a parallel poisson generator using parallel prefix in this paper we use the renewal theory to develop a poisson random number algorithm without restart a parallel poisson random number generator is designed based on this algorithm and prefix computation this generator iteratively produces m poisson random numbers with mean in average time complexity o m n f n p on erew pram where f n p is the time for computing an n element parallel prefix on p processors in each iteration assuming that parallel uniform random numbers can be generated at the rate of one number per unit time per processor if n is selected near m it achieves linear speedup when p is small and the average time complexity is o log m when p is o m

parallel minimal norm method for tridiagonal linear systems based on the parallel minimal norm method an algorithm is derived to solve tridiagonal linear systems with a high degree of parallelism no conditions need to be posed with respect to the system experiments indicate that the numerical stability of the algorithm is similar to gaussian elimination with partial pivoting

extension of plurisubharmonic currents let a be a closed subset of an open subset of n and t be a negative current on a of bidimension p p assume that t is psh and a is complete pluripolar such that the hausdorff measure cal h 2p overline rm supp t cap a 0 then t extends to a negative psh current on we also show that if t is psh or if dd ct extends to a current with locally finite mass on then the trivial extension widetilde t of t by zero across a exists in both cases a is the zero set of a k convex function with k p 1 or cal h 2 p 1 overline rm supp t cap a 0 our basic tool is the following theorem el3 let a be a closed complete pluripolar subset of an open subset of n and t be a positive current of bidimension p p on a suppose that widetilde t and widetilde dd ct exist resp widetilde t exists and dd ct 0 on a then there exists a positive resp closed positive current s supported in a such that widetilde dd ct dd c widetilde t s furthermore we give a generalization of some theorems done by siu and ben messaoud el mir and alessandrini bassanelli without requiring anything from dt

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

unified architecture for divide and conquer based tridiagonal system solvers the solution of tridiagonal systems is a topic of great interest in many areas of numerical analysis several algorithms have recently been proposed for solving triadiagonal systems based on the divide and conquer dc strategy in this work we propose a unified parallel architecture for dc algorithms which present the data flows of the successive doubling recursive doubling and parallel cyclic reduction methods the architecture is based in the perfect unshuffle permutation which transforms these data flows into a constant geometry one the partition of the data arises in a natural manner giving way to a systolic data flow with a wired control section we conclude that the constant geometry cyclic reduction architecture is the most appropriate one for solving tridiagonal systems and from the point of view of integration in vlsi technology is the one which uses the least amount of area and the smallest number of pins

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

a parallel alternating direction implicit preconditioning method abstract the alternating direction implicit adi iterative method is an efficient iterative method to solve systems of linear equations due to its extremely fast convergence the adi method has also been used successfully as a preconditioner in some other iterative methods such as the preconditioned conjugate gradient in this paper a parallel algorithm for the adi preconditioning is proposed in this algorithm several steps of the adi iteration are computed simultaneously this means that several tridiagonal systems that are traditionally solved sequentially are now solved concurrently the high performance of this algorithm is achieved by increasing the degree of parallelism and reducing memory contention the algorithm can easily be implemented in a multiprocessor architecture experiments have been conducted on the myrias sps 2 computer with 64 processors and good performance of this algorithm is observed

complex projective structures lyapunov exponent degree and harmonic measure we study several new invariants associated to a holomorphic projective struc ture on a riemann surface of finite analytic type the lyapunov exponent of its holonomy which is of probabilistic dynamical nature and was introduced in our previous work the degree which measures the asymptotic covering rate of the developing map and a family of harmonic measures on the riemann sphere previously introduced by hussenot we show that the degree and the lyapunov exponent are related by a simple formula and give estimates for the hausdorff dimension of the harmonic measures in terms of the lyapunov exponent in accordance with the famous sullivan dictionary this leads to a descrip tion of the space of such projective structures that is reminiscent of that of the space of polynomials in holomorphic dynamics

edge ratio and community structure in networks a hierarchical divisive algorithm is proposed for identifying communities in complex networks to that effect the definition of community in the weak sense of radicchi et al proc natl acad sci u s a 101 2658 2004 is extended into a criterion for a bipartition to be optimal one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges a mathematical program is used within a dichotomous search to do this in an optimal way for each bipartition this includes an exact solution of the problem of detecting indivisible communities the resulting hierarchical divisive algorithm is compared with exact modularity maximization on both artificial and real world data sets for two problems of the former kind optimal solutions are found for five problems of the latter kind the edge ratio algorithm always appears to be competitive moreover it provides additional information in several cases notably through the use of the dendrogram summarizing the resolution finally both algorithms are compared on reduced versions of the data sets of girvan and newman proc natl acad sci u s a 99 7821 2002 and of lancichinetti et al phys rev e 78 046110 2008 results for these instances appear to be comparable

accuracy and precision of methods for community identification in weighted networks based on brief review of approaches for community identification and measurement for sensitivity characterization the accuracy and precision of several approaches for detecting communities in weighted networks are investigated in weighted networks the community structure should take both links and link weights into account and the partition of networks should be evaluated by weighted modularity q w the results reveal that link weight has important effects on communities especially in dense networks potts model and weighted extremal optimization weo algorithm work well on weighted networks then potts model and weo algorithms are used to detect communities in rhesus monkey network the results gives nice understanding for real community structure

efficient tridiagonal solvers on multicomputers three parallel algorithms namely the parallel partition lu ppt algorithm the parallel partition hybrid pph algorithm and the parallel diagonal dominant pdd algorithm are proposed for solving tridiagonal linear systems on multicomputers these algorithms are based on the divide and conquer parallel computation model the ppt and pph algorithms support both pivoting and nonpivoting the ppt algorithm is good when the number of processors is small otherwise the pph algorithm is better when the system is diagonal dominant the pdd algorithm is highly parallel and provides an approximate solution which equals the exact solution within machine accuracy computation and communication complexities of the three algorithms are presented all three methods have been implemented on a 64 node ncube 1 multicomputer the analytic results closely match the results measured from the ncube 1 machine

the inductive wedge product of positive currents we define the wedge product of positive currents our main issue is about studying the convergence of ddcgj t where gj is a given sequence of plurisubharmonic functions and t is a positive current

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

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

a recursive doubling algorithm for solution of tridiagonal systems on hypercube multiprocessors abstract the recursive doubling algorithm as developed by stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using o log n parallel arithmetic steps in this paper we give a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using o n p log p parallel arithmetic steps on a parallel computer with p n processors the main technique relies on fast parallel prefix algorithms which can be efficiently mapped on the hypercube architecture using the binary reflected gray code for p n this algorithm achieves linear speedup and constant efficiency over its sequential implementation as well as over the sequential lu decomposition algorithm these results are confirmed by numerical experiments obtained on an intel ipsc d5 hypercube multiprocessor

detecting the community structure in complex networks based on quantum mechanics abstract in this paper we develop a novel method to detect the community structure in complex networks this approach is based on the combination of kernel based clustering using quantum mechanics the spectral clustering technique and the concept of the bayesian information criterion we test the proposed algorithm on zachary s karate club network and the world of american college football experimental results indicate that our algorithm is efficient and effective at finding both the optimal number of clusters and the best clustering of community structures

j pluripolar subsets and currents on almost complex manifolds we prove that every almost complex submanifold of an almost complex manifold is locally j pluripolar this generalizes a result of rosay for j holomorphic submanifolds our second main result is an almost complex version of el mir s theorem for the extension of positive currents across locally complete pluripolar sets as a consequence we extend some results proved by dabbek elkhadhra el mir and dinh sibony in the standard complex case we also obtain a version of the well known results of federer and bassanelli for flat and mathbb c flat currents in the almost complex setting

efficient modularity optimization by multistep greedy algorithm and vertex mover refinement identifying strongly connected substructures in large networks provides insight into their coarse grained organization several approaches based on the optimization of a quality function e g the modularity have been proposed we present here a multistep extension of the greedy algorithm msg that allows the merging of more than one pair of communities at each iteration step the essential idea is to prevent the premature condensation into few large communities upon convergence of the msg a simple refinement procedure called vertex mover vm is used for reassigning vertices to neighboring communities to improve the final modularity value with an appropriate choice of the step width the combined msg vm algorithm is able to find solutions of higher modularity than those reported previously the multistep extension does not alter the scaling of computational cost of the greedy algorithm

a cutting plane algorithm for a clustering problem in this paper we consider a clustering problem that arises in qualitative data analysis this problem can be transformed to a combinatorial optimization problem the clique partitioning problem we have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope these theoretical results are utilized in this paper we describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before we discuss some details of the implementation of our code and present our computational results we mention applications from e g zoology economics and the political sciences

modularity and extreme edges of the internet we study the spectral properties of a diffusion process taking place on the internet network focusing on the slowest decaying modes these modes identify an underlying modular structure roughly corresponding to individual countries for instance in the slowest decaying mode the diffusion current flows from russia to u s military sites quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale free network we propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network for the 100 slowest decaying modes of the internet this fraction is 30 finally we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes

perturbation theory for evaluation algorithms of arithmetic expressions the paper presents the theoretical foundation of a forward error analysis of numerical algorithms under data perturbations rounding error in arithmetic floating point operations and approximations in built in functions the error analysis is based on the linearization method that has been proposed by many authors in various forms fundamental tools of the forward error analysis are systems of linear absolute and relative a priori and a posteriori error equations and associated condition numbers constituting optimal bounds of possible accumulated or total errors derivations representations and properties of these condition numbers are studied in detail the condition numbers enable simple general quantitative definitions of numerical stability backward analysis welland ill conditioning of a problem and an algorithm the well known illustration of algorithms and their linear error equations by graphs is extended to a method of deriving condition numbers and associated bounds for many algorithms the associated condition numbers can be determined analytically a priori and be computed numerically a posteriori the theoretical results of the paper have been applied to a series of concrete algorithms including gaussian elimination and have proved to be very effective means of both a priori and a posteriori error analysis introduction evaluation algorithms are defined by finite sequences f fo f of input operations evaluations of built in functions and arithmetic operations for determining sequences u uo u of input data intermediate and final results in the form 1 ut f u t 0 n it is presupposed in the following that fo is a constant function and the function values ft x depend on xo xt1 but not on xt x for t 1 i n under perturbations an evaluation algorithm yields approximations vt of ut that can be written in the form 2 vt 1 e ft v t o n the so called local errors et are the relative errors of the data input function evaluation or rounding in the arithmetic floating point operation in step t of the algorithm we shall assume that the local errors are bounded by je1j yt7 for t o n where yt are suitable nonnegative weights and q is an accuracy constant received june 12 1979 revised november 26 1979 and august 27 1980 1980 mathematics subject classification primary 65g05

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