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Local Events and Dynamics on Weighted Complex Networks
ZHAO Hui,GAO Zi-You,

中国物理快报 , 2006,
Abstract: We examine the weighted networks grown and evolved by local events, such as the addition of new vertices and links and we show that depending on frequency of the events, a generalized power-law distribution of strength can emerge. Continuum theory is used to predict the scaling function as well as the exponents, which is in good agreement with the numerical simulation results. Depending on event frequency, power-law distributions of degree and weight can also be expected. Probability saturation phenomena for small strength and degree in many real world networks can be reproduced. Particularly, the non-trivial clustering coefficient, assortativity coefficient and degree-strength correlation in our model are all consistent with empirical evidences.
Growing community networks with local events  [PDF]
Xin-Jian Xu,Xun Zhang,J. F. F. Mendes
Physics , 2009, DOI: 10.1016/j.physa.2008.12.022
Abstract: The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes' degrees.
Accuracy and Precision of Methods for Community Identification in Weighted Networks  [PDF]
Ying Fan,Menghui Li,Peng Zhang,Jinshan Wu,Zengru Di
Physics , 2006, DOI: 10.1016/j.physa.2006.11.036
Abstract: 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.
Role Assorted Community Discovery for Weighted Networks  [cached]
Ruixin Ma,Guishi Deng,Xiao Wang
Journal of Software , 2011, DOI: 10.4304/jsw.6.12.2441-2448
Abstract: This paper considers the difficulties in community discovery, and comes up with a community discovery algorithm on the basis of role assorted thoughts. Previous work indicates that a robust approach to community detection is the maximization of inner communication and the minimization of the in-out interaction. Here we show that this problem can be solved accords to the role assorted method which give distinguish labels to vertices in the same community. This method leads us to a number of possible algorithms for detecting community structures in both unweighted and weighted networks. The applicability and expandability of algorithms proposed are illustrated with application to a variety of computer-generated networks and real-world complex networks.
Generating functions for weighted Hurwitz numbers  [PDF]
Mathieu Guay-Paquet,J. Harnad
Physics , 2014,
Abstract: Double Hurwitz numbers enumerating weighted $n$-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of $S_n$ generated by transpositions are determined by an associated weight generating function. A uniquely determined $1$-parameter family of 2D Toda $\tau$-functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers, for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as weight generator, three new types of weighted enumerations are introduced. These determine {\em quantum} Hurwitz numbers depending on a deformation parameter $q$. By suitable interpretation of $q$, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.
Generating events with style  [PDF]
Matthieu Boutier,Gabriel Kerneis
Computer Science , 2012,
Abstract: Threads and events are two common abstractions for writing concurrent programs. Because threads are often more convenient, but events more efficient, it is natural to want to translate the former into the latter. However, whereas there are many different event-driven styles, existing translators often apply ad-hoc rules which do not reflect this diversity. We analyse various control-flow and data-flow encodings in real-world event-driven code, and we observe that it is possible to generate any of these styles automatically from threaded code, by applying certain carefully chosen classical program transformations. In particular, we implement two of these transformations, lambda lifting and environments, in CPC, an extension of the C language for writing concurrent systems. Finally, we find out that, although rarely used in real-world programs because it is tedious to perform manually, lambda lifting yields better performance than environments in most of our benchmarks.
Generating target probability sequences and events  [PDF]
Vaignana Spoorthy Ella
Computer Science , 2013,
Abstract: Cryptography and simulation of systems require that events of pre-defined probability be generated. This paper presents methods to generate target probability events based on the oblivious transfer protocol and target probabilistic sequences using probability distribution functions.
Correlations in weighted networks  [PDF]
M. Angeles Serrano,Marian Boguna,Romualdo Pastor-Satorras
Physics , 2006, DOI: 10.1103/PhysRevE.74.055101
Abstract: We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary $P(k,s)$ to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.
A New Weighted Information Generating Function for Discrete Probability Distributions  [PDF]
Amit Srivastava,Shikha Maheshwari
Mathematics , 2015,
Abstract: The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have also been studied.
Community detection in bipartite networks using weighted symmetric binary matrix factorization  [PDF]
Zhong-Yuan Zhang,Yong-Yeol Ahn
Computer Science , 2015, DOI: 10.1142/S0129183115500965
Abstract: In this paper we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describe relationships between two types of nodes. Our method improves performance by recognizing the distinction between two types of missing edges---ones among the nodes in each node type and the others between two node types. Our method can also explicitly assign community membership and distinguish outliers from overlapping nodes, as well as incorporating existing knowledge on the network. We propose a generalized partition density for bipartite networks as a quality function, which identifies the most appropriate number of communities. The experimental results on both synthetic and real-world networks demonstrate the effectiveness of our method.
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