community detection algorithms a comparative analysis uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents many algorithms have been proposed so far but none of them has been subjected to strict tests to evaluate their performance most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure which is very uncommon in real systems here we test several methods against a recently introduced class of benchmark graphs with heterogeneous distributions of degree and community size the methods are also tested against the benchmark by girvan and newman proc natl acad sci u s a 99 7821 2002 and on random graphs as a result of our analysis three recent algorithms introduced by rosvall and bergstrom proc natl acad sci u s a 104 7327 2007 proc natl acad sci u s a 105 1118 2008 blondel et al j stat mech theory exp 2008 p10008 and ronhovde and nussinov phys rev e 80 016109 2009 have an excellent performance with the additional advantage of low computational complexity which enables one to analyze large systems

computationally efficient measure of topological redundancy of biological and social networks it is well known that biological and social interaction networks have a varying degree of redundancy though a consensus of the precise cause of this is so far lacking in this paper we introduce a topological redundancy measure for labeled directed networks that is formal computationally efficient and applicable to a variety of directed networks such as cellular signaling and metabolic and social interaction networks we demonstrate the computational efficiency of our measure by computing its value and statistical significance on a number of biological and social networks with up to several thousands of nodes and edges our results suggest a number of interesting observations 1 social networks are more redundant that their biological counterparts 2 transcriptional networks are less redundant than signaling networks 3 the topological redundancy of the c elegans metabolic network is largely due to its inclusion of currency metabolites and 4 the redundancy of signaling networks is highly negatively correlated with the monotonicity of their dynamics

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

a vector partitioning approach to detecting community structure in complex networks in recent years the problem of community structure detection has attracted more and more attention and many approaches have been proposed recently newman pointed out that this issue can be transformed into the problem of constrained maximization of the assignment matrix over possible divisions of a network he presents further that this maximization process can be written in terms of the eigenspectrum of the modularity matrix on the basis of this work and the vector partition approach in computer science we propose a kind of multiway division approach for detecting community structure of complex networks experimental results indicate that the algorithm works well and is effective at finding both good communities and the appropriate number of communities

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

detect overlapping and hierarchical community structure in networks abstract clustering and community structure is crucial for many network systems and the related dynamic processes it has been shown that communities are usually overlapping and hierarchical however previous methods investigate these two properties of community structure separately this paper proposes an algorithm eagle to detect both the overlapping and hierarchical properties of complex community structure together this algorithm deals with the set of maximal cliques and adopts an agglomerative framework the quality function of modularity is extended to evaluate the goodness of a cover the examples of application to real world networks give excellent results

fuzzy control rules and their natural laws abstract we consider the convergence of fuzzy controllers as the number of fuzzy rules tends to infinity we assume that the fuzzy rules are regular and show the existence of limit laws for five different fuzzy control rules

analysis of directed networks via partial singular value decomposition and gauss quadrature abstract large scale networks arise in many applications it is often of interest to be able to identify the most important nodes of a network or to determine the ease of traveling between them we are interested in carrying out these tasks for directed networks these networks have a nonsymmetric adjacency matrix a benzi et al 6 recently proposed that these tasks can be accomplished by studying certain matrix functions such as hyperbolic cosine and sine of a t a and a a t for small to medium sized networks the required computations can be easily carried out by first computing the singular value decomposition of a however for large networks this is impractical we propose to first compute a partial singular value decomposition of a which allows us to determine a subset of nodes that contains the most important nodes or a subset of nodes between which it is easy to travel we then apply gauss quadrature to rank the nodes in these subsets several computed examples illustrate the performance of the approach proposed

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

stabilized interface methods for mechanical joints physics based models and variationally consistent embedding abstract this paper presents the application of a new method for interfacial modeling utilizing a merger of continuous galerkin and discontinuous galerkin concepts to simulate the behavior of mechanical joints the interfacial flux terms arising naturally from the discontinuous galerkin treatment provide a mechanism to embed friction models in a variationally consistent fashion due to the unbiased implementation of the interface facilitated by avoiding the master slave concept the deformation of the two interacting surfaces conforms to the local material and geometric attributes of the surfaces this results in a better preservation of physics in interface mechanics additionally the method is incorporated into a variational multiscale framework that comes equipped with a built in error estimation module providing numerical estimation of convergence and distinguishing discretization errors from modeling errors a series of quasi static numerical simulations of a lap joint under fretting conditions are conducted to compare the performance of two friction models i classical coulomb friction model and ii physics based multiscale model hysteresis study of a three dimensional double bolted lap joint for the two friction models is also presented and the computed results are shown to be consistent between conforming and nonconforming meshes

a unified formulation for interface coupling and frictional contact modeling with embedded error estimation summary we present a derivation of a new interface formulation via a merger of continuous galerkin and discontinuous galerkin concepts enhanced by the variational multiscale method developments herein provide treatment for the pure displacement form and mixed form of small deformation elasticity as applied to the solution of two problem classes domain decomposition and contact mechanics with friction the proposed framework seamlessly accommodates merger of different element types within subregions of the computational domain and nonmatching element faces along embedded interfaces these features are retained in the treatment of multibody small deformation contact problems as well where an unbiased treatment of the contact interface stands in contrast to classical master slave constructs numerical results for problems in two and three spatial dimensions illustrate the robustness and versatility of the proposed method copyright 2012 john wiley sons ltd

detecting community structure using label propagation with weighted coherent neighborhood propinquity abstract community detection has become an important methodology to understand the organization and function of various real world networks the label propagation algorithm lpa is an almost linear time algorithm proved to be effective in finding a good community structure however lpa has a limitation caused by its one hop horizon specifically each node in lpa adopts the label shared by most of its one hop neighbors much network topology information is lost in this process which we believe is one of the main reasons for its instability and poor performance therefore in this paper we introduce a measure named weighted coherent neighborhood propinquity weighted cnp to represent the probability that a pair of vertices are involved in the same community in label update a node adopts the label that has the maximum weighted cnp instead of the one that is shared by most of its neighbors we propose a dynamic and adaptive weighted cnp called entropic cnp by using the principal of entropy to modulate the weights furthermore we propose a framework to integrate the weighted cnp in other algorithms in detecting community structure we test our algorithm on both computer generated networks and real world networks the experimental results show that our algorithm is more robust and effective than lpa in large scale networks

advanced modularity specialized label propagation algorithm for detecting communities in networks abstract a modularity specialized label propagation algorithm lpam for detecting network communities was recently proposed this promising algorithm offers some desirable qualities however lpam favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space to escape local maxima we employ a multistep greedy agglomerative algorithm msg that can merge multiple pairs of communities at a time combining lpam and msg we propose an advanced modularity specialized label propagation algorithm lpam experiments show that lpam successfully detects communities with higher modularity values than ever reported in two commonly used real world networks moreover lpam offers a fair compromise between accuracy and speed

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

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

stepping community detection algorithm based on label propagation and similarity abstract community or module structure is one of the most common features in complex networks the label propagation algorithm lpa is a near linear time algorithm that is able to detect community structure effectively nevertheless when labeling a node the lpa adopts the label belonging to the majority of its neighbors which means that it treats all neighbors equally in spite of their different effects on the node another disadvantage of lpa is that the results it generates are not unique in this paper we propose a modified lpa called stepping lpa s in which labels are propagated by similarity furthermore our algorithm divides networks using a stepping framework and uses an evaluation function proposed in this paper to select the final unique partition we tested this algorithm on several artificial and real world networks the results show that stepping lpa s can obtain accurate and meaningful community structure without priori information

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

multistep greedy algorithm identifies community structure in real world and computer generated networks we have recently introduced a multistep extension of the greedy algorithm for modularity optimization the extension is based on the idea that merging l pairs of communities l 1 at each iteration prevents premature condensation into few large communities here an empirical formula is presented for the choice of the step width l that generates partitions with close to optimal modularity for 17 real world and 1100 computer generated networks furthermore an in depth analysis of the communities of two real world networks the metabolic network of the bacterium e coli and the graph of coappearing words in the titles of papers coauthored by martin karplus provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity but also according to objective criteria in other words the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions

an accurate cog defuzzifier design using lamarckian co adaptation of learning and evolution this paper proposes a design technique of optimal center of gravity cog defuzzifier using the lamarckian coadaptation of learning and evolution the proposed cog defuzzifier is specified by various design parameters such as the centers widths and modifiers of mfs the design parameters are adjusted with the lamarckian co adaptation of learning and evolution where the learning performs a local search of design parameters in an individual cog defuzzifier but the evolution performs a global search of design parameters among a population of various cog defuzzifiers this co adaptation scheme allows to evolve much faster than the non learning case and gives a higher possibility of finding an optimal solution due to its wider searching capability an application to the truck backer upper control problem of the proposed co adaptive design method of cog defuzzifier is presented the approximation ability and control performance are compared with those of the conventionally simplified cog defuzzifier in terms of the fuzzy logic controller s approximation error and the average tracing distance respectively

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

a deep stochastic model for detecting community in complex networks discovering community structures is an important step to understanding the structure and dynamics of real world networks in social science biology and technology in this paper we develop a deep stochastic model based on non negative matrix factorization to identify communities in which there are two sets of parameters one is the community membership matrix of which the elements in a row correspond to the probabilities of the given node belongs to each of the given number of communities in our model another is the community community connection matrix of which the element in the i th row and j th column represents the probability of there being an edge between a randomly chosen node from the i th community and a randomly chosen node from the j th community the parameters can be evaluated by an efficient updating rule and its convergence can be guaranteed the community community connection matrix in our model is more precise than the community community connection matrix in traditional non negative matrix factorization methods furthermore the method called symmetric nonnegative matrix factorization is a special case of our model finally based on the experiments on both synthetic and real world networks data it can be demonstrated that our algorithm is highly effective in detecting communities

density shrinking algorithm for community detection with path based similarity abstract community structure is ubiquitous in real world complex networks finding the communities is the key to understand the functions of those networks a lot of works have been done in designing algorithms for community detection but it remains a challenge in the field traditional modularity optimization suffers from the resolution limit problem recent researches show that combining the density based technique with the modularity optimization can overcome the resolution limit and an efficient algorithm named denshrink was provided the main procedure of denshrink is repeatedly finding and merging micro communities broad sense into super nodes until they cannot merge analyses in this paper show that if the procedure is replaced by finding and merging only dense pairs both of the detection accuracy and runtime can be obviously improved thus an improved density based algorithm imds is provided since the time complexity path based similarity indexes are difficult to be applied in community detection for high performance in this paper the path based katz index is simplified and used in the imds algorithm

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

eigenvectors of network complement reveal community structure more accurately abstract we propose a general spectral method to find communities of a network based on network complement and anti community concepts analytical and numerical results show that the eigenspace of matrices corresponding to a network complement reveals the community structure of a network more accurately than the eigenspace of matrices corresponding to the network itself it is shown that the laplacian eigenspace is the best candidate for spectral community detection especially in networks with a heterogeneous community structure the method is applied to some computer generated and real world networks with known community structures

a class of improved algorithms for detecting communities in complex networks abstract detecting communities in complex networks is of considerable importance for understanding both the structure and function of the networks here we propose a class of improved algorithms for community detection by combining the betweenness algorithm of girvan and newman with the edge weight defined by the edge clustering coefficient the improved algorithms are tested on some artificial and real world networks and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases in addition the technique for improving the betweenness algorithm in this paper thanks to its compatibility can directly be applied to various detection algorithms

approximation and numerical realization of 2d contact problems with coulomb friction and a solution dependent coefficient of friction the paper analyzes discrete contact problems with the coulomb law of friction which involves a solution dependent coefficient of friction f solutions to these problems are defined as fixed points of an auxiliary mapping it is shown that there exists at least one solution provided that f is bounded and continuous in r 1 further conditions guaranteeing uniqueness of the solution are studied the paper is completed by numerical results of several model examples

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

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

defuzzification of fuzzy intervals abstract this paper deals with defuzzification of fuzzy intervals classified as regular or irregular based on the defuzzification method used a fuzzy interval is regular if its membership function is maximized at its defuzzified value otherwise the fuzzy interval is irregular three methods for defuzzification are presented in this paper 1 mean of maxima mom method 2 center of area coa method and 3 fuzzy mean fm method fuzzy intervals with symmetrical membership function are regular and all three defuzzification methods give the same results for any regular fuzzy interval based on the coa method its defuzzified value is equal to the middle point of the corresponding mean value interval for irregular fuzzy intervals two approaches are proposed one is to apply the defuzzification method but relax the reasonable but not necessary rnn requirement another is to apply the rnn requirement but relax the defuzzification method this paper shows that the regularity of a fuzzy interval is preserved after applying an arithmetic operation with a nonzero real number the formulas for calculating the defuzzified value of the arithmetic operations between a regular fuzzy interval and a real number are derived this paper also shows that the regularity of two fuzzy intervals based on the coa method is preserved after applying addition or subtraction operation between them the formulas for calculating the defuzzified value of the sum and the difference of regular fuzzy intervals are derived the properties of fuzzy intervals discussed in this paper can be taken into consideration before or when a defuzzification method is selected

modularity and community detection in bipartite networks the modularity of a network quantifies the extent relative to a null model network to which vertices cluster into community groups we define a null model appropriate for bipartite networks and use it to define a bipartite modularity the bipartite modularity is presented in terms of a modularity matrix b some key properties of the eigenspectrum of b are identified and used to describe an algorithm for identifying modules in bipartite networks the algorithm is based on the idea that the modules in the two parts of the network are dependent with each part mutually being used to induce the vertices for the other part into the modules we apply the algorithm to real world network data showing that the algorithm successfully identifies the modular structure of bipartite networks

phase transition model for community detection abstract motivated by social and biological interactions a novel type of phase transition model is provided in order to investigate the emergence of the clustering phenomenon in networks the model has two types of interactions one is attractive and the other is repulsive in each iteration the phase of a node or an agent moves toward the average phase of its neighbors and moves away from the average phase of its non neighbors the velocities of the two types of phase transition are controlled by two parameters respectively it is found that the phase transition phenomenon is closely related to the topological structure of the underlying network and thus can be applied to identify its communities and overlapping groups by giving each node of the network a randomly generated initial phase and updating these phases by the phase transition model until they reach stability one or two communities will be detected according to the nodes stable phases confusable nodes are moved into a set named o f by removing the detected communities and the nodes in o f another one or two communities will be detected by an iteration of the algorithm in this way all communities and the overlapping nodes are detected simulations on both real world networks and the lfr benchmark graphs have verified the efficiency of the proposed scheme

when are networks truly modular abstract the study of cluster or community structure of complex networks contributes to the understanding of networks at a functional level in many networks latent classes of nodes are suspected which manifest themselves as communities i e groups of nodes with a high link density among the nodes of the same class and low link density between nodes of different classes community detection algorithms are used to infer these classes e g by finding a partition of the network which maximizes a quality function such as the network modularity q m newman m girvan finding and evaluating community structure in networks phys rev e 69 2004 026113 however it is known from numerical experiments that even purely random networks display intrinsic modularity and may be partitioned yielding high values of q extending on our earlier results j reichardt s bornholdt statistical mechanics of community detection phys rev e 74 2006 016110 the mapping of the community detection problem onto finding the ground state of a spin glass is exploited in order to derive analytical expressions for the expected modularity in random graphs and assess the theoretical limits to community detection the results are independent of any specific community detection algorithm and allow for differentiation between modularity arising purely due to the search process in the large configuration space of possible partitionings on the one hand or due to the actual presence of different classes of nodes on the other hand

robustness of centrality measures against network manipulation abstract node centrality is an important quantity to consider in studying complex networks as it is related to many applications ranging from the prediction of network structure to the control of dynamics on networks in the literature much effort has been devoted to design new centrality measurements however the reliability of these centrality measurements has not been fully assessed particularly with respect to the fact that many real networks are facing different kinds of manipulations such as addition removal or rewiring of links in this paper we focus on the robustness of classic centrality measures against network manipulation our analysis is based on both artificial and real networks we find that the centrality measurements are generally more robust in heterogeneous networks biased link manipulation could more seriously distort the centrality measures than random link manipulation moreover the top part of the centrality ranking is more resistant to manipulation

flexible stability criteria for a linguistic fuzzy dynamic system abstract this paper considers the stability problems of continuous and discrete type fuzzy control systems respectively on the basis of matrix measures and matrix norms several stability criteria for the systems are proposed some of these criteria are flexible with different chosen parameter p that means the trade off between the conservativeness and the computing convenience of the criteria depends on the chosen value of p totally

a multiscale computational approach for contact problems we introduce a two scale computational strategy for the resolution of contact problems with friction possibly with numerous contact surfaces the structure studied may also be highly heterogeneous the description of micro and macro quantities is performed on the interfaces arising from the decomposition of the structure studied into an assembly of substructures and interfaces the efficiency and robustness of the method are illustrated on several examples this iterative computational strategy is suitable for parallel computing it can be interpreted as a mixed multilevel domain decomposition method its scalability has been demonstrated and comparisons with other domain decomposition methods are also given

numerical derivation of contact mechanics interface laws using a finite element approach for large 3d deformation in this work a homogenization method is presented to obtain by numerical simulation interface laws for normal contact pressure based on statistical surface models for this purpose and assuming elastic behaviour of the asperities the interface law of kragelsky et al friction and wear calculation methods pergamon 1982 is chosen for comparison the non penetration condition and interface models for contact that take into account the surface micro structure are investigated in detail a theoretical basis for the three dimensional contact problem with finite deformations is shortly presented the augmented lagrangian method is then used to solve the contact problem with friction the algorithms for frictional contact are derived based on a slip rule using backward euler integration like in plasticity special attention was dedicated to the consistent derivation of the contact equations between finite element surfaces a matrix formulation for a node to surface contact element is derived consisting of a master surface segment with four nodes and a contacting slave node it was also necessary to consider the special cases of node to edge contact and node to node contact in order to achieve the desired asymptotic quadratic convergence in the newton method a numerical example is selected to show the ability of the contact formulation and the algorithm to represent interface law for rough surfaces copyright 2003 john wiley sons ltd

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

adaptive multi resolution modularity for detecting communities in networks abstract community structure is a common topological property of complex networks which attracted much attention from various fields optimizing quality functions for community structures is a kind of popular strategy for community detection such as modularity optimization here we introduce a general definition of modularity by which several classical multi resolution modularity can be derived and then propose a kind of adaptive multi resolution modularity that can combine the advantages of different modularity by applying the modularity to various synthetic and real world networks we study the behaviors of the methods showing the validity and advantages of the multi resolution modularity in community detection the adaptive modularity as a kind of multi resolution method can naturally solve the first type limit of modularity and detect communities at different scales it can quicken the disconnecting of communities and delay the breakup of communities in heterogeneous networks and thus it is expected to generate the stable community structures in networks more effectively and have stronger tolerance against the second type limit of modularity

quadratic program based modularity maximization for fuzzy community detection in social networks one of the most important elements of social network analysis is community detection i e finding groups of similar people based on their traits in this paper we present the fuzzy modularity maximization fmm approach for community detection which finds overlapping that is fuzzy communities where appropriate by maximizing a generalized form of newman s modularity the first proposed fmm solution uses a tree based structure to find a globally optimal solution while the second proposed solution uses alternating optimization to efficiently search for a locally optimal solution both of these approaches are based on a proposed algorithm called one step modularity maximization osmm which computes the optimal cluster memberships for one person in the social network we prove that osmm can be formulated as a simplified quadratic knapsack optimization problem which is o n time complexity we then propose a tree based algorithm called fmm find best leaf node fmm fbln which represents sequences of osmm steps in a tree based structure it is proved that fmm fbln finds globally optimal solutions for fmm however the time complexity of fmm fbln is o n d d ge 2 thus it is impractical for most real world networks to combat this inefficiency we propose five heuristic based alternating optimization schemes i e fmm h1 h5 which are all shown to be o n 2 time complexity we compare the results of the fmm h solutions with those of state of the art community detection algorithms multicut spectral fcm msfcm and gals and with those of two fuzzy community detection algorithms called ga and vertex similarity based gradient descent method vsgd on ten real world datasets we conclude that one of the five heuristic algorithms fmm h2 is very competitive with gals and much more effective than msfcm ga and vsgd furthermore all of the fmm h schemes are at least two orders of magnitude faster than gals in run time finally fmm h unlike gals which only produces crisp partitions and msfcm which always finds fuzzy partitions is the only fuzzy community detection algorithm to date that can find the max modularity partition fuzzy or crisp

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

ordered community structure in networks abstract community structure in networks is often a consequence of homophily or assortative mixing based on some attribute of the vertices for example researchers may be grouped into communities corresponding to their research topic this is possible if vertex attributes have unordered discrete values but many networks exhibit assortative mixing by some ordered discrete or continuous attribute such as age or geographical location in such cases the identification of discrete communities may be difficult or impossible we consider how the notion of community structure can be generalized to networks that have assortative mixing by ordered attributes we propose a method of generating synthetic networks with ordered communities and investigate the effect of ordered community structure on the spread of infectious diseases we also show that current community detection algorithms fail to recover community structure in ordered networks and evaluate an alternative method using a layout algorithm to recover the ordering

detecting communities by the core vertex and intimate degree in complex networks abstract in this paper we present a new approach to extract communities in the complex networks with considerable accuracy we introduce the core vertex and the intimate degree between the community and its neighboring vertices first we find the core vertices as the initial community these core vertices are then expanded using intimate degree function during extracting community structure from the given network in addition our algorithm successfully finds common nodes between communities experimental results using some real world networks data shows that the performance of our algorithm is satisfactory

detection of community structure in networks based on community coefficients abstract determining community structure in networks is fundamental to the analysis of the structural and functional properties of those networks including social networks computer networks and biological networks modularity function q which was proposed by newman and girvan was once the most widely used criterion for evaluating the partition of a network into communities however modularity q is subject to a serious resolution limit in this paper we propose a new function for evaluating the partition of a network into communities this is called community coefficient c using community coefficient c we can automatically identify the ideal number of communities in the network without any prior knowledge we demonstrate that community coefficient c is superior to the modularity q and does not have a resolution limit we also compared the two widely used community structure partitioning methods the hierarchical partitioning algorithm and the normalized cuts ncut spectral partitioning algorithm we tested these methods on computer generated networks and real world networks whose community structures were already known the ncut algorithm and community coefficient c were found to produce better results than hierarchical algorithms unlike several other community detection methods the proposed method effectively partitioned the networks into different community structures and indicated the correct number of communities

the effects of membership function on fuzzy reasoning abstract fuzzy modus ponens has been considered a generalization of the classic modus ponens logic inference rule it has been expected to provide a more powerful and useful inference capability in the process of fuzzy reasoning the definitions of membership functions of fuzzy sets used in the reasoning process may however adversely affect the reasoning results if the insignificant parts of the membership functions are incompatible this paper explains these undesirable effects and proposes a method to resolve this problem in addition an algorithm for the compositional rule of inference is developed to perform the fuzzy modus ponens syllogism test results shown in this paper indicate that the algorithm and the underlying proposed methods are reasonable approaches to a robust fuzzy logic reasoning system

network ensemble comparisons with stochastic rewiring and von neumann entropy assessing whether a given network is typical or atypical for a random network ensemble i e network ensemble comparison has widespread applications ranging from null model selection and hypothesis testing to clustering and classifying networks we develop a framework for network ensemble comparison by subjecting the network to stochastic rewiring we study two rewiring processes uniform and degree preserved rewiring which yield random network ensembles that converge to the erdos renyi and configuration model ensembles respectively we study convergence through von neumann entropy vne a network summary statistic measuring information content based on the spectra of a laplacian matrix and develop a perturbation analysis for the expected effect of rewiring on vne our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble offering a computationally efficient quantity for network ensemble comparison that does not require

fuzzy control theory the linear case abstract a linear fuzzy proportional integral pi controller with one input and one output is defined in terms of piecewise linear membership functions for fuzzification control rules and defuzzification algorithm it is shown that a linear fuzzy controller is not equivalent to a linear non fuzzy pi controller if the rules are evaluated using the zadeh probability or lukasiewicz fuzzy logic alone however the linear fuzzy controller is precisely equivalent to a linear non fuzzy pi controller if mixed fuzzy logic is used to evaluate the control rules when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves this finding has relevance to the selection of fuzzy logics in fuzzy expert systems and for fuzzy logics in general

a weighted nitsche stabilized method for small sliding contact on frictional surfaces abstract we propose a weighted nitsche framework for small sliding frictional contact problems on three dimensional interfaces the proposed method inherits the advantages of both augmented lagrange multiplier and penalty methods while also addressing their shortcomings algorithmic details of the traction update and consistent linearization in the presence of nitsche terms are provided several benchmark numerical experiments are conducted and the results are compared with existing studies the results are encouraging and indicate accurate satisfaction of the non interpenetration constraint stable tractions and asymptotic quadratic convergence of the newton raphson method

fast graph clustering with a new description model for community detection efficiently describing and discovering communities in a network is an important research concept for graph clustering in the paper we present a community description model that evaluates the local importance of a node in a community and its importance concentration in all communities to reflect its representability to the community based on the description model we propose a new evaluation criterion and an iterative search algorithm for community detection iscd the new algorithm can quickly discover communities in a large scale network due to the average linear time complexity with the number of edges furthermore we provide an initial method of input parameters including the number of communities and the initial partition before algorithm implementation which can enhance the local search quality of the iterative algorithm the proposed algorithm with the initial method is called iscd finally we compare the effectiveness and efficiency of the iscd algorithm with six representative algorithms on several real network data sets the experimental results illustrate that the proposed algorithm is suitable to address large scale networks

stablization of an inverted pendulum by a high speed fuzzy logic controller hardware system abstract a high speed fuzzy controller hardware system employing min max operations is presented it has fifteen control rule boards and one defuzzifier grades of membership are represented with 0 v 5 v corresponding to 0 0 1 0 this fuzzy controller facilitates approximate reasoning at 1 000 000 fips fuzzy inferences per second and is able to be used for various purposes by programming on each control rule board it handles fuzzy linguistic information of the form nl negative large nm negative medium ns negative small zr approximately zero ps positive small pm positive medium pl positive large and ng negation this fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules two pendulums 5 mm diameter 15 cm length 3 5 g weight respectively 10 mm 50 cm and 50 g can be stabilized by the same rule set it is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum this fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite an automatic aircraft landing system pattern recognition stabilization of nuclear fuel rods in a reactor an intelligent sensor and many other applications which need swift approximate reasoning

detecting network communities by propagating labels under constraints we investigate the recently proposed label propagation algorithm lpa for identifying network communities we reformulate the lpa as an equivalent optimization problem giving an objective function whose maxima correspond to community solutions by considering properties of the objective function we identify conceptual and practical drawbacks of the label propagation approach most importantly the disparity between increasing the value of the objective function and improving the quality of communities found to address the drawbacks we modify the objective function in the optimization problem producing a variety of algorithms that propagate labels subject to constraints of particular interest is a variant that maximizes the modularity measure of community quality performance properties and implementation details of the proposed algorithms are discussed bipartite as well as unipartite networks are considered

optimizing at the ergodic edge abstract using a simple annealed model some of the key features of the recently introduced extremal optimization heuristic are demonstrated in particular it is shown that the dynamics of local search possesses a generic critical point under the variation of its sole parameter separating phases of too greedy non ergodic jammed and too random ergodic exploration comparison of various local search methods within this model suggests that the existence of the critical point is essential for the optimal performance of the heuristic

community mining with new node similarity by incorporating both global and local topological knowledge in a constrained random walk abstract detection of community is a crucial step to understand the structure and dynamics of complex networks most of conventional community detection methods focus on optimizing a certain objective function or on clustering nodes based on their similarities which leads to a phenomenon that they have preference for specific types of networks but are not general using constrained random walk we exploit global and local topology structures of network to propose a modified transition matrix and further to define a new similarity metric named isim between two nodes in contrast to the existing similarities isim does not work directly on the observed data but in a convergent stable space this feature makes isim robust to the observed noisy data in real world networks isim not only measures node s distance but also captures node s topology structure in network experiments on synthetic and real world networks demonstrate that isim can be successfully applied to community detection in broader types of networks and outperforms other community detection methods

exploring the structural regularities in networks in this paper we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups specifically we propose a general statistical model to describe network structure in this model a group is viewed as a hidden or unobserved quantity and it is learned by fitting the observed network data using the expectation maximization algorithm compared with existing models the most prominent strength of our model is the high flexibility this strength enables it to possess the advantages of existing models and to overcome their shortcomings in a unified way as a result not only can broad types of structure be detected without prior knowledge of the type of intrinsic regularities existing in the target network but also the type of identified structure can be directly learned from the network moreover by differentiating outgoing edges from incoming edges our model can detect several types of structural regularities beyond competing models tests on a number of real world and artificial networks demonstrate that our model outperforms the state of the art model in shedding light on the structural regularities of networks including the overlapping community structure multipartite structure and several other types of structure which are beyond the capability of existing models

modularity from fluctuations in random graphs and complex networks the mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection we show that finding the modularity of a network is analogous to finding the ground state energy of a spin system moreover we demonstrate that due to fluctuations stochastic network models give rise to modular networks specifically we show both numerically and analytically that random graphs and scale free networks have modularity we argue that this fact must be taken into consideration to define statistically significant modularity in complex networks

partition of networks into basins of attraction we study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree each node is associated with or attracted to its neighbor of maximal degree as long as the degree is increasing a node that has no neighbors of higher degree is a peak attracting all the nodes in its basin maximally random scale free networks exhibit different behavior based on their degree distribution exponent gamma for small gamma broad distribution networks are dominated by a giant basin whereas for large gamma narrow distribution there are numerous basins with peaks attracting mainly their nearest neighbors we derive expressions for the first two moments of the number of basins we also obtain the complete distribution of basin sizes for a class of hierarchical deterministic scale free networks that resemble random nets finally we generalize the problem to regular networks and lattices where all degrees are equal and thus the attractiveness of a node must be determined by an assigned weight rather than the degree we derive the complete distribution of basins of attraction resulting from randomly assigned weights in one dimensional chains

limits of modularity maximization in community detection modularity maximization is the most popular technique for the detection of community structure in graphs the resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure with tunable resolution parameters we show that multiresolution modularity suffers from two opposite coexisting problems the tendency to merge small subgraphs which dominates when the resolution is low the tendency to split large subgraphs which dominates when the resolution is high in benchmark networks with heterogeneous distributions of cluster sizes the simultaneous elimination of both biases is not possible and multiresolution modularity is not capable to recover the planted community structure not even when it is pronounced and easily detectable by other methods for any value of the resolution parameter this holds for other multiresolution techniques and it is likely to be a general problem of methods based on global optimization

detecting community structure in complex networks based on a measure of information discrepancy abstract properties of complex networks such as small world property power law degree distribution network transitivity and network community structure which seem to be common to many real world networks have attracted great interest among researchers in this study global information of the networks is considered by defining the profile of any node based on the shortest paths between it and all the other nodes in the network then a useful iterative procedure for community detection based on a measure of information discrepancy and the popular modular function q is presented the new iterative method does not need any prior knowledge about the community structure and can detect an appropriate number of communities which can be hub communities or non hub communities the computational results of the method on real networks confirm its capability

a variational multiscale method for inelasticity application to superelasticity in shape memory alloys this paper presents a variational multiscale method for developing stabilized finite element formulations for small strain inelasticity the multiscale method arises from a decomposition of the displacement field into coarse resolved and fine unresolved scales the resulting finite element formulation allows arbitrary combinations of interpolation functions for the displacement and the pressure fields and thus yields a family of stable and convergent elements specifically equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition become stable and convergent an important feature of the present method is that it does not lock in the incompressible limit a nonlinear constitutive model for the superelastic behavior of shape memory alloys is integrated in the multiscale formulation numerical tests of the performance of the elements are presented and representative simulations of the superelastic behavior of shape memory alloys are shown 2005 elsevier b v all rights reserved

primal interface formulation for coupling multiple pdes a consistent derivation via the variational multiscale method abstract this paper presents a primal interface formulation that is derived in a systematic manner from a lagrange multiplier method to provide a consistent framework to couple different partial differential equations pde as well as to tie together nonconforming meshes the derivation relies crucially on concepts from the variational multiscale vms approach wherein an additive multiscale decomposition is applied to the primary solution field modeling the fine scales locally at the interface using bubble functions consistent residual based terms on the boundary are obtained that are subsequently embedded into the coarse scale problem the resulting stabilized lagrange multiplier formulation is converted into a robust discontinuous galerkin dg method by employing a discontinuous interpolation of the multipliers along the segments of the interface as a byproduct analytical expressions are derived for the stabilizing terms and weighted numerical flux that reflect the jump in material properties governing equation or element geometry across the interface also a procedure is proposed for automatically generating the fine scale bubble functions that is inspired by a performance study of residual free bubbles for the interface problem a series of numerical tests confirms the robustness of the method for solving interface problems with heterogeneous elements materials and or governing equations and also highlights the benefit and importance of deriving the flux and stabilization terms

identifying overlapping communities in networks using evolutionary method abstract community structure is a typical property of real world networks and has been recognized as a key to understand the dynamics of the networked systems in most of the networks overwhelming nodes apparently live in a community while there often exists a few nodes straddling several communities hence an ideal algorithm for community detection is that which can identify the overlapping communities in these networks we present an evolutionary method for detecting overlapping community structure in the network to represent an overlapping division of a network we develop an encoding scheme composed of two segments the first one represents a disjoint partition and the second one represents an extension of the partition that allows of multiple memberships we give two measures for the informativeness of a node and present a coevolutionary scheme between two segments over the population for solving the overlapping partition of the network experimental results show this method can give a better solution to a network it is also revealed that a best overlapping partition of the network might not be rooted from a best disjoint partition

loops and multiple edges in modularity maximization of networks the modularity maximization model proposed by newman and girvan for the identification of communities in networks works for general graphs possibly with loops and multiple edges however the applications usually correspond to simple graphs these graphs are compared to a null model where the degree distribution is maintained but edges are placed at random therefore in this null model there will be loops and possibly multiple edges sharp bounds on the expected number of loops and their impact on the modularity are derived then building upon the work of massen and doye but using algebra rather than simulation we propose modified null models associated with graphs without loops but with multiple edges graphs with loops but without multiple edges and graphs without loops nor multiple edges we validate our models by using the exact algorithm for clique partitioning of grotschel and wakabayashi

spectral methods for community detection and graph partitioning we consider three distinct and well studied problems concerning network structure community detection by modularity maximization community detection by statistical inference and normalized cut graph partitioning each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network we show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are in fact identical and hence that at least within the spectral approximations used here there is no difference between the modularity and inference based community detection methods or between either and graph partitioning

quantum behaved discrete multi objective particle swarm optimization for complex network clustering abstract complex network research has attracted lots of attention in both academic community and various application fields complex network clustering as one of the key issues in complex network explores the internal organization of the nodes in a complex network the discrete particle swarm optimization strategy has been successfully proposed for network clustering while the existing method works with weak robust in this paper we model the task of complex network clustering as a multi objective optimization problem and solve the problem with the quantum mechanism based particle swarm optimization algorithm which is a parallel algorithm to our knowledge this is the first attempt to apply the quantum mechanism based discrete particle swarm optimization algorithm into network clustering in addition the non dominant sorting selection operation is employed for individual replacement consequently a quantum behaved discrete multi objective particle swarm optimization algorithm is proposed for complex network clustering the experimental results demonstrate that the proposed algorithm performs effectively and achieves competitive performance with the state of the art approaches on the extension of girvan and newman benchmarks and real world networks especially on large scale networks

semi supervised community detection based on discrete potential theory abstract in recent studies of the complex network most of the community detection methods only consider the network topological structure without background information this leads to a relatively low accuracy in this paper a novel semi supervised community detection algorithm is proposed based on the discrete potential theory it effectively incorporates individual labels the labels of corresponding communities to guide the community detection process for achieving better accuracy specifically a number of vertices with user defined labels are first identified to act as unit elementary charges which can generate different electrostatic fields then community detection can be translated into a potential transmission problem by formulating the problem using combinational dirichlet labels of those unlabeled vertices can be determined by the labels for which the greatest potential is calculated finally a better community partition can be obtained our extensive numerical experiments in both artificial and real networks lead to two key observations first individual labels play an important role in community detection and second our proposed semi supervised community detection algorithm outperforms existing counterparts in both accuracy and time complexity especially for obscure networks

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

neuro fuzzy rule generation survey in soft computing framework the present article is a novel attempt in providing an exhaustive survey of neuro fuzzy rule generation algorithms rule generation from artificial neural networks is gaining in popularity in recent times due to its capability of providing some insight to the user about the symbolic knowledge embedded within the network fuzzy sets are an aid in providing this information in a more human comprehensible or natural form and can handle uncertainties at various levels the neuro fuzzy approach symbiotically combining the merits of connectionist and fuzzy approaches constitutes a key component of soft computing at this stage to date there has been no detailed and integrated categorization of the various neuro fuzzy models used for rule generation we propose to bring these together under a unified soft computing framework moreover we include both rule extraction and rule refinement in the broader perspective of rule generation rules learned and generated for fuzzy reasoning and fuzzy control are also considered from this wider viewpoint models are grouped on the basis of their level of neuro fuzzy synthesis use of other soft computing tools like genetic algorithms and rough sets are emphasized rule generation from fuzzy knowledge based networks which initially encode some crude domain knowledge are found to result in more refined rules finally real life application to medical diagnosis is provided

uncovering the overlapping community structure of complex networks by maximal cliques abstract in this paper a unique algorithm is proposed to detect overlapping communities in the un weighted and weighted networks with considerable accuracy the maximal cliques overlapping vertex bridge vertex and isolated vertex are introduced first all the maximal cliques are extracted by the algorithm based on the deep and bread searching then two maximal cliques can be merged into a larger sub graph by some given rules in addition the proposed algorithm successfully finds overlapping vertices and bridge vertices between communities experimental results using some real world networks data show that the performance of the proposed algorithm is satisfactory

locally optimal heuristic for modularity maximization of networks community detection in networks based on modularity maximization is currently done with hierarchical divisive or agglomerative as well as partitioning heuristics hybrids and in a few papers exact algorithms we consider here the case of hierarchical networks in which communities should be detected and propose a divisive heuristic which is locally optimal in the sense that each of the successive bipartitions is done in a provably optimal way this heuristic is compared with the spectral based hierarchical divisive heuristic of newman proc natl acad sci usa 103 8577 2006 and with the hierarchical agglomerative heuristic of clauset newman and moore phys rev e 70 066111 2004 computational results are given for a series of problems of the literature with up to 4941 vertices and 6594 edges they show that the proposed divisive heuristic gives better results than the divisive heuristic of newman and than the agglomerative heuristic of clauset et al

parameterized centrality metric for network analysis a variety of metrics have been proposed to measure the relative importance of nodes in a network one of these alpha centrality p bonacich am j sociol 92 1170 1987 measures the number of attenuated paths that exist between nodes we introduce a normalized version of this metric and use it to study network structure for example to rank nodes and find community structure of the network specifically we extend the modularity maximization method for community detection to use this metric as the measure of node connectivity normalized alpha centrality is a powerful tool for network analysis since it contains a tunable parameter that sets the length scale of interactions studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures we apply the proposed metric to several benchmark networks and show that it leads to better insights into network structure than alternative metrics

on the issue of defuzzification and selection based on a fuzzy set abstract we are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set a problem which manifests itself in the defuzzification step in fuzzy logic controllers we provide a unifying approach to this selection process among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework we show that this selection can be viewed as a three step operation transformation of the decision fuzzy set normalization to probability distribution selection based on the probability distribution a number of different procedures for selection are discussed

a variational multiscale a posteriori error estimation method for mixed form of nearly incompressible elasticity this paper presents an error estimation framework for a mixed displacement pressure finite element method for nearly incompressible elasticity the proposed method is based on variational multiscale vms concepts wherein the displacement field is decomposed into coarse scales that can be resolved by a given finite element mesh and fine scales that are beyond the resolution capacity of the mesh variational projection of fine scales onto the coarse scale space via variational embedding of the fine scale solution into the coarse scale formulation leads to the stabilized method with two major attributes first it is free of volumetric locking and second it accommodates arbitrary combinations of interpolation functions for the displacement and pressure fields this vms based stabilized method is equipped with naturally derived error estimators and offers various options for numerical computation of the error specifically two error estimators are explored the first method employs an element based strategy and a representation of error via a fine scale error equation defined over element interiors which is evaluated by a direct post solution evaluation this quantity when combined with the global pollution error results in a simple explicit error estimator the second method involves solving the fine scale error equation through localization to overlapping patches spread across the domain thereby leading to an implicit calculation of the local error this implicit calculation when combined with the global pollution error results in an implicit error estimator the performance of the stabilized method and the error estimators is investigated through numerical convergence tests conducted for two model problems on uniform and distorted meshes the sharpness and robustness of the estimators is shown to be consistent across the test cases employed

handling the nonlinearity of a fuzzy logic controller at the transition between rules abstract a fuzzy logic controller approximates a desired control surface by using the outputs of its fuzzy control rules the shape of this control surface is mainly influenced by the linguistic variables of the rule base the basic operators of the fuzzy sets the implication the inference and the defuzzification method the linearity nonlinearity of this control surface is discussed in many studies however none of those studies has explicitly considered the linearity nonlinearity at the transition between fuzzy logic rules in this paper a simple approach to control the linearity nonlinearity at this transition by a modified center of gravity defuzzification method is proposed namely by introducing the so called defuzzification weights to the overlapping areas of the consequent those defuzzification weights can be determined heuristically or automatically both cases will be demonstrated for the latter a feedforward neural network is employed