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

community detection in graphs using singular value decomposition a spectral algorithm for community detection is presented the algorithm consists of three stages 1 matrix factorization of two matrix forms square signless laplacian for unipartite graphs and rectangular adjacency matrix for bipartite graphs using singular value decompostion svd 2 dimensionality reduction using an optimal linear approximation and 3 clustering vertices using dot products in reduced dimensional space the algorithm reveals communities in graphs without placing any restriction on the input network type or the output community type it is applicable on unipartite or bipartite unweighted or weighted networks it places no requirement on strict community membership and automatically reveals the number of clusters their respective sizes and overlaps and hierarchical modular organization by representing vertices as vectors in real space expressed as linear combinations of the orthogonal bases described by svd orthogonality becomes the metric for classifying vertices into communities results on several test and real world networks are presented including cases where a mix of disjointed overlapping or hierarchical communities are known to exist in the network

fuzzy communities and the concept of bridgeness in complex networks we consider the problem of fuzzy community detection in networks which complements and expands the concept of overlapping community structure our approach allows each vertex of the graph to belong to multiple communities at the same time determined by exact numerical membership degrees even in the presence of uncertainty in the data being analyzed we create an algorithm for determining the optimal membership degrees with respect to a given goal function based on the membership degrees we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities bridge vertices that have significant membership in more than one single community and regular vertices that fundamentally restrict their interactions within their own community while also being able to quantify the centrality of a vertex with respect to its dominant community the method can also be used for prediction in case of uncertainty in the data set analyzed the number of communities can be given in advance or determined by the algorithm itself using a fuzzified variant of the modularity function the technique is able to discover the fuzzy community structure of different real world networks including but not limited to social networks scientific collaboration networks and cortical networks with high confidence

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

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

statistical models of partial volume effect statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived the models assume either gaussian system sampling noise or intrinsic material variances with gaussian or poisson statistics in particular a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing or the material could have nondistinct values with a poisson distribution as might be the case in nuclear medicine images general forms of the probability density functions are presented for the n material cases and particular forms for two and three material cases are derived these models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component

two stage algorithm using influence coefficient for detecting the hierarchical non overlapping and overlapping community structure abstract community detection is one of the most important problems in complex networks many algorithms have been proposed in the last decade and most of them focus on the non overlapping community structures in the early days overlapping and hierarchical structures are another two important properties in complex networks which have attracted researchers extensive concern in recent years in this paper we proposed a two stage method which can detect the hierarchical non overlapping and overlapping community structures in complex networks in this method the cnm algorithm a fast hierarchical agglomerative algorithm proposed by clauset newman and moore is used in the first stage in the second stage a new evaluation function named as influence coefficient based on the local community structure is proposed which can get the overlapping community structures at different overlapping levels by adjusting a tunable parameter besides the proposed evaluation function can detect the wrongly classified nodes in the partition of the first stage and correct them finally the computational complexity of the algorithm is low the experimental results on both synthetic and real world network datasets show the efficiency of our method

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

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

statistical approach to x ray ct imaging and its applications in image analysis ii a new stochastic model based image segmentation technique for x ray ct image for pt i see ibid vol 11 no 1 p 53 61 1992 based on the statistical properties of x ray ct imaging given in pt i an unsupervised stochastic model based image segmentation technique for x ray ct images is presented this technique utilizes the finite normal mixture distribution and the underlying gaussian random field grf as the stochastic image model the number of image classes in the observed image is detected by information theoretical criteria aic or mdl the parameters of the model are estimated by expectation maximization em and classification maximization cm algorithms image segmentation is performed by a bayesian classifier results from the use of simulated and real x ray computerized tomography ct image data are presented to demonstrate the promise and effectiveness of the proposed technique

partial volume bayesian classification of material mixtures in mr volume data using voxel histograms the authors present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with magnetic resonance imaging mri or computed tomography ct because the authors allow for mixtures of materials and treat voxels as regions their technique reduces errors that other classification techniques can create along boundaries between materials and is particularly useful for creating accurate geometric models and renderings from volume data it also has the potential to make volume measurements more accurately and classifies noisy low resolution data well there are two unusual aspects to the authors approach first they assume that due to partial volume effects or blurring voxels can contain more than one material e g both muscle and fat the authors compute the relative proportion of each material in the voxels second they incorporate information from neighboring voxels into the classification process by reconstructing a continuous function spl rho x from the samples and then looking at the distribution of values that spl rho x takes on within the region of a voxel this distribution of values is represented by a histogram taken over the region of the voxel the mixture of materials that those values measure is identified within the voxel using a probabilistic bayesian approach that matches the histogram by finding the mixture of materials within each voxel most likely to have created the histogram the size of regions that the authors classify is chosen to match the sparing of the samples because the spacing is intrinsically related to the minimum feature size that the reconstructed continuous function can represent

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

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

efficient low redundancy codes for correcting multiple deletions we consider the problem of constructing binary codes to recover from k bit deletions with efficient encoding decoding for a fixed k the single deletion case is well understood with the varshamov tenengolts levenshtein code from 1965 giving an asymptotically optimal construction with approx 2 n n codewords of length n i e at most log n bits of redundancy however even for the case of two deletions there was no known explicit construction with redundancy less than n omega 1 for any fixed k we construct a binary code with c k log n redundancy that can be decoded from k deletions in o k n log 4 n time the coefficient c k can be taken to be o k 2 log k which is only quadratically worse than the optimal non constructive bound of o k we also indicate how to modify this code to allow for a combination of up to k insertions and deletions we also note that among linear codes capable of correcting k deletions the k 1 fold repetition code is essentially the best possible

a spatially constrained mixture model for image segmentation gaussian mixture models gmms constitute a well known type of probabilistic neural networks one of their many successful applications is in image segmentation where spatially constrained mixture models have been trained using the expectation maximization em framework in this letter we elaborate on this method and propose a new methodology for the m step of the em algorithm that is based on a novel constrained optimization formulation numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach

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

quantitative function for community detection we propose a quantitative function for community partition i e modularity density or d value we demonstrate that this quantitative function is superior to the widely used modularity q and also prove its equivalence with the objective function of the kernel k means both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that existing approaches cannot achieve but also can correctly identify the number of communities

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

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

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

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

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

bayesian pixel classification using spatially variant finite mixtures and the generalized em algorithm a spatially variant finite mixture model is proposed for pixel labeling and image segmentation for the case of spatially varying mixtures of gaussian density functions with unknown means and variances an expectation maximization em algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities an a priori density function is formulated for the spatially variant mixture weights a generalized em algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived this algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent gaussian densities have been used for simplicity but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities the accuracy of the algorithm is quantitatively evaluated through monte carlo simulation and its performance is qualitatively assessed via experimental images from computerized tomography ct and magnetic resonance imaging mri

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

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

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

the information content of mr images the theoretical information content defined by c e shannon 1948 is proposed as an objective measure of mr magnetic resonance image quality this measure takes into account the contrast to noise ratio cnr scan resolution and field of view it is used to derive an optimum in the tradeoff problem between image resolution and cnr and as a criterion to assess the usefulness of high resolution 512 sup 2 mr images the result tells that for a given total acquisition time an optimum value of the resolution can be found this optimum is very broad to apply shannon s theory on information constant to mr images a model for the spatial spectral power density of these images is required such a model has been derived from experimental observations of ordinary mr images as well as from theoretical considerations

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

a multiple insertion deletion correcting code for run length limited sequences a code construction is proposed to add a multiple insertion deletion error correcting capability to a run length limited sequence the codewords of this code are themselves run length limited the insertion deletion correcting capability is achieved by requiring several weighted sums of run lengths in the codewords to satisfy certain congruences modulo primes the construction is similar to the number theoretic code proposed by dolecek and anantharam which can correct multiple repetition errors or equivalently multiple insertions of zeros it is shown that if the codewords in this code are run length limited then the code is capable of correcting both insertions and deletions of zeros and ones an algorithm is proposed for decoding over a multiple insertion deletion channel following the work of dolecek and anantharam a systematic encoding method is also proposed for the codes furthermore it is shown that the proposed construction has a higher rate asymptotically than the helberg code which is unconstrained in terms of run lengths even though our construction has the additional run length constraints the need for run length limited codes that can correct insertion deletion errors is motivated by bit patterned media for magnetic recording

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

deletion codes in the high noise and high rate regimes the noise model of deletions poses significant challenges in coding theory with basic questions like the capacity of the binary deletion channel still being open in this paper we study the harder model of worst case deletions with a focus on constructing efficiently decodable codes for the two extreme regimes of high noise and high rate specifically we construct polynomial time decodable codes with the following tradeoffs for any varepsilon 0 1 codes that can correct a fraction 1 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon over an alphabet of size mathop mathrm poly nolimits 1 varepsilon 2 binary codes of rate 1 tilde o sqrt varepsilon that can correct a fraction varepsilon of deletions and 3 binary codes that can be list decoded from a fraction 1 2 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon this paper gives the first efficient constructions which meet the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets and correcting a constant fraction of bit deletions with rate approaching 1 over a fixed alphabet the above mentioned results bring our understanding of deletion code constructions in these regimes to a similar level as worst case errors

statistical approach to x ray ct imaging and its applications in image analysis i statistical analysis of x ray ct imaging a statistical description of x ray ct computerized tomography imaging from the projection data to the reconstructed image is presented the gaussianity of the pixel image generated by the convolution image reconstruction algorithm is justified the conditions for two pixel images to be statistically independent for a given probability and the conditions for a group of pixel images to be a spatial stationary random process and ergodic in mean and autocorrelations are derived these properties provide the basis for establishing the stochastic image model and conducting the statistical image analysis of x ray ct images

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

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

list decoding of insertions and deletions list decoding of insertions and deletions in the levenshtein metric is considered the levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other in this paper a johnson like upper bound on the maximum list size when list decoding in the levenshtein metric is derived this bound depends only on the length and minimum levenshtein distance of the code the length of the received word and the alphabet size it shows that polynomial time list decoding beyond half the levenshtein distance is possible for many parameters further we also prove a lower bound on list decoding of deletions with the well known binary varshamov tenengolts codes which shows that the maximum list size grows exponentially with the number of deletions finally an efficient list decoding algorithm for two insertions deletions with vt codes is given this decoder can be modified to a polynomial time list decoder of any constant number of insertions deletions

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

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

an improvement to levenshtein s upper bound on the cardinality of deletion correcting codes we consider deletion correcting codes over a q ary alphabet it is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions to obtain asymptotic upper bounds on code size we apply a packing argument to channels that perform different mixtures of insertions and deletions even though the set of codes is identical for all of these channels the bounds that we obtain vary prior to this paper only the bounds corresponding to the all insertion case and the all deletion case were known we recover these as special cases the bound from the all deletion case due to levenshtein has been the best known for more than 45 years our generalized bound is better than levenshtein s bound whenever the number of deletions to be corrected is larger than the alphabet size

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

uncovering fuzzy community structure in complex networks there has been an increasing interest in properties of complex networks such as small world property power law degree distribution and network transitivity which seem to be common to many real world networks in this study a useful community detection method based on non negative matrix factorization nmf technique is presented based on a popular modular function a proper feature matrix from diffusion kernel and nmf algorithm the presented method can detect an appropriate number of fuzzy communities in which a node may belong to more than one community the distinguished characteristic of the method is its capability of quantifying how much a node belongs to a community the quantification provides an absolute membership degree for each node to each community which can be employed to uncover fuzzy community structure the computational results of the method on artificial and real networks confirm its ability

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

detecting and refining overlapping regions in complex networks with three way decisions the three way representation of communities as a triple of positive boundary and negative regions brings more insight into interpretation of communities the overlapping regions are further refined into 4 macro types and 8 micro types the three way decision strategies are introduced to detect the overlapping communities based on the introduced relation graph a new fitness function is devised to adapt to processing networks with overlapping the refinement of overlapping regions can reveal the different significance to impact forming or changing of communities the identification of communities is crucial to an understanding of the structural and functional properties of a complex network many methods and algorithms have been developed to detect overlapping communities a problem that has not been addressed satisfactorily is the relationship or difference between vertices in overlapping regions during the formation and growth of communities this paper investigates methods that not only detect the overlapping communities but also refine the overlapping regions we give a three way representation of a community by using interval sets and re formalize the problem of community detection as three way clustering we suggest four macro types and eight micro types of vertices to characterize members in overlapping regions for their refinement we propose an overlapping community detection algorithm by classifying the vertices into core vertices bone vertices and trivial vertices the main strategy of this algorithm is to find an initial cluster core to expand the core to a preliminary community according to a new fitness function and to merge trivial vertices based on three way decision strategies the experimental results on both real world social networks and computer generated artificial networks show the effectiveness and efficiency of the proposed methods

identification of overlapping community structure in complex networks using fuzzy c means clustering abstract identification of overlapping communities clusters in a complex network is a general problem in data mining of network data sets in this paper we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing ng s q function an approximation mapping of network nodes into euclidean space and fuzzy c means clustering experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters

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

an em approach to map solution of segmenting tissue mixtures a numerical analysis this work presents an iterative expectation maximization em approach to the maximum a posteriori map solution of segmenting tissue mixtures inside each image voxel each tissue type is assumed to follow a normal distribution across the field of view fov furthermore all tissue types are assumed to be independent from each other under these assumptions the summation of all tissue mixtures inside each voxel leads to the image density mean value at that voxel the summation of all the tissue mixtures unobservable random processes leads to the observed image density at that voxel and the observed image density value also follows a normal distribution image data are observed to follow a normal distribution in many applications by modeling the underlying tissue distributions as a markov random field across the fov the conditional expectation of the posteriori distribution of the tissue mixtures inside each voxel is determined given the observed image data and the current iteration estimation of the tissue mixtures estimation of the tissue mixtures at next iteration is computed by maximizing the conditional expectation the iterative em approach to a map solution is achieved by a finite number of iterations and reasonable initial estimate this map em framework provides a theoretical solution to the partial volume effect which has been a major cause of quantitative imprecision in medical image processing numerical analysis demonstrated its potential to estimate tissue mixtures accurately and efficiently

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

quantification of mr brain images by mixture density and partial volume modeling the problem of automatic quantification of brain tissue by utilizing single valued single echo magnetic resonance imaging mri brain scans is addressed it is shown that this problem can be solved without classification or segmentation a method that may be particularly useful in quantifying white matter lesions where the range of values associated with the lesions and the white matter may heavily overlap the general technique utilizes a statistical model of the noise and partial volume effect together with a finite mixture density description of the tissues the quantification is then formulated as a minimization problem of high order with up to six separate densities as part of the mixture this problem is solved by tree annealing with and without partial volume utilized the results compared and the sensitivity of the tree annealing algorithm to various parameters is exhibited the actual quantification is performed by two methods a classification based method called bayes quantification and parameter estimation results from each method are presented for synthetic and actual data

deterministic sampling a new technique for fast pattern matching consider the following three stage strategy for recognizing patterns in larger scenes mimic randomization deterministically sample several positions of the pattern search for sample find all occurrences of the sample in the scene verify for each occurrence of the sample verify occurrence of the full pattern this strategy has led to the core of the new idea given in this paper consider the string matching problem given the pattern a sample of its positions is carefully selected whose size is at most logarithmic the deterministic sample then the sample is searched for for nonperiodic patterns the sample has the following perhaps surprising property it is possible to disqualify all occurrences of the sample positions but one within each neighborhood of locations in the text without any further comparisons of characters this provides sparse verification this approach enables the text analysis stages search for sample and verify to be performed in o log n time and optimal spe

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

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

capacity upper bounds for deletion type channels we develop a systematic approach based on convex programming and real analysis for obtaining upper bounds on the capacity of the binary deletion channel and more generally channels with i i d insertions and deletions other than the classical deletion channel we give special attention to the poisson repeat channel introduced by mitzenmacher and drinea ieee transactions on information theory 2006 our framework can be applied to obtain capacity upper bounds for any repetition distribution the deletion and poisson repeat channels corresponding to the special cases of bernoulli and poisson distributions our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate real valued and often concave function over a bounded interval the corresponding univariate function is carefully designed according to the underlying distribution of repetitions and the choices vary depending on the desired strength of the upper bounds as well as the desired simplicity of the function e g being only efficiently computable versus having an explicit closed form expression in terms of elementary or common special functions among our results we show the following 1 the capacity of the binary deletion channel with deletion probability d is at most 1 d p for d 1 2 and assuming that the capacity function is convex is at most 1 d log 4 p for d 2 we derive the first set of capacity upper bounds for the poisson repeat channel our results uncover further striking connections between this channel and the deletion channel and suggest somewhat counter intuitively that the poisson repeat channel is actually analytically simpler than the deletion channel and may be of key importance to a complete understanding of the deletion channel 3 we derive several novel upper bounds on the capacity of the deletion channel all upper bounds are maximums of efficiently computable and concave univariate real functions over a bounded domain in turn we upper bound these functions in terms of explicit elementary and standard special functions whose maximums can be found even more efficiently and sometimes analytically for example for d e 1 2

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

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

detecting complex network modularity by dynamical clustering based on cluster desynchronization properties of phase oscillators we introduce an efficient method for the detection and identification of modules in complex networks the performance of the algorithm is tested on computer generated and real world networks whose modular structure is already known or has been studied by means of other methods the algorithm attains a high level of precision especially when the modular units are very mixed and hardly detectable by the other methods with a computational effort o kn on a generic graph with n nodes and k links

asymptotically good codes correcting insertions deletions and transpositions we present simple polynomial time encodable and decodable codes which are asymptotically good for channels allowing insertions deletions and transpositions as a corollary they achieve exponential error probability in a stochastic model of insertion deletion