10,555 research outputs found
The interleaved multichromatic number of a graph
For , we consider interleaved -tuple colorings of the nodes of a
graph, that is, assignments of distinct natural numbers to each node in
such a way that nodes that are connected by an edge receive numbers that are
strictly alternating between them with respect to the relation . If it takes
at least distinct numbers to provide graph with such a
coloring, then the interleaved multichromatic number of is
and is known to be given by a
function of the simple cycles of under acyclic orientations if is
connected [1]. This paper contains a new proof of this result. Unlike the
original proof, the new proof makes no assumptions on the connectedness of ,
nor does it resort to the possible applications of interleaved -tuple
colorings and their properties
Local heuristics and the emergence of spanning subgraphs in complex networks
We study the use of local heuristics to determine spanning subgraphs for use
in the dissemination of information in complex networks. We introduce two
different heuristics and analyze their behavior in giving rise to spanning
subgraphs that perform well in terms of allowing every node of the network to
be reached, of requiring relatively few messages and small node bandwidth for
information dissemination, and also of stretching paths with respect to the
underlying network only modestly. We contribute a detailed mathematical
analysis of one of the heuristics and provide extensive simulation results on
random graphs for both of them. These results indicate that, within certain
limits, spanning subgraphs are indeed expected to emerge that perform well in
respect to all requirements. We also discuss the spanning subgraphs' inherent
resilience to failures and adaptability to topological changes
Probabilistic heuristics for disseminating information in networks
We study the problem of disseminating a piece of information through all the
nodes of a network, given that it is known originally only to a single node. In
the absence of any structural knowledge on the network other than the nodes'
neighborhoods, this problem is traditionally solved by flooding all the
network's edges. We analyze a recently introduced probabilistic algorithm for
flooding and give an alternative probabilistic heuristic that can lead to some
cost-effective improvements, like better trade-offs between the message and
time complexities involved. We analyze the two algorithms both mathematically
and by means of simulations, always within a random-graph framework and
considering relevant node-degree distributions
A novel evolutionary formulation of the maximum independent set problem
We introduce a novel evolutionary formulation of the problem of finding a
maximum independent set of a graph. The new formulation is based on the
relationship that exists between a graph's independence number and its acyclic
orientations. It views such orientations as individuals and evolves them with
the aid of evolutionary operators that are very heavily based on the structure
of the graph and its acyclic orientations. The resulting heuristic has been
tested on some of the Second DIMACS Implementation Challenge benchmark graphs,
and has been found to be competitive when compared to several of the other
heuristics that have also been tested on those graphs
Topics in Born-Infeld Electrodynamics
Classical version of Born-Infeld electrodynamics is recalled and its most
important properties discussed. Then we analyze possible abelian and
non-abelian generalizations of this theory, and show how certain soliton-like
configurations can be obtained. The relationship with the Standard Model of
electroweak interactions is also mentioned.Comment: (One new reference added). 15 pages, LaTeX. To be published in the
Proceedings of XXXVII Karpacz Winter School edited in the Proceedings Series
of American Mathematical Society, editors J. Lukierski and J. Rembielinsk
Lossy radial diffusion of relativistic Jovian electrons
The radial diffusion equation with synchrotron losses was solved by the Laplace transform method for near-equatorially mirroring relativistic electrons. The evolution of a power law distribution function was found and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient. Emissivity from the radiation belts of Jupiter was studied. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided
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