Role extraction for digraphs via neighborhood pattern similarity.

We analyze the recovery of different roles in a network modeled by a directed graph, based on the so-called Neighborhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that, when assuming that the graph is generated as a particular stochastic block model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles.

Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis.

In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems.

TreeScaper: Visualizing and Extracting Phylogenetic Signal from Sets of Trees.

Modern phylogenomic analyses often result in large collections of phylogenetic trees representing uncertainty in individual gene trees, variation across genes, or both. Extracting phylogenetic signal from these tree sets can be challenging, as they are difficult to visualize, explore, and quantify. To overcome some of these challenges, we have developed TreeScaper, an application for tree set visualization as well as the identification of distinct phylogenetic signals.

Significant scales in community structure.

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods.

Dynamical models explaining social balance and evolution of cooperation.

Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge.