Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure

Communities, Knowledge Creation, and Information Diffusion

In this paper, we examine how patterns of scientific collaboration contribute to knowledge creation. Recent studies have shown that scientists can benefit from their position within collaborative networks by being able to receive more information of better quality in a timely fashion, and by presiding over communication between collaborators. Here we focus on the tendency of scientists to cluster into tightly-knit communities, and discuss the implications of this tendency for scientific performance. We begin by reviewing a new method for finding communities, and we then assess its benefits in terms of computation time and accuracy. While communities often serve as a taxonomic scheme to map knowledge domains, they also affect how successfully scientists engage in the creation of new knowledge. By drawing on the longstanding debate on the relative benefits of social cohesion and brokerage, we discuss the conditions that facilitate collaborations among scientists within or across communities. We show that successful scientific production occurs within communities when scientists have cohesive collaborations with others from the same knowledge domain, and across communities when scientists intermediate among otherwise disconnected collaborators from different knowledge domains. We also discuss the implications of communities for information diffusion, and show how traditional epidemiological approaches need to be refined to take knowledge heterogeneity into account and preserve the system's ability to promote creative processes of novel recombinations of idea

SMART: Unique splitting-while-merging framework for gene clustering

Copyright @ 2014 Fa et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named “splitting merging awareness tactics” (SMART), which does not require any a priori knowledge of either the number of clusters or even the possible range of this number. Unlike existing self-splitting algorithms, which over-cluster the dataset to a large number of clusters and then merge some similar clusters, our framework has the ability to split and merge clusters automatically during the process and produces the the most reliable clustering results, by intrinsically integrating many clustering techniques and tasks. The SMART framework is implemented with two distinct clustering paradigms in two algorithms: competitive learning and finite mixture model. Nevertheless, within the proposed SMART framework, many other algorithms can be derived for different clustering paradigms. The minimum message length algorithm is integrated into the framework as the clustering selection criterion. The usefulness of the SMART framework and its algorithms is tested in demonstration datasets and simulated gene expression datasets. Moreover, two real microarray gene expression datasets are studied using this approach. Based on the performance of many metrics, all numerical results show that SMART is superior to compared existing self-splitting algorithms and traditional algorithms. Three main properties of the proposed SMART framework are summarized as: (1) needing no parameters dependent on the respective dataset or a priori knowledge about the datasets, (2) extendible to many different applications, (3) offering superior performance compared with counterpart algorithms.National Institute for Health Researc

Achieving Small World Properties using Bio-Inspired Techniques in Wireless Networks

It is highly desirable and challenging for a wireless ad hoc network to have self-organization properties in order to achieve network wide characteristics. Studies have shown that Small World properties, primarily low average path length and high clustering coefficient, are desired properties for networks in general. However, due to the spatial nature of the wireless networks, achieving small world properties remains highly challenging. Studies also show that, wireless ad hoc networks with small world properties show a degree distribution that lies between geometric and power law. In this paper, we show that in a wireless ad hoc network with non-uniform node density with only local information, we can significantly reduce the average path length and retain the clustering coefficient. To achieve our goal, our algorithm first identifies logical regions using Lateral Inhibition technique, then identifies the nodes that beamform and finally the beam properties using Flocking. We use Lateral Inhibition and Flocking because they enable us to use local state information as opposed to other techniques. We support our work with simulation results and analysis, which show that a reduction of up to 40% can be achieved for a high-density network. We also show the effect of hopcount used to create regions on average path length, clustering coefficient and connectivity.Comment: Accepted for publication: Special Issue on Security and Performance of Networks and Clouds (The Computer Journal

Network dynamics in regional clusters: The perspective of an emerging economy

Regional clusters are spatial agglomerations of firms operating in the same or connected industries, which enable innovation and economic performance for firms. A wealth of empirical literature shows that one of key elements of the success of regional clusters is that they facilitate the formation of local inter-organizational networks, which act as conduits of knowledge and innovation. While most studies analyze the benefits and characteristics of regional cluster networks and focus on advanced economies and high tech Ôhot spotsÕ, this paper advances with the existing literature by analyzing network dynamics and taking an emerging economyÕs perspective. Using longitudinal data of a wine cluster in Chile and stochastic actor-oriented models for network dynamics, this paper examines what micro-level effects influence the formation of new knowledge ties among wineries. It finds that the coexistence of cohesion effects (reciprocity and transitivity) and the presence of inter-firm knowledge base heterogeneity contribute to the stability of an informal hierarchical network structure over time. Empirical results have interesting implications for cluster competitiveness and network studies, and for the burgeoning literature on corporate behavior in emerging economies.Regional clusters, knowledge networks, network dynamics, wine industry, Chile

Collective Memory, Consensus, and Learning Explained by Network Connectivity

Humans cluster in social groups where they discuss their shared past, problems, and the potential solutions; they learn collectively when they repeat activities; they synchronize when they sing or dance together; and they bond through social cohesion. By representing a group network with a Laplacian matrix, the outcomes of these activities, as well as the group's cohesion, can be predicted by its second smallest eigenvalue, called the algebraic connectivity. It predicts when processes converge toward a consensus or focal activity, but it cannot predict divergence, such as division of labor or polarization