Hierarchies of Predominantly Connected Communities

We consider communities whose vertices are predominantly connected, i.e., the vertices in each community are stronger connected to other community members of the same community than to vertices outside the community. Flake et al. introduced a hierarchical clustering algorithm that finds such predominantly connected communities of different coarseness depending on an input parameter. We present a simple and efficient method for constructing a clustering hierarchy according to Flake et al. that supersedes the necessity of choosing feasible parameter values and guarantees the completeness of the resulting hierarchy, i.e., the hierarchy contains all clusterings that can be constructed by the original algorithm for any parameter value. However, predominantly connected communities are not organized in a single hierarchy. Thus, we develop a framework that, after precomputing at most $2(n-1)$ maximum flows, admits a linear time construction of a clustering \C(S) of predominantly connected communities that contains a given community $S$ and is maximum in the sense that any further clustering of predominantly connected communities that also contains $S$ is hierarchically nested in \C(S). We further generalize this construction yielding a clustering with similar properties for $k$ given communities in $O(kn)$ time. This admits the analysis of a network's structure with respect to various communities in different hierarchies.Comment: to appear (WADS 2013

Distance, dissimilarity index, and network community structure

We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized. Each community is characterized by an upper and a lower dissimilarity threshold. The algorithm is applied to several artificial and real-world networks, and excellent results are obtained. In the case of artificially generated random modular networks, this method outperforms the algorithm based on the concept of edge betweenness centrality. For yeast's protein-protein interaction network, we are able to identify many clusters that have well defined biological functions.Comment: 10 pages, 7 figures, REVTeX4 forma

Application of semidefinite programming to maximize the spectral gap produced by node removal

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.Comment: 1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013

Network Landscape from a Brownian Particle's Perspective

Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global attractor of $i$ if $d_{i,j}\leq d_{i,k}$ for any $k$ of the graph; it is a local attractor of $i$, if $j\in E_i$ (the set of nearest-neighbors of $i$) and $d_{i,j}\leq d_{i,l}$ for any $l\in E_i$. Based on the intuition that each node should have a high probability to be in the same community as its global (local) attractor on the global (local) scale, we present a simple method to uncover a network's community structure. This method is applied to several real networks and some discussion on its possible extensions is made.Comment: 5 pages, 4 color-figures. REVTeX 4 format. To appear in PR

Bi-Objective Community Detection (BOCD) in Networks using Genetic Algorithm

A lot of research effort has been put into community detection from all corners of academic interest such as physics, mathematics and computer science. In this paper I have proposed a Bi-Objective Genetic Algorithm for community detection which maximizes modularity and community score. Then the results obtained for both benchmark and real life data sets are compared with other algorithms using the modularity and MNI performance metrics. The results show that the BOCD algorithm is capable of successfully detecting community structure in both real life and synthetic datasets, as well as improving upon the performance of previous techniques.Comment: 11 pages, 3 Figures, 3 Tables. arXiv admin note: substantial text overlap with arXiv:0906.061

A Memetic Algorithm for Community Detection in Complex Networks

Community detection is an important issue in the field of complex networks. Modularity is the most popular partition-based measure for community detection of networks represented as graphs. We present a hybrid algorithm mixing a dedicated crossover operator and a multi-level local optimization procedure. Experimental evaluations on a set of 11 well-known benchmark graphs show that the proposed algorithm attains easily all the current best solutions and even improves 6 of them in terms of maximum modularity

Mucedorus: the last ludic playbook, the first stage Arcadia

This article argues that two seemingly contradictory factors contributed to and sustained the success of the anonymous Elizabethan play Mucedorus (c. 1590; pub. 1598). First, that both the initial composition of Mucedorus and its Jacobean revival were driven in part by the popularity of its source, Philip Sidney's Arcadia. Second, the playbook's invitation to amateur playing allowed its romance narrative to be adopted and repurposed by diverse social groups. These two factors combined to create something of a paradox, suggesting that Mucedorus was both open to all yet iconographically connected to an elite author's popular text. This study will argue that Mucedorus pioneered the fashion for “continuations” or adaptations of the famously unfinished Arcadia, and one element of its success in print was its presentation as an affordable and performable version of Sidney's elite work. The Jacobean revival of Mucedorus by the King's Men is thus evidence of a strategy of engagement with the Arcadia designed to please the new Stuart monarchs. This association with the monarchy in part determined the cultural functions of the Arcadia and Mucedorus through the Interregnum to the close of the seventeenth century

The association among cytochrome P450 3A, progesterone receptor polymorphisms, plasma 17-alpha hydroxyprogesterone caproate concentrations, and spontaneous preterm birth

Background Infants born <37 weeks’ gestation are of public health concern since complications associated with preterm birth are the leading cause of mortality in children <5 years of age and a major cause of morbidity and lifelong disability. The administration of 17-alpha hydroxyprogesterone caproate reduces preterm birth by 33% in women with history of spontaneous preterm birth. We demonstrated previously that plasma concentrations of 17-alpha hydroxyprogesterone caproate vary widely among pregnant women and that women with 17-alpha hydroxyprogesterone caproate plasma concentrations in the lowest quartile had spontaneous preterm birth rates of 40% vs rates of 25% in those women with higher concentrations. Thus, plasma concentrations are an important factor in determining drug efficacy but the reason 17-alpha hydroxyprogesterone caproate plasma concentrations vary so much is unclear. Predominantly, 17-alpha hydroxyprogesterone caproate is metabolized by CYP3A4 and CYP3A5 enzymes. Objective We sought to: (1) determine the relation between 17-alpha hydroxyprogesterone caproate plasma concentrations and single nucleotide polymorphisms in CYP3A4 and CYP3A5; (2) test the association between progesterone receptor single nucleotide polymorphisms and spontaneous preterm birth; and (3) test whether the association between plasma concentrations of 17-alpha hydroxyprogesterone caproate and spontaneous preterm birth varied by progesterone receptor single nucleotide polymorphisms. Study Design In this secondary analysis, we evaluated genetic polymorphism in 268 pregnant women treated with 17-alpha hydroxyprogesterone caproate, who participated in a placebo-controlled trial to evaluate the benefit of omega-3 supplementation in women with history of spontaneous preterm birth. Trough plasma concentrations of 17-alpha hydroxyprogesterone caproate were measured between 25-28 weeks of gestation after a minimum of 5 injections of 17-alpha hydroxyprogesterone caproate. We extracted DNA from maternal blood samples and genotyped the samples using TaqMan (Applied Biosystems, Foster City, CA) single nucleotide polymorphism genotyping assays for the following single nucleotide polymorphisms: CYP3A4*1B, CYP3A4*1G, CYP3A4*22, and CYP3A5*3; and rs578029, rs471767, rs666553, rs503362, and rs500760 for progesterone receptor. We adjusted for prepregnancy body mass index, race, and treatment group in a multivariable analysis. Differences in the plasma concentrations of 17-alpha hydroxyprogesterone caproate by genotype were evaluated for each CYP single nucleotide polymorphism using general linear models. The association between progesterone receptor single nucleotide polymorphisms and frequency of spontaneous preterm birth was tested using logistic regression. A logistic model also tested interaction between 17-alpha hydroxyprogesterone caproate concentrations with each progesterone receptor single nucleotide polymorphism for the outcome of spontaneous preterm birth. Results The association between CYP single nucleotide polymorphisms *22, *1G, *1B, and *3 and trough plasma concentrations of 17-alpha hydroxyprogesterone caproate was not statistically significant (P =.68,.44,.08, and.44, respectively). In an adjusted logistic regression model, progesterone receptor single nucleotide polymorphisms rs578029, rs471767, rs666553, rs503362, and rs500760 were not associated with the frequency of spontaneous preterm birth (P =.29,.10,.76,.09, and.43, respectively). Low trough plasma concentrations of 17-alpha hydroxyprogesterone caproate were statistically associated with a higher frequency of spontaneous preterm birth (odds ratio, 0.78; 95% confidence ratio, 0.61–0.99; P =.04 for trend across quartiles), however no significant interaction with the progesterone receptor single nucleotide polymorphisms rs578029, rs471767, rs666553, rs503362, and rs500760 was observed (P =.13,.08,.10,.08, and.13, respectively). Conclusion The frequency of recurrent spontaneous preterm birth appears to be associated with trough 17-alpha hydroxyprogesterone caproate plasma concentrations. However, the wide variation in trough 17-alpha hydroxyprogesterone caproate plasma concentrations is not attributable to polymorphisms in CYP3A4 and CYP3A5 genes. Progesterone receptor polymorphisms do not predict efficacy of 17-alpha hydroxyprogesterone caproate. The limitations of this secondary analysis include that we had a relative small sample size (n = 268) and race was self-reported by the patients