition we show that our method possesses these desirable properties for general multi time step cases too unlike the gc method which is dissipative greater computational efficiency is also achieved through our method by limiting the computation of interface forces to the largest time step as opposed to the smallest time step in the gc method copyright 2004 john wiley sons ltd

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

finding local community structure in networks although the inference of global community structure in networks has recently become a topic of great interest in the physics community all such algorithms require that the graph be completely known here we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time this algorithm runs in time o k2d for general graphs when d is the mean degree and k is the number of vertices to be explored for graphs where exploring a new vertex is time consuming the running time is linear o k we show that on computer generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge as an application we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer

a local multiresolution algorithm for detecting communities of unbalanced structures abstract in complex networks such as computer and information networks social networks or biological networks a community structure is a common and important property community detection in complex networks has attracted a lot of attention in recent years community detection is the problem of finding closely related groups within a network modularity optimisation is a widely accepted method for community detection it has been shown that the modularity optimisation has a resolution limit because it is unable to detect communities with sizes smaller than a certain number of vertices defined with network size in this paper we propose a metric for describing community structures that enables community detection better than other metrics we present a fast local expansion algorithm for community detection the proposed algorithm provides online multiresolution community detection from a source vertex experimental results show that the proposed algorithm is efficient in both real world and synthetic networks

a time staggered partitioned coupling algorithm for transient heat conduction we present a time staggered partitioned coupling algorithm for transient heat conduction finite element simulations this algorithm divides a large structural mesh into a number of smaller subdomains solves the individual subdomains separately and couples the solutions to obtain the response to the original problem the proposed algorithm is a mixed multi timestep algorithm and enables arbitrary time integration schemes and meshes to be coupled with different timesteps in the various subdomains in this procedure the solution of each partition is separately evaluated over a system timestep after which the interfacial conditions are enforced making this a staggered algorithm that facilitates parallel computation we present examples showing the feasibility of the coupling algorithm and discuss the merits in terms of convergence and stability

tolerating the community detection resolution limit with edge weighting communities of vertices within a giant network such as the world wide web are likely to be vastly smaller than the network itself however fortunato and barthelemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than l 2 edges where l is the number of edges in the entire network this resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks fortunato and barthelemy s argument can be extended to networks with weighted edges as well and we derive this corollary argument we conclude that weighted modularity algorithms may fail to resolve communities with less than we 2 total edge weight where w is the total edge weight in the network and e is the maximum weight of an intercommunity edge if e is small then small communities can be resolved given a weighted or unweighted network we describe how to derive new edge weights in order to achieve a low e we modify the clauset newman and moore cnm community detection algorithm to maximize weighted modularity and we show that the resulting algorithm has greatly improved accuracy in experiments with an emerging community standard benchmark we find that our simple cnm variant is competitive with the most accurate community detection methods yet proposed

an approach to the connection between subdomains with non matching meshes for transient mechanical analysis this paper describes a general method for coupling non matching linear finite element meshes in transient dynamic analysis we propose a method based on schur s dual formulation whose main advantage is to provide equilibrium as well as kinematic continuity throughout the interface the essence of our work lies in the particular discretization of the space of lagrange multipliers and in the validation of the method through two and three dimensional static calculations as well as two dimensional dynamic calculations an example is also presented and the results are compared to those of the mortar method copyright 2002 john wiley sons ltd

weak signal transmission in complex networks and its application in detecting connectivity we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks through both theoretical analysis and numerical simulations we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses this finding can be conveniently used to detect the topology of unknown network such as the degree distribution clustering coefficient and community structure etc by repeatedly choosing different nodes as the signal source through four typical networks i e the regular one dimensional small world random and scale free networks we show that the features of network can be approximately given by investigating many fewer nodes than the network size thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size

local resolution limit free potts model for community detection we report on an exceptionally accurate spin glass type potts model for community detection with a simple algorithm we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise it is also competitive with the best currently available algorithms in terms of speed and size of solvable systems we find that the computational demand often exhibits superlinear scaling o l 1 3 where l is the number of edges in the system and we have applied the algorithm to synthetic systems as large as 40 ifmmode times else texttimes fi 10 6 nodes and over 1 ifmmode times else texttimes fi 10 9 edges a previous stumbling block encountered by popular community detection methods is the so called resolution limit being a local measure of community structure our potts model is free from this resolution limit effect and it further remains a local measure on weighted and directed graphs we also address the mitigation of resolution limit effects for two other popular potts models

a monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics a new hybrid multi time method for multi time scales structural dynamics simulations is described a monolithic method in a schur dual domain decomposition framework is proposed and allows to consider heterogeneous time integrators with their own time discretization and possible large ratio between the time steps for each subdomain in the proposed method zero numerical dissipation is ensured at the interface this implies that the global stability of the coupling method is governed by the stability of each time integrator without influence of the interface for that purpose velocity continuity is ensured in a weak sense at the interfaces and time integrators newmark hht simo krenk verlet are introduced in a unified framework incremental velocity formulation furthermore dynamics governing equations are introduced from a weak formulation in time in other words equilibrium equation is no more ensured in a strong sense at a given time step but rather on average on a time interval some numerical examples illustrate the efficiency and the robustness of the proposed method for ratio of time scales close to 1000 without any numerical dissipation at the interfaces

stability of multi time step partitioned integrators for first order finite element systems abstract mixed time integration procedures are those in which different time steps and different integrators are used in different parts of the mesh a rigorous stability analysis is provided for the first time for this type of time integration for first order semidiscretizations such as arise in diffusion problems the stability analysis is verified by some numerical examples

a new bipenalty formulation for ensuring time step stability in time domain computational dynamics summary it is well known that use of standard penalty methods can decrease the critical time step of time domain dynamic finite element analyses the bipenalty method utilises both stiffness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the finite element system one way of achieving this goal is to find a ratio of stiffness and mass penalty parameters the critical penalty ratio cpr that does not affect the maximum eigenfrequency and therefore for conditionally stable solution schemes the critical time step of a system in this contribution we develop a new method of calculating the cpr associated with a finite element formulation by examining the eigenvalue problem in detail advantages of the method compared with previous solutions include increased simplicity and generality and the ability to consider multiple constraints the method is demonstrated by deriving cprs for a few finite element formulations which are then verified using simple numerical examples the superiority of the bipenalty method over standard mass penalty methods is also demonstrated copyright 2011 john wiley sons ltd

on multi time step monolithic coupling algorithms for elastodynamics we present a way of constructing multi time step monolithic coupling methods for elastodynamics the governing equations for constrained multiple subdomains are written in dual schur form and the continuity of velocities is enforced at system time levels the resulting equations will be in the form of differential algebraic equations to crystallize the ideas we shall employ newmark family of time stepping schemes the proposed method can handle multiple subdomains and allows different time steps as well as different time stepping schemes from the newmark family in different subdomains we shall use the energy method to assess the numerical stability and quantify the influence of perturbations under the proposed coupling method two different notions of energy preservation are introduced and employed to assess the performance of the proposed method several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method we shall also compare the proposed multi time step coupling method with some other methods available in the literature

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

multi time step integration using nodal partitioning an algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators since the nodal groups are updated independently no unsymmetric systems need be solved stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value the element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells

mass lumping strategies for x fem explicit dynamics application to crack propagation this paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method more precisely we are interested in explicit algorithms we prove that by using a specific lumping technique the critical time step is exactly the same as if no crack were present this somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack the new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids to be precise the results obtained are valid only when the crack is modelled by the heaviside enrichment note also that the resulting lumped matrix is block diagonal blocks of size 2 2 for constant strain elements linear simplex elements the critical time step is not modified when the element is cut thanks to the lumped mass matrix the critical time step never tends to zero moreover the lumping techniques conserve kinetic energy for rigid motions in addition tensile stress waves do not propagate through the discontinuity hence the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack both these techniques will be used in a numerical experiment copyright 2007 john wiley sons ltd

communities and bottlenecks trees and treelike networks have high modularity much effort has gone into understanding the modular nature of complex networks communities also known as clusters or modules are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other groups in the network discovering high quality communities is a difficult and important problem in a number of areas the most popular approach is the objective function known as modularity used both to discover communities and to measure their strength to understand the modular structure of networks it is then crucial to know how such functions evaluate different topologies what features they account for and what implicit assumptions they may make we show that trees and treelike networks can have unexpectedly and often arbitrarily high values of modularity this is surprising since trees are maximally sparse connected graphs and are not typically considered to possess modular structure yet the nonlocal null model used by modularity assigns low probabilities and thus high significance to the densities of these sparse tree communities we further study the practical performance of popular methods on model trees and on a genealogical data set and find that the discovered communities also have very high modularity often approaching its maximum value statistical tests reveal the communities in trees to be significant in contrast with known results for partitions of sparse random graphs

a study of the stability of subcycling algorithms in structural dynamics algorithms for explicit integration of structural dynamics problems with multiple time steps subcycling are investigated only one such algorithm due to smolinski and sleith has proved to be stable in a classical sense a simplified version of this algorithm that retains its stability is presented however as with the original version it can be shown to sacrifice accuracy to achieve stability another algorithm in use is shown to be only statistically stable in that a probability of stability can be assigned if appropriate time step limits are observed this probability improves rapidly with the number of degrees of freedom in a finite element model the stability problems are shown to be a property of the central difference method itself which is modified to give the subcycling algorithm a related problem is shown to arise when a constraint equation in time is introduced into a time continuous space time finite element model

two feti based heterogeneous time step coupling methods for newmark and α schemes derived from the energy method abstract the purpose of this paper is to describe a general methodology to obtain multi time step coupling methods for different time integration schemes newmark hht wbz ch on the basis of energetic considerations the general framework of the feti method is considered for building the heterogeneous time step coupling methods by ensuring the gluing of subdomains with lagrange multipliers the proposed methods for coupling subdomains with different time integration schemes and time steps fine and large time steps are based on the pseudo energy measure as introduced by hughes in the so called energy method employed for proving the stability of implicit explicit algorithms assuming a given variation of the lagrange multipliers over the large time step kinematic conditions are derived by ensuring the zero pseudo energy at the interface two methods will be derived in this paper the first new method for which the interface problem involving the lagrange multipliers is solved at the large time scale can handle the popular dissipative schemes hht wbz ch in the particular case of the newmark schemes the new method matches with the ph method proposed by prakash and hjelmstad the second new method is based at the micro time scale it can be viewed as an extension of the method proposed by gravouil and combescure gc method for the coupling of the schemes nonetheless like the gc method the new micro time based method turns out to be dissipative when non dissipative second order accurate schemes are involved and looses one order of accuracy

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

adjusting from disjoint to overlapping community detection of complex networks abstract the investigation of community structures is one of the most important problems in the field of complex networks and has countless applications in different disciplines biology computer social sciences etc many community detection algorithms have been developed in various fields recently the vast majority of these algorithms only find disjoint communities however in many real world networks communities often overlap to some extent in this paper we propose an efficient method for adjusting these classical algorithms to match the requirement for discovering overlapping communities in complex networks which is based on a local definition of community strength the method can in principle be applied with any clustering algorithm tests on a set of computer generated and real world networks give excellent results in particular we show that the method can also allow one to availably analyze the problem of unstable nodes in community detection which is very helpful for understanding the structural properties of the networks correctly and comprehensively

differential equations as a tool for community identification we consider the task of identification of a cluster structure in random networks the results of two methods are presented i the newman algorithm m e j newman and m girvan phys rev e 69 026113 2004 and ii our method based on differential equations a series of computer experiments is performed to check if in applying these methods we are able to determine the structure of the network the trial networks consist initially of well defined clusters and are disturbed by introducing noise into their connectivity matrices further we show that an improvement of the previous version of our method is possible by an appropriate choice of the threshold parameter beta with this change the results obtained by the two methods above are similar and our method works better for all the computer experiments we have done

subcycling first and second order generalizations of the trapezoidal rule subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first and second order systems of equations arising in finite element analysis as well as for integration using explicit implicit partitions of a model the author has recently extended this work to implicit implicit multi timestep partitions of both first and second order systems in this paper improved algorithms for multi timestep implicit integration are introduced that overcome some weaknesses of those proposed previously in particular in the second order case improved stability is obtained some of the energy conservation properties of the newmark family of algorithms are shown to be preserved in the new multi timestep extensions of the newmark method in the first order case the generalized trapezoidal rule is extended to multiple timesteps in a simple way that permits an implicit implicit partition explicit special cases of the present algorithms exist these are compared to algorithms proposed previously c 1998 john wiley sons ltd

local network community detection with continuous optimization of conductance and weighted kernel k means local network community detection is the task of finding a single community of nodes concentrated around few given seed nodes in a localized way conductance is a popular objective function used in many algorithms for local community detection this paper studies a continuous relaxation of conductance we show that continuous optimization of this objective still leads to discrete communities we investigate the relation of conductance with weighted kernel k means for a single community which leads to the introduction of a new objective function conductance conductance is obtained by setting to 0 two algorithms emc and pgdc are proposed to locally optimize conductance and automatically tune the parameter they are based on expectation maximization and projected gradient descent respectively we prove locality and give performance guarantees for emc and pgdc for a class of dense and well separated communities centered around the seeds experiments are conducted on networks with ground truth communities comparing to state of the art graph diffusion algorithms for conductance optimization on large graphs results indicate that emc and pgdc stay localized and produce communities most similar to the ground while graph diffusion algorithms generate large communities of lower quality

explicit newmark verlet algorithm for time integration of the rotational dynamics of rigid bodies we reformulate the traditional velocity based vector space newmark algorithm for the rotational dynamics of rigid bodies that is for the setting of the so 3 lie group we show that the most naive re write of the vector space algorithm possesses the properties of symplecticity and almost momentum conservation thus we obtain an explicit algorithm for rigid body dynamics that matches or exceeds performance of existing algorithms but which curiously does not seem to have been considered in the open literature so far copyright 2005 john wiley sons ltd

a partial velocity approach to subcycling structural dynamics subcycling or the use of different timesteps at different nodes can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions the method that has been most widely adopted uses a nodal partition extending the central difference method in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes this approach leads to narrow bands of unstable timesteps or statistical stability it also can be in error due to lack of momentum conservation on the timestep interface the author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability however these sacrifice accuracy to achieve stability an approach to conserve momentum on an element interface by adding partial velocities is considered here applied to extend the central difference method this approach is simple and has accuracy advantages the method can be programmed by summing impulses of internal forces evaluated using local element timesteps in order to predict a velocity change at a node however it is still only statistically stable so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary by replacing the central difference method with the explicit generalized alpha method it is possible to gain stability by dissipating the high frequency response that leads to stability problems however coding the algorithm is less elegant as the response depends on previous partial accelerations extension to implicit integration is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface c 2002 elsevier science b v all rights reserved

spectral tripartitioning of networks we formulate a spectral graph partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step in so doing we extend the recursive bipartitioning methods developed by newman m e j newman proc natl acad sci u s a 103 8577 2006 phys rev e 74 036104 2006 to allow one to consider the best available two way and three way divisions at each recursive step we illustrate the method using simple bucket brigade examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of u s congressional networks inferred from roll call voting similarities

a community detection method based on local similarity and degree clustering information community detection is of great importance to understand the structures and functions of networks in this paper a novel algorithm is proposed based on local similarity and degree clustering information local similarity is employed to measure the similarity between nodes and their neighbors in order to form communities within which nodes are closely connected degree clustering information a hybrid criterion combining local neighborhood ratio with degree ratio make a large number of nodes with low degree to embrace a small amount of nodes with high degree furthermore each node in small scale communities has the duty to try to connect the nodes with high degree to expand communities and finally the optimal community structure can be obtained simulation results on real and artificial networks show that the proposed algorithm has the excellent performance in terms of accuracy

variational time integrators the purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest in particular the conservation properties of both synchronous and asynchronous variational integrators avis are discussed in detail we present selected numerical examples which demonstrate the excellent accuracy conservation and convergence characteristics of avis in these tests avis are found to result in substantial speed ups at equal accuracy relative to explicit newmark a mathematical proof of convergence of the avis is also presented in this paper finally we develop the subject of horizontal variations and configurational forces in discrete dynamics this theory leads to exact path independent characterizations of the configurational forces acting on discrete systems notable examples are the configurational forces acting on material nodes in a finite element discretisation and the j integral at the tip of a crack in a finite element mesh

detect local communities in networks with an outside rate coefficient abstract in this paper we present a local method for detecting communities in networks we define an outside rate coefficient o u t in our method o u t has a very simple form and is easy to calculate the local community enclosing a starting node can be detected by agglomerating the node with the smallest o u t at each time step when there are two or more nodes having the same smallest outside rate coefficient o u t we agglomerate the node with the largest k i n this operation is remarkably beneficial to the accuracy of our method and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

criterions for locally dense subgraphs abstract community detection is one of the most investigated problems in the field of complex networks although several methods were proposed there is still no precise definition of communities as a step toward a definition i highlight two necessary properties of communities separation and internal cohesion the latter being a new concept i propose a local method of community detection based on two dimensional local optimization which i tested on common benchmarks and on the word association database

detecting overlapping communities of weighted networks via a local algorithm abstract identification of communities is significant in understanding the structures and functions of networks since some nodes naturally belong to several communities the study of overlapping communities has attracted increasing attention recently and many algorithms have been designed to detect overlapping communities in this paper an overlapping communities detecting algorithm is proposed whose main strategies are finding an initial partial community from a node with maximal node strength and adding tight nodes to expand the partial community seven real world complex networks and one synthetic network are used to evaluate the algorithm experimental results demonstrate that the algorithm proposed is efficient for detecting overlapping communities in weighted networks