Investigation of the Interior of Colored Black Holes and the Extendability of Solutions of the Einstein-Yang/Mills Equations

We prove that any asymptotically flat solution to the spherically symmetric SU(2) Einstein-Yang/Mills equations is globally defined. This result applies in particular to the interior of colored black holes.Comment: Latex, 8 gif figure

On the rank of a product of manifolds

This note gives an example of closed smooth manifolds $M$ and $N$ for which the rank of $M\times N$ is strictly greater than $rank M + rank N$

Reissner-Nordstrom-like solutions of the SU(2) Einstein-Yang/Mills (EYM) equations

In this paper we study a new type of solution of the spherically symmetric, Einstein-Yang/Mills (EYM) equations with SU(2) gauge group. These solutions are well-behaved in the far-field, and have a Reissner-Nordstrom type essential singularity at the origin. These solutions display some novel features which are not present in particle-like, or black-hole solutions. Any spherically symmetric solution to the EYM equations, defined in the far-field, is either a particle-like solution, a black-hole solution, or one of these RNL solutions.Comment: 5 pages, latex, no figures, Submitted to Comm. Math. Phys. January 15, 199

Extending algebraic actions

Sin resume

Spatial energy spectrum of primordial magnetic fields

Here, we analyze the primordial magnetic field transition between a radiative and a matter-dominated universe. The gravitational structure formation affects its evolution and energy spectrum. The structure excitation can trigger magnetic field amplification and the steepening of its energy density spectrum.Comment: 8 pages, 2 figures, accepted for A&

Local modularity measure for network clusterizations

Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity $Q$ has been introduced as a measure to assess the quality of clusterizations. $Q$ has a global view, while in many real-world networks clusters are linked mainly \emph{locally} among each other (\emph{local cluster-connectivity}). Here, we introduce a new measure, localized modularity $LQ$, which reflects local cluster structure. Optimization of $Q$ and $LQ$ on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.Comment: 5 pages, 4 figures, RevTex4; Changed conten

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