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A general framework for weighted gene coexpression network analysis
 STATISTICAL APPLICATIONS IN GENETICS AND MOLECULAR BIOLOGY 4: ARTICLE 17
, 2005
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An Empirical Bayes Approach to Inferring LargeScale Gene Association Networks
 BIOINFORMATICS
, 2004
"... Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standar ..."
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Cited by 237 (6 self)
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Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an “illposed” inverse problem. Methods: We introduce a novel framework for smallsample inference of graphical models from gene expression data. Specifically, we focus on socalled graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (i) improved (regularized) smallsample point estimates of partial correlation, (ii) an exact test of edge inclusion with adaptive estimation of the degree of freedom, and (iii) a heuristic network search based on false discovery rate multiple testing. Steps (ii) and (iii) correspond to an empirical Bayes estimate of the network topology. Results: Using computer simulations we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for smallsample data sets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding largescale gene association network for 3,883 genes. Availability: The authors have implemented the approach in the R package “GeneTS ” that is freely available from
Scalefree networks in cell biology
 JOURNAL OF CELL SCIENCE
"... A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an everchanging environ ..."
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Cited by 203 (6 self)
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A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an everchanging environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from wholecell function require integrated, theoretical descriptions of the relationships between different cellular components. Recent
Weak pairwise correlations imply strongly correlated network states in a neural population.
, 2006
"... Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higherorder interactions among large groups of elements have an important role. Here we show, ..."
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Cited by 191 (4 self)
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Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higherorder interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higherorder interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or errorcorrecting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons. Much of what we know about biological networks has been learned by studying one element at a timerecording the electrical activity of single neurons, the expression levels of single genes or the concentrations of individual metabolites. On the other hand, important aspects of biological function must be shared among many elements Here we address these questions in the context of the vertebrate retina, where it is possible to make long, stable recordings from many neurons simultaneously as the system responds to complex, naturalistic inputs The scale of correlations Throughout the nervous system, individual elements communicate by generating discrete pulses termed action potentials or spikes The small values of the correlation coefficients suggest an approximation in which the cells are completely independent. For most pairs, this is true with a precision of a few per cent, but if we extrapolate this approximation to the whole population of 40 cells, it fails disastrously. In
Towards a theory of scalefree graphs: Definition, properties, and implications
 Internet Mathematics
, 2005
"... Abstract. There is a large, popular, and growing literature on “scalefree ” networks with the Internet along with metabolic networks representing perhaps the canonical examples. While this has in many ways reinvigorated graph theory, there is unfortunately no consistent, precise definition of scale ..."
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Cited by 137 (12 self)
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Abstract. There is a large, popular, and growing literature on “scalefree ” networks with the Internet along with metabolic networks representing perhaps the canonical examples. While this has in many ways reinvigorated graph theory, there is unfortunately no consistent, precise definition of scalefree graphs and few rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and that the most celebrated claims regarding the Internet and biology are verifiably false. In this paper, we introduce a structural metric that allows us to differentiate between all simple, connected graphs having an identical degree sequence, which is of particular interest when that sequence satisfies a power law relationship. We demonstrate that the proposed structural metric yields considerable insight into the claimed properties of SF graphs and provides one possible measure of the extent to which a graph is scalefree. This structural view can be related to previously studied graph properties such as the various notions of selfsimilarity, likelihood, betweenness and assortativity. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the current literature, and offers a rigorous and quantitative alternative, while suggesting the potential for a rich and interesting theory. This paper is aimed at readers familiar with the basics of Internet technology and comfortable with a theoremproof style of exposition, but who may be unfamiliar with the existing literature on scalefree networks. 1.
Biological network comparison using graphlet degree distribution
 Bioinformatics
"... Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degr ..."
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Cited by 102 (1 self)
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Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it
Partial Correlation Estimation by Joint Sparse Regression Models
 JASA
, 2008
"... In this article, we propose a computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for selecting nonzero partial correlations under the highdimensionlowsamplesize setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse re ..."
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Cited by 94 (8 self)
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In this article, we propose a computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for selecting nonzero partial correlations under the highdimensionlowsamplesize setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.
WEBbased GEne SeT AnaLysis Toolkit (WebGestalt): update 2013. Nucleic Acids Res. 2013;41(Web Server issue):W77–83
"... Functional enrichment analysis is an essential task for the interpretation of gene lists derived from largescale genetic, transcriptomic and proteomic studies. WebGestalt (WEBbased GEne SeT AnaLysis Toolkit) has become one of the popular software tools in this field since its publication in 2005. ..."
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Cited by 87 (0 self)
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Functional enrichment analysis is an essential task for the interpretation of gene lists derived from largescale genetic, transcriptomic and proteomic studies. WebGestalt (WEBbased GEne SeT AnaLysis Toolkit) has become one of the popular software tools in this field since its publication in 2005. For the last 7 years, WebGestalt data holdings have grown substantially to satisfy the requirements of users from different research areas. The current version of WebGestalt supports 8 organisms and 201 gene identifiers from various databases and different technology platforms, making it directly available to the fast growing omics community. Meanwhile, by integrating functional categories derived from centrally and publicly curated databases as well as computational analyses, WebGestalt has significantly increased the coverage of functional categories in various biological contexts including Gene Ontology, pathway, network module, gene–phenotype association, gene–disease association, gene–drug association and chromosomal location, leading to a total of 78 612 functional categories. Finally, new interactive features, such as pathway map, hierarchical network visualization and phenotype ontology visualization have been added to WebGestalt to help users better understand the enrichment results. WebGestalt can be freely accessed through