Stefansen Floyd (pumabeard4)

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent approach for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but potentially inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between the connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By incorporating edge correlations, we find that prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously purchased grocery products.How the internal degree of freedom of particles influences self-organization is explored by considering cluster formation in many-particle systems. We analyze a general class of dynamical systems in which the interactions between particles depend on their spatial distance and the difference of their internal states. In particular, we analyze a three-particle system in which two types of steady patterns exist, namely, (i) a regular triangle (two-dimensional cluster) and (ii) a straight line (one-dimensional cluster). The results show that the linear pattern can be stable when the internal degree of freedom exists, while it is always unstable when the dynamics depend only on the spatial distance. Based on this analysis, we can understand why this difference occurs. If the internal states can cause asymmetry of the interactions, this can enable the particles to remain in a one-dimensional cluster.Structural changes in a network representation of a system, due to different experimental conditions, different connectivity across layers, or to its time evolution, can provide insight on its organization, function, and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is maybe the most incisive demonstration of the gains obtained through this differential network analysis point of view, which led to an explosion of new numeric techniques in the last decade. However, where to focus one's attention, or how to navigate through the differential structures in the context of large networks, can be overwhelming even for a few experimental conditions. In this paper, we propose a theory and a methodological implementation for the characterization of shared "structural roles" of nodes simultaneously within and between networks. Inspired by recent methodological advances in chaotic phase synchronization analysis, we show how the information abed to pinpoint unexpected shared structure, leading to further investigations and providing new insights. Finally, the method is flexible to address different research-field-specific questions, by not restricting what scientific-meaningful characteristic (or relevant feature) of a node shall be used.In this paper, we examine the virial- and the potential-energy correlation for quasireal model systems. This correlation constitutes the framework of the theory of the isomorph in the liquid phase diagram commonly examined using simple liquids. Interestingly, our results show that for the systems characterized by structural anisotropy and flexible bonds, the instantaneous values of total virial and total potential energy are entirely uncorrelated. It is due to the presence of the