On existence of mini-boson stars

We prove the existence of a countable family of globally regular solutions of spherically symmetric Einstein-Klein-Gordon equations. These solutions, known as mini-boson stars, were discovered numerically many years ago.Comment: 15 pages, 1 eps figure, LaTe

Self-similar solutions of semilinear wave equations with a focusing nonlinearity

We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\Delta u = u^p$ with $p\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio

Analysis of relative influence of nodes in directed networks

Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts, rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PageRank. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.Comment: 9 figure

Relaxation dynamics of maximally clustered networks

We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics---the double-edge swap, corresponding to degree-preserving randomization of the configuration model, and single edge replacement, corresponding to full randomization of the Erd\H{o}s--R\'enyi random graph. We derive expressions for the time evolution of the degree distribution, edge multiplicity distribution and clustering coefficient. We show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed. We calculate the position of the phase transition analytically using the Erd\H{o}s--R\'enyi phenomenology

On the existence of self-similar spherically symmetric wave maps coupled to gravity

We present a detailed analytical study of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using a shooting argument we prove that there is a countable family of solutions which are analytic inside the past self-similarity horizon. In addition, we show that for sufficiently small values of the coupling constant these solutions possess a regular future self-similarity horizon and thus are examples of naked singularities. One of the solutions constructed here has been recently found as the critical solution at the threshold of black hole formation.Comment: 15 pages, LaTe

Social dynamics in conferences: analyses of data from the Live Social Semantics application

Popularity and spread of online social networking in recent years has given a great momentum to the study of dynamics and patterns of social interactions. However, these studies have often been confined to the online world, neglecting its interdependencies with the offline world. This is mainly due to the lack of real data that spans across this divide. The Live Social Semantics application is a novel platform that dissolves this divide, by collecting and integrating data about people from (a) their online social networks and tagging activities from popular social networking sites, (b) their publications and co-authorship networks from semantic repositories, and (c) their real-world face-to-face contacts with other attendees collected via a network of wearable active sensors. This paper investigates the data collected by this application during its deployment at three major conferences, where it was used by more than 400 people. Our analyses show the robustness of the patterns of contacts at various conferences, and the influence of various personal properties (e.g. seniority, conference attendance) on social networking patterns

Centrality scaling in large networks

Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling vs L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5*10^6 nodes and 2.7*10^7 links