detection of community overlap according to belief propagation and conflict abstract most existing methods for detection of community overlap cannot balance efficiency and accuracy for large and densely overlapping networks to quickly identify overlapping communities for such networks we propose a new method that uses belief propagation and conflict pcb to occupy communities we first identify triangles with maximal clustering coefficients as seed nodes and sow a new type of belief to the seed nodes then the beliefs explore their territory by occupying nodes with high assent ability the beliefs propagate their strength along the graph to consolidate their territory and conflict with each other when they encounter the same node simultaneously finally the node membership is judged from the belief vectors the pcb time complexity is nearly linear and its space complexity is linear the algorithm was tested in extensive experiments on three real world social networks and three computer generated artificial graphs the experimental results show that pcb is very fast and highly reliable tests on real and artificial networks give excellent results compared with three newly proposed overlapping community detection algorithms

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

empirical bayes estimation for combinations of multivariate bioassays summary this article presents a new empirical bayes estimator ebe and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on jeffreys rules the ebe can account for any extra variability among the bioassays and if this extra variability is 0 then the ebe reduces to the maximum likelihood estimator for combinations of multivariate bioassays the shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay with the weights depending on the prior variance

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

multi objective clustering technique based on k nodes update policy and similarity matrix for mining communities in social networks abstract this paper proposes a relatively all purpose network clustering technique based on the framework of multi objective evolutionary algorithms which can effectively dispose the issue of community detection in unsigned social networks as well as in signed social networks firstly we formulate a generalized similarity function to construct a similarity matrix and then a pre partitioning strategy is projected according to the similarity matrix the pre partitioning strategy merely considers nodes with high similarity values which avoids the interference of noise nodes during the label update phase in this way at the initial phase of the algorithm nodes with strong connections are fleetly gathered into sub communities secondly we elaborately devise a crossover operator called cross merging operator to merge sub communities generated by the pre partitioning technique moreover a special mutation operator based on the similarity matrix of nodes is implemented to adjust boundary nodes connecting different communities finally to handle different types of networks we therefore have presented the novel multi objective optimization models for this issue through a bulk of rigorous experiments on both unsigned and signed social networks the preeminent clustering performance illustrate that the proposed algorithm is capable of mining communities effectively

personalized pagerank clustering a graph clustering algorithm based on random walks abstract graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications in addition exponential growth of real world graphs such as social networks biological networks and electrical circuits demands clustering algorithms with nearly linear time and space complexity in this paper we propose personalized pagerank clustering ppc that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph we combine random walks and modularity to precisely and efficiently reveal the clusters of a graph ppc is a top down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly linear approaches that are mainly bottom up it also gives a hierarchy of clusters that is useful in many applications ppc has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets furthermore its top down approach makes it a flexible solution for clustering problems with different requirements

on the first sign change of hecke eigenvalues of newforms let f be a non zero cusp form of even integral weight k 2 and level n with real fourier coefficients a n n n using a classical theorem of landau together with the facts that the hecke l function of f is entire and the rankin selberg zeta function of f has a pole at its abscissa of convergence with residue essentially equal to the square of the petersson norm of f one easily shows that there are infinitely many n n such that a n 0 as well as infinitely many n with a n 1 siegel s argument does not apply and the result above is not known now suppose that n is squarefree and f is a newform which is a normalized hecke eigenform so a 1 1 and a n is the n th hecke eigenvalue of f we shall prove

on fourier coefficients of modular forms of half integral weight at squarefree integers we show that the dirichlet series associated to the fourier coefficients of a half integral weight hecke eigenform at squarefree integers extends analytically to a holomorphic function in the half plane re s tfrac 1 2 this exhibits a high fluctuation of the coefficients at squarefree integers

multivariate slope ratio assay with repeated measurements summary a method is given for analyzing a slope ratio assay in which a test drug is compared with a standard drug two or more response variates being measured on each subject at each of several successively increased drug doses the method requires i all subjects to receive the same number of doses ii all subjects on the same drug to receive the same doses iii the ratio of corresponding doses of the two drugs to be constant over the successive increases and iv response variables to be measured only once on each subject at each dose with no missing data allowed the technique is also applicable when doses are randomly assigned provided there is no carry over effect between doses for each of the j response variates the relative potency of the test drug with respect to the standard is defined and estimated in the usual way a 100 1 confidence region is then obtained for the vector of the j relative potencies a procedure is given for testing the equality of some or all of the j relative potencies an estimator of a common relative potency is obtained by a standard multivariate least squares method a common relative potency is of interest because the multiple outcome variables are often different indicators of a general physiologic response the procedures in the paper are illustrated by a simple example concerning the effects of two anesthetics on children

sequential algorithm for fast clique percolation in complex network research clique percolation introduced by palla der enyi and vicsek nature london 435 814 2005 is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network here we present a sequential clique percolation algorithm scp to do fast community detection in weighted and unweighted networks for cliques of a chosen size this method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure unlike existing algorithms the scp method allows for detecting k clique communities at multiple weight thresholds in a single run and can simultaneously produce a dendrogram representation of hierarchical community structure in sparse weighted networks the scp algorithm can also be used for implementing the weighted clique percolation method recently introduced by farkas et al new j phys 9 180 2007 the computational time of the scp algorithm scales linearly with the number of k cliques in the network as an example the method is applied to a product association network revealing its nested community structure

cuspidality of symmetric powers with applications the purpose of this paper is to prove that the symmetric fourth power of a cusp form on rm gl 2 whose existence was proved earlier by the first author is cuspidal unless the corresponding automorphic representation is of dihedral tetrahedral or octahedral type as a consequence we prove a number of results toward the ramanujan petersson and sato tate conjectures in particular we establish the bound q sp 1 9 sb v for unramified hecke eigenvalues of cusp forms on rm gl 2 over an arbitrary number field this is the best bound available at present

the number of hecke eigenvalues of same signs we give the best possible lower bounds in order of magnitude for the number of positive and negative hecke eigenvalues this improves upon a recent work of kohnen lau and shparlinski also we study an analogous problem for short intervals

rational eigenvectors in spaces of ternary forms we describe the explicit computation of linear combinations of ternary quadratic forms which are eigenvectors with rational eigenvalues under all hecke operators we use this process to construct for each elliptic curve e of rank zero and conductor n 2000 for which n or n 4 is square free a weight 3 2 cusp form which is potentially a preimage of the weight two newform e under the shimura correspondence

the dirichlet series of koecher and maas and modular forms of weight 3 2 the basis problem for modular forms is the question which modular forms can be expressed as linear combinations of theta series in order that this question makes sense one has of course to specify which type of theta series should be taken into account we want here to follow in a special case the approach taken e g in b61 w a l l which in its general form asks which cuspidal modular forms f of degree n and weight k for the group foc n can be expressed as linear combinations of the theta series of degree n of integral quadratic forms of rank m 2 k and the same level n moreover one wants to derive an explicit expression for such a linear combination in terms of the petersson inner products of f with the theta series involved the representation theoretic version of this question is to ask which cuspidat automorphic representations of the adelic symplectic or metaplectic group

repeated measures bioassay with correlated errors and heterogeneous variances a monte carlo study summary the relative potency of two drugs may be estimated from a small experiment in which all k doses of each drug are given in order of increasing dose level to each of n animals at one testing session fiducial limits are often estimated from fieller s theorem with the 2k l n l degree offreedom error term obtained from a two way analysis of variance monte carlo results indicate that this method can yield limits which are far too narrow when there is serial correlation between successive doses the jackknife confidence limits are found to behave well for the models investigated 1 intwoductioil biologists frequently wish to estimate the relative potency of two substances as well as 95 o limits for that relative potency from a small repeated measures experiment that is each of n animals receives k doses equally spaced on a log scale of each of the standard and unknown substances table 1 provides an example of data from a repeated measures bioassay design in this case all three doses of g 17 were administered in increasing order on one test day and all three doses of g 10 were administered in increasing order on another test day the surgical preparation of gastric fistula dogs is time consuming and expensive and repeated testing of the same animals is therefore necessary the purpose of the bioassay experiment is to estimate the relative potency of the unknown with respect to the standard that is if we let g d be the expected response to dose d of the standard then we assume that g trd is the response to dose d of the unknown where the factor lr is by definition the relative potency in many cases over the range of interest the function g d is adequately approximated as

fourier coefficients of cusp forms of half integral weight let mathfrak f be a cusp form of half integral weight whose fourier coefficients mathfrak a mathfrak f n are all real we study the sign change problem of mathfrak a mathfrak f n when n runs over some specific sets of integers lower bounds of the best possible order of magnitude are established for the number of those coefficients that have the same signs these give an improvement on some recent results of bruinier and kohnen modular forms on schiermonnikoong cambridge university press cambridge 57 66 2008 and kohnen int j number theory 6 1255 1259 2010