a coupled finite volume solver for the solution of incompressible flows on unstructured grids this paper reports on a newly developed fully coupled pressure based algorithm for the solution of laminar incompressible flow problems on collocated unstructured grids the implicit pressure velocity coupling is accomplished by deriving a pressure equation in a procedure similar to a segregated simple algorithm using the rhie chow interpolation technique and assembling the coefficients of the momentum and continuity equations into one diagonally dominant matrix the extended systems of continuity and momentum equations are solved simultaneously and their convergence is accelerated by using an algebraic multigrid solver the performance of the coupled approach as compared to the segregated approach exemplified by simple is tested by solving five laminar flow problems using both methodologies and comparing their computational costs results indicate that the number of iterations needed by the coupled solver for the solution to converge to a desired level on both structured and unstructured meshes is grid independent for relatively coarse meshes the cpu time required by the coupled solver on structured grid is lower than the cpu time required on unstructured grid on dense meshes however this is no longer true for low and moderate values of the grid aspect ratio the number of iterations required by the coupled solver remains unchanged while the computational cost slightly increases for structured and unstructured grid systems the required number of iterations is almost independent of the grid size at any value of the grid expansion ratio recorded cpu time values show that the coupled approach substantially reduces the computational cost as compared to the segregated approach with the reduction rate increasing as the grid size increases

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

weighted modularity optimization for crisp and fuzzy community detection in large scale networks abstract community detection is a classic and very difficult task in the field of complex network analysis principally for its applications in domains such as social or biological networks analysis one of the most widely used technologies for community detection in networks is the maximization of the quality function known as modularity however existing work has proved that modularity maximization algorithms for community detection may fail to resolve communities in small size here we present a new community detection method which is able to find crisp and fuzzy communities in undirected and unweighted networks by maximizing weighted modularity the algorithm derives new edge weights using the cosine similarity in order to go around the resolution limit problem then a new local moving heuristic based on weighted modularity optimization is proposed to cluster the updated network finally the set of potentially attractive clusters for each node is computed to further uncover the crisply fuzzy partition of the network we give demonstrative applications of the algorithm to a set of synthetic benchmark networks and six real world networks and find that it outperforms the current state of the art proposals even those aimed at finding overlapping communities in terms of quality and scalability

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

generation of arbitrarily two point correlated random networks random networks are intensively used as null models to investigate properties of complex networks we describe an efficient and accurate algorithm to generate arbitrarily two point degree degree correlated undirected random networks without self edges or multiple edges among vertices with the goal to systematically investigate the influence of two point correlations we furthermore develop a formalism to construct a joint degree distribution p j k which allows one to fix an arbitrary degree distribution p k and an arbitrary average nearest neighbor function k nn k simultaneously using the presented algorithm this formalism is demonstrated with scale free networks p k proportional variantk gamma and empirical complex networks p k taken from network as examples finally we generalize our algorithm to annealed networks which allows networks to be represented in a mean field like manner

on the least squares residual anomaly determination this paper discusses an approach to determine the least squares optimum order of the regional surface which when subtracted from the bouguer gravity anomaly data minimizes distortion of the residual component of the field the least squares method was applied to theoretical composite gravity fields each consisting of a constant residual component sphere or vertical cylinder and a regional component of different order using successively increasing orders of polynomial regionals for residual determination the overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables similarity between residual maps of the lowest orders verified by good correlation may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component the residual map of the lower order in this well correlated doublet is considered the most plausible one and may be used

genuinely multidimensional upwinding for the 2d shallow water equations a multidimensional upwinding technique is applied to the simulation of 2d shallow water flows it is adapted from fluctuation splitting methods recently proposed for the solution of the euler system of equations on unstructured triangular grids the basis of the numerical method is stated and the particular adaptation to the shallow water system is described numerical results of interest to hydraulic engineers are presented despite the complexities advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use

an explicit residual based approach for shallow water flows we describe fully explicit residual based discretizations of the shallow water equations with friction on unstructured grids the schemes are obtained by properly adapting the explicit construction proposed in ricchiuto and abgrall 2010 57 in particular previous work on well balanced integration ricchiuto 2011 56 and preservation of the depth non negativity ricchiuto and bollermann 2009 60 is reformulated in the context of a genuinely explicit time stepping still based on a weighted residual approximation the paper discusses in depth how to achieve in this context an exact preservation of all the simple known steady equilibria and how to obtain a super consistent approximation for smooth non trivial moving equilibria the treatment of the wetting drying interface is also discussed giving formal conditions for the preservation of the non negativity of the depth for a particular case based on a nonlinear variant of a lax friedrichs type scheme the approach is analyzed and tested thoroughly the quality of the numerical results shows the interest in the proposed approach over previously proposed schemes in terms of accuracy and efficiency

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

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

identification of intrinsic long range degree correlations in complex networks many real world networks exhibit degree degree correlations between nodes separated by more than one step such long range degree correlations lrdcs can be fully described by one joint and four conditional probability distributions with respect to degrees of two randomly chosen nodes and shortest path distance between them while lrdcs are induced by nearest neighbor degree correlations nndcs between adjacent nodes some networks possess intrinsic lrdcs which cannot be generated by nndcs here we develop a method to extract intrinsic lrdc in a correlated network by comparing the probability distributions for the given network with those for nearest neighbor correlated random networks we also demonstrate the utility of our method by applying it to several real world networks

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

a validity index approach for network partitions abstract the validity index has been used to evaluate the fitness of partitions produced by clustering algorithms for points in euclidean space in this paper we propose a new validity index for network partitions which can provide a measure of goodness for the community structure of networks it is defined as a product of two factors and involves the compactness and separation for each partition the simulated annealing strategy is used to minimize such a validity index function in coordination with our previous k means algorithm based on the optimal reduction of a random walker markovian dynamics on the network it is demonstrated that the algorithm can efficiently find the community structure during the cooling process the number of communities can be automatically determined without any prior knowledge of the community structure moreover the algorithm is successfully applied to three real world networks

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

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

shape and depth solutions from gravity data using correlation factors between successive least squares residuals the gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape shape factor and depth variables with an amplitude coefficient related to the mass correlation factors between successive least squares residual gravity anomalies from a buried vertical cylinder horizontal cylinder and sphere are used to determine the shape and depth of the buried geologic structure for each shape factor value the depth is determined automatically from the correlation value the computed depths are plotted against the shape factor representing a continuous correlation curve the solution for the shape and depth of the buried structure is read at the common intersection of correlation curves this method can be applied to a bouguer anomaly profile consisting of a residual component caused by local structure and a regional component this is a powerful technique for automatically separating the bouguer data into residual and regional polynomial components this method is tested on theoretical examples and a field example in both cases the results obtained are in good agreement with drilling results

grid independent upwind scheme for multidimensional flow recent advances in the development of a grid independent finite volume scheme for the euler equations of gas dynamics are described in the proposed method flowfield gradient data are reconstructed locally on a triangle using five elementary planar waves and an upwind numerical flux function for grid oblique waves is developed to model the effect of the passage of these waves on the data in a cell numerical examples for several two dimensional test problems are included

clustering coefficient and community structure of bipartite networks abstract many real world networks display natural bipartite structure where the basic cycle is a square in this paper with the similar consideration of standard clustering coefficient in binary networks a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed in order to detect community structures in bipartite networks two different edge clustering coefficients l c 4 and l c 3 of bipartite networks are defined which are based on squares and triples respectively with the algorithm of cutting the edge with the least clustering coefficient communities in artificial and real world networks are identified the results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks

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

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

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

anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

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

resilience to damage of graphs with degree correlations the existence or nonexistence of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking in this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena we obtain some general expressions that allow the computation of the transition thresholds or their bounds using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks

accurate flux vector splitting for shocks and shear layers a multidimensional upwinding technique is applied to the simulation of 2d shallow water flows it is adapted from fluctuation splitting methods recently proposed for the solution of the euler system of equations on unstructured triangular grids the basis of the numerical method is state and the particular adaptation to the shallow water system is described numerical results of interest to hydraulic engineers are presented despite the complexities advantages related to the use of a discretisation based on triangles would seem to make the schemes competitive with those currently in use 16 refs 23 figs

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

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

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

semi supervised clustering algorithm for community structure detection in complex networks abstract discovering a community structure is fundamental for uncovering the links between structure and function in complex networks in this paper we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization snmf and the maximum optimization of modularity density based on this equivalence we develop a new algorithm named the so called snmf ss by combining snmf and a semi supervised clustering approach previous nmf based algorithms often suffer from the restriction of measuring network topology from only one perspective but our algorithm uses a semi supervised mechanism to get rid of the restriction the algorithm is illustrated and compared with spectral clustering and nmf by using artificial examples and other classic real world networks experimental results show the significance of the proposed approach particularly in the cases when community structure is obscure

general formulation of long range degree correlations in complex networks we provide a general framework for analyzing degree correlations between nodes separated by more than one step i e beyond nearest neighbors in complex networks one joint and four conditional probability distributions are introduced to fully describe long range degree correlations with respect to degrees k and k of two nodes and shortest path length l between them we present general relations among these probability distributions and clarify the relevance to nearest neighbor degree correlations unlike nearest neighbor correlations some of these probability distributions are meaningful only in finite size networks furthermore as a baseline to determine the existence of intrinsic long range degree correlations in a network other than inevitable correlations caused by the finite size effect the functional forms of these probability distributions for random networks are analytically evaluated within a mean field approximation the utility of our argument is demonstrated by applying it to real world networks

on computing the diameter of real world undirected graphs we propose a new algorithm for the classical problem of computing the diameter of undirected unweighted graphs namely the maximum distance among all the pairs of nodes where the distance of a pair of nodes is the number of edges contained in the shortest path connecting these two nodes although its worst case complexity is o nm time where n is the number of nodes and m is the number of edges of the graph we experimentally show that our algorithm works in o m time in practice requiring few breadth first searches to complete its task on almost 200 real world graphs

reshuffling scale free networks from random to assortative to analyze the role of assortativity in networks we introduce an algorithm which produces assortative mixing to a desired degree this degree is governed by one parameter p changing this parameter one can construct networks ranging from fully random p 0 to totally assortative p 1 we apply the algorithm to a barabasi albert scale free network and show that the degree of assortativity is an important parameter governing the geometrical and transport properties of networks thus the average path length of the network increases dramatically with the degree of assortativity moreover the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different the behavior of the clustering coefficient is also discussed

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

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

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

adaptive extremal optimization by detrended fluctuation analysis global optimization is one of the key challenges in computational physics as several problems e g protein structure prediction the low energy landscape of atomic clusters detection of community structures in networks or model parameter fitting can be formulated as global optimization problems extremal optimization eo has become in recent years one particular successful approach to the global optimization problem as with almost all other global optimization approaches eo is driven by an internal dynamics that depends crucially on one or more parameters recently the existence of an optimal scheme for this internal parameter of eo was proven so as to maximize the performance of the algorithm however this proof was not constructive that is one cannot use it to deduce the optimal parameter itself a priori in this study we analyze the dynamics of eo for a test problem spin glasses based on the results we propose an online measure of the performance of eo and a way to use this insight to reformulate the eo algorithm in order to construct optimal values of the internal parameter online without any input by the user this approach will ultimately allow us to make eo parameter free and thus its application in general global optimization problems much more efficient

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

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

statistical significance of communities in networks nodes in real world networks are usually organized in local modules these groups called communities are intuitively defined as subgraphs with a larger density of internal connections than of external links in this work we define a measure aimed at quantifying the statistical significance of single communities extreme and order statistics are used to predict the statistics associated with individual clusters in random graphs these distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph the method is successfully applied in the case of real world networks for the evaluation of the significance of their communities

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

epidemic spreading in correlated complex networks we study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node s connectivities for the case of markovian complex networks showing only correlations between pairs of nodes we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links which from a node with connectivity k go to nodes with connectivity k ensuremath numerical simulations on a correlated growing network model provide support for our conclusions

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

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

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

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

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

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

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

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

modularity optimization by conformational space annealing we propose a modularity optimization method mod csa based on stochastic global optimization algorithm conformational space annealing csa our method outperforms simulated annealing in terms of both efficiency and accuracy finding higher modularity partitions with less computational resources required the high modularity values found by our method are higher than or equal to the largest values previously reported in addition the method can be combined with other heuristic methods and implemented in parallel fashion allowing it to be applicable to large graphs with more than 10 000 nodes

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

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

asymptotic properties of degree correlated scale free networks the possible correlation profiles of networks with a given scale free degree distribution are restricted and bounded by maximally correlated configurations dissortative networks consist of nested bilayers in which low degree vertices are connected to high degree vertices the number of these bilayers attains a constant value for large network size n assortative networks exhibit monolayers of low degree vertices the number of which grows monotonously with n analytical relations for the pearson correlation coefficient r of these extremal configurations are derived and shown to provide lower and upper bounds on the possible r values both bounds are found to vanish for large networks

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

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

measuring mixing patterns in complex networks by spearman rank correlation coefficient abstract in this paper we utilize spearman rank correlation coefficient to measure mixing patterns in complex networks compared with the widely used pearson coefficient spearman coefficient is rank based nonparametric and size independent thus it is more effective to assess linking patterns of diverse networks especially for large size networks we demonstrate this point by testing a variety of empirical and artificial networks moreover we show that normalized spearman ranks of stubs are subject to an interesting linear rule where the correlation coefficient is just the spearman coefficient this compelling linear relationship allows us to directly produce networks with any prescribed spearman coefficient our method apparently has an edge over the well known uncorrelated configuration model

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

response of degree correlated scale free networks to stimuli the response of degree correlated scale free attractor networks to stimuli is studied we show that degree correlated scale free networks are robust to random stimuli as well as the uncorrelated scale free networks while assortative disassortative scale free networks are more less sensitive to directed stimuli than uncorrelated networks we find that the degree correlation of scale free networks makes the dynamics of attractor systems different from uncorrelated ones the dynamics of correlated scale free attractor networks results in the effects of degree correlation on the response to stimuli

measuring degree degree association in networks the pearson correlation coefficient is commonly used for quantifying the global level of degree degree association in complex networks here we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy tailed degree distributions theoretical arguments together with our numerical study indicate that pearson s coefficient often depends on the size of networks with equal association structure impeding a systematic comparison of real world networks in contrast kendall gibbons ensuremath tau b is a considerably more robust measure of the degree degree association

unsteady free surface flow simulation over complex topography with a multidimensional upwind technique in the context of numerical techniques for solving unsteady free surface problems finite element and finite volume approximations are widely used a class of upwind methods which attempts to model the equations in a genuinely multidimensional manner has been recently introduced as an alternative multidimensional upwind schemes mus were developed initially for the approximation of steady state solutions of the two dimensional euler equations on unstructured grids although they can be applicable to any system of hyperbolic conservation laws such as the shallow water equations the formal analogy between the two systems of equations is useful for simple cases however in practical applications of interest in hydraulics complex geometries and bottom slope variation can lead to important numerical errors produced by an inadequate source term discretization this problem has been analyzed and in this work the necessity of a multidimensional upwind discretization of the source terms is justified the basis of the numerical method is stated and the particular adaptation to unsteady shallow water flows over irregular geometry is described as test cases laboratory experimental data are used together with academic tests for validation

three least squares minimization approaches to depth shape and amplitude coefficient determination from gravity data three different least squares approaches are developed to determine successively the depth shape shape factor and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly by defining the anomaly value g max at the origin on the profile the problem of depth determination is transformed into the problem of solving a nonlinear equation f z 0 formulas are derived for spheres and cylinders knowing the depth and applying the least squares method the shape factor and the amplitude coefficient are determined using two simple linear equations in this way the depth shape and amplitude coefficient are determined individually from all observed gravity data a procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources the method is applied to synthetic data with and without random errors in all the cases examined the maximum error in depth shape and amplitude coeffic

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

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

zero pearson coefficient for strongly correlated growing trees we obtained pearson s coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by m edges we found that the pearson coefficient is exactly zero in the infinite network limit for the recursive trees m 1 if the number of connections of new vertices exceeds one mg1 then the pearson coefficient in the infinite networks equals zero only when the degree distribution exponent ensuremath gamma does not exceed 4 we calculated the pearson coefficient for finite networks and observed a slow power law like approach to an infinite network limit our findings indicate that pearson s coefficient strongly depends on size and details of networks which makes this characteristic virtually useless for quantitative comparison of different networks

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

selection of influential spreaders in complex networks using pareto shell decomposition abstract the selection of prominent nodes in order to maximize the ability of spreading is very crucial in complex networks the well known k shell method which comprises nodes located at the core of a network is better than the degree centrality and betweenness centrality in capturing the spreading ability for a single origin spreader as per the multiple origin spreaders the k shell method fails to yield similar results when compared to the degree centrality current research proposes a pareto shell decomposition it employs pareto front function it s pareto optimal set comprises non dominated spreads with the ratio of high out degree to in degree and high in degree pareto shell decomposition outperforms the k shell and the degree centrality for multiple origin spreaders with the simulation of epidemic spreading process

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

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

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

upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries in this paper we consider the solution of the enhanced boussinesq equations of madsen and sorensen 1992 55 by means of residual based discretizations in particular we investigate the applicability of upwind and stabilized variants of continuous galerkin finite element and residual distribution schemes for the simulation of wave propagation and transformation over complex bathymetries these techniques have been successfully applied to the solution of the nonlinear shallow water equations see e g hauke 1998 39 and ricchiuto and bollermann 2009 61 in a first step toward the construction of a hybrid model coupling the enhanced boussinesq equations with the shallow water equations in breaking regions this paper shows that equal order and even low order second upwind stabilized techniques can be used to model non hydrostatic wave propagation over complex bathymetries this result is supported by theoretical truncation and dispersion error analyses and by thorough numerical validation

a new method for shape and depth determinations from gravity data we have developed a simple method to determine simultaneously the shape and depth of a buried structure from residualized gravity data using filters of successive window lengths the method is similar to euler deconvolution but it solves for shape and depth independently the method involves using a relationship between the shape factor and the depth to the source and a combination of windowed observations the relationship represents a parametric family of curves window curves for a fixed window length the depth is determined for each shape factor the computed depths are plotted against the shape factors representing a continuous monotonically increasing curve the solution for the shape and depth of the buried structure is read at the common intersection of the window curves this method can be applied to residuals as well as to the bouguer gravity data of a short or long profile length the method is applied to theoretical data with and without random errors and is tested on a known field example from the united states in all cases the shape and depth solutions obtained are in good agreement with the actual ones

modularity density of network community divisions the problem of dividing a network into communities is extremely complex and grows very rapidly with the number of nodes and edges that are involved in order to develop good algorithms to identify optimal community divisions it is extremely beneficial to identify properties that are similar for most networks we introduce the concept of modularity density the distribution of modularity values as a function of the number of communities and find strong indications that the general features of this modularity density are quite similar for different networks the region of high modularity generally has very low probability density and occurs where the number of communities is small the properties and shape of the modularity density may give valuable information and aid in the search for efficient algorithms to find community divisions with high modularities

gravity interpretation using correlation factors between successive least squares residual anomalies the correlation factors between successive least squares residual or regional gravity anomalies from a buried sphere a two dimensional 2 d horizontal cylinder and a vertical cylinder and the first horizontal derivative of the gravity from a 2 d thin faulted layer are computed correlation values are used to determine the depth to the center of the buried structure and the radius of the sphere or the cylinder and the thickness of the fault are estimated the method can be applied not only to residuals but also to the bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order the method is easy to apply and may be automated if desired it can also be applied to the derivative anomalies of the gravity field the validity of the method is tested on two field examples from the united states and denmark

higher derivatives analysis of 2 d magnetic data this paper presents a new approach for determining the depth of a buried structure from numerical second third and fourth horizontal derivative anomalies obtained from 2 d magnetic data using filters of successive graticule spacings the problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form z f z formulas have been derived for a horizontal cylinder and a dike the depths obtained from the second third and fourth derivative anomaly values can be used to determine simultaneously the actual depth to the buried structure and the optimum order of the regional magnetic field along the profile this powerful technique can solve two major potential field problems regional residual separation and depth determination the method is applied to theoretical data with and without random errors and is tested on a field example from arizona

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

replica inference approach to unsupervised multiscale image segmentation we apply a replica inference based potts model method to unsupervised image segmentation on multiple scales this approach was inspired by the statistical mechanics problem of community detection and its phase diagram specifically the problem is cast as identifying tightly bound clusters communities or solutes against a background or solvent within our multiresolution approach we compute information theory based correlations among multiple solutions replicas of the same graph over a range of resolutions significant multiresolution structures are identified by replica correlations manifest by information theory overlaps we further employ such information theory measures such as normalized mutual information and variation of information thermodynamic quantities such as the system entropy and energy and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases within the solvable phase transitions between contending solutions such as those corresponding to segmentations on different scales may also appear with the aid of these correlations as well as thermodynamic measures the phase diagram of the corresponding potts model is analyzed at both zero and finite temperatures optimal parameters corresponding to a sensible unsupervised segmentations appear within the easy phase of the potts model our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images

robust polynomial fitting method for regional gravity estimation standard polynomial fitting methods are inconsistent in their formulation the regional field is approximated by a polynomial fitted to the observed field as a result in addition to the nonuniqueness in the definition of the regional field the fitted polynomial is strongly influenced by the residual field observed field minus regional field we present a regional residual separation method for gravity data which uses a robust procedure to determine the coefficients of a polynomial fitted to the observations under the hypothesis that the regional can be modeled correctly by the polynomial surface the proposed method minimizes the influence of the residual field in the fitted surface the proposed method was applied to real gravity data from ceara state brazil and produced information on zones of possible crustal thickening and the occurrence of lower crustal granulitic rocks thrust into the shallow subsurface