6,524 research outputs found
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 and for which
the rank of is strictly greater than
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
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 has been introduced as a measure to assess the
quality of clusterizations. 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 , which reflects local cluster structure. Optimization
of and 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
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