Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Quantifying and identifying the overlapping community structure in networks

It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of assuming that one node can only belong to one community, our metric assumes that a maximal clique only belongs to one community. In this way, the overlaps between communities are allowed. To identify the overlapping community structure, we construct a maximal clique network from the original network, and prove that the optimization of our metric on the original network is equivalent to the optimization of Newman's modularity on the maximal clique network. Thus the overlapping community structure can be identified through partitioning the maximal clique network using any modularity optimization method. The effectiveness of our metric is demonstrated by extensive tests on both the artificial networks and the real world networks with known community structure. The application to the word association network also reproduces excellent results.Comment: 9 pages, 7 figure

Detecting the overlapping and hierarchical community structure of complex networks

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results.Comment: 20 pages, 8 figures. Final version published on New Journal of Physic

Determining and interpreting correlations in lipidomic networks found in glioblastoma cells

Background: Intelligent and multitiered quantitative analysis of biological systems rapidly evolves to a key technique in studying biomolecular cancer aspects. Newly emerging advances in both measurement as well as bio-inspired computational techniques have facilitated the development of lipidomics technologies and offer an excellent opportunity to understand regulation at the molecular level in many diseases. Results: We present computational approaches to study the response of glioblastoma U87 cells to gene- and chemo-therapy. To identify distinct biomarkers and differences in therapeutic outcomes, we develop a novel technique based on graph-clustering. This technique facilitates the exploration and visualization of co-regulations in glioblastoma lipid profiling data. We investigate the changes in the correlation networks for different therapies and study the success of novel gene therapies targeting aggressive glioblastoma. Conclusions: The novel computational paradigm provides unique “fingerprints” by revealing the intricate interactions at the lipidome level in glioblastoma U87 cells with induced apoptosis (programmed cell death) and thus opens a new window to biomedical frontiers. Background Glioblastoma are highly invasive brain tumors. Th

Localized Fetomaternal Hyperglycemia: Spatial and Kinetic Definition by Positron Emission Tomography

to isolated hyperglycemia in the pregnant rat. mg/dL) localized to the left uterine artery was sustained for at least 48 hours while maternal euglycemia was maintained. fetal effects of isolated hyperglycemia. Broadly, this approach can be extended to study a variety of maternal-sided perturbations suspected to directly affect fetal health

Mining Social Interaction Data in Virtual Worlds

Virtual worlds and massively multi-player online games are rich sources of information about large-scale teams and groups, offering the tantalizing possibility of harvesting data about group formation, social networks, and network evolution. However these environments lack many of the cues that facilitate natural language processing in other conversational settings and different types of social media. Public chat data often features players who speak simultaneously, use jargon and emoticons, and only erratically adhere to conversational norms. This chapter presents techniques for inferring the existence of social links from unstructured conversational data collected from groups of participants in the Second Life virtual world

Identification and Analysis of Co-Occurrence Networks with NetCutter

BACKGROUND: Co-occurrence analysis is a technique often applied in text mining, comparative genomics, and promoter analysis. The methodologies and statistical models used to evaluate the significance of association between co-occurring entities are quite diverse, however. METHODOLOGY/PRINCIPAL FINDINGS: We present a general framework for co-occurrence analysis based on a bipartite graph representation of the data, a novel co-occurrence statistic, and software performing co-occurrence analysis as well as generation and analysis of co-occurrence networks. We show that the overall stringency of co-occurrence analysis depends critically on the choice of the null-model used to evaluate the significance of co-occurrence and find that random sampling from a complete permutation set of the bipartite graph permits co-occurrence analysis with optimal stringency. We show that the Poisson-binomial distribution is the most natural co-occurrence probability distribution when vertex degrees of the bipartite graph are variable, which is usually the case. Calculation of Poisson-binomial P-values is difficult, however. Therefore, we propose a fast bi-binomial approximation for calculation of P-values and show that this statistic is superior to other measures of association such as the Jaccard coefficient and the uncertainty coefficient. Furthermore, co-occurrence analysis of more than two entities can be performed using the same statistical model, which leads to increased signal-to-noise ratios, robustness towards noise, and the identification of implicit relationships between co-occurring entities. Using NetCutter, we identify a novel protein biosynthesis related set of genes that are frequently coordinately deregulated in human cancer related gene expression studies. NetCutter is available at http://bio.ifom-ieo-campus.it/NetCutter/). CONCLUSION: Our approach can be applied to any set of categorical data where co-occurrence analysis might reveal functional relationships such as clinical parameters associated with cancer subtypes or SNPs associated with disease phenotypes. The stringency of our approach is expected to offer an advantage in a variety of applications