39,937 research outputs found
Adjacency labeling schemes and induced-universal graphs
We describe a way of assigning labels to the vertices of any undirected graph
on up to vertices, each composed of bits, such that given the
labels of two vertices, and no other information regarding the graph, it is
possible to decide whether or not the vertices are adjacent in the graph. This
is optimal, up to an additive constant, and constitutes the first improvement
in almost 50 years of an bound of Moon. As a consequence, we
obtain an induced-universal graph for -vertex graphs containing only
vertices, which is optimal up to a multiplicative constant,
solving an open problem of Vizing from 1968. We obtain similar tight results
for directed graphs, tournaments and bipartite graphs
High Density Preheating Effects on Q-ball Decays and MSSM Inflation
Non-perturbative preheating decay of post-inflationary condensates often
results in a high density, low momenta, non-thermal gas. In the case where the
non-perturbative classical evolution also leads to Q-balls, this effect shields
them from instant dissociation, and may radically change the thermal history of
the universe. For example, in a large class of inflationary scenarios,
motivated by the MSSM and its embedding in string theory, the reheat
temperature changes by a multiplicative factor of .Comment: 4 page
Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method
Using the Fock-Schwinger proper time method, we calculate the induced
Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum
electrodynamics with a term. Our
result to all orders in coincides with a recent linear-in- calculation
by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by
Chung [Phys. Lett. {\bf B461} (1999) 138] and P\'{e}rez-Victoria [Phys. Rev.
Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with
the nonperturbative-in- propagator.Comment: 11 pages, no figur
From Lyapunov modes to the exponents for hard disk systems
We demonstrate the preservation of the Lyapunov modes by the underlying
tangent space dynamics of hard disks.
This result is exact for the zero modes and correct to order for
the transverse and LP modes where is linear in the mode number.
For sufficiently large mode numbers the dynamics no longer preserves the mode
structure.
We propose a Gram-Schmidt procedure based on orthogonality with respect to
the centre space that determines the values of the Lyapunov exponents for the
modes.
This assumes a detailed knowledge of the modes, but from that predicts the
values of the exponents from the modes.
Thus the modes and the exponents contain the same information
Dilaton-Axion hair for slowly rotating Kerr black holes
Campbell et al. demonstrated the existence of axion ``hair'' for Kerr black
holes due to the non-trivial Lorentz Chern-Simons term and calculated it
explicitly for the case of slow rotation. Here we consider the dilaton coupling
to the axion field strength, consistent with low energy string theory and
calculate the dilaton ``hair'' arising from this specific axion source.Comment: 13 pages + 1 fi
O-atom degradation mechanisms of materials
The low Earth orbit environment is described and the critical issues relating to oxygen atom degradation are discussed. Some analytic techniques for studying the problem and preliminary results on the underlying degradation mechanisms are presented
Mind the Gap: A Study in Global Development through Persistent Homology
The Gapminder project set out to use statistics to dispel simplistic notions
about global development. In the same spirit, we use persistent homology, a
technique from computational algebraic topology, to explore the relationship
between country development and geography. For each country, four indicators,
gross domestic product per capita; average life expectancy; infant mortality;
and gross national income per capita, were used to quantify the development.
Two analyses were performed. The first considers clusters of the countries
based on these indicators, and the second uncovers cycles in the data when
combined with geographic border structure. Our analysis is a multi-scale
approach that reveals similarities and connections among countries at a variety
of levels. We discover localized development patterns that are invisible in
standard statistical methods
Diameters in preferential attachment models
In this paper, we investigate the diameter in preferential attachment (PA-)
models, thus quantifying the statement that these models are small worlds. The
models studied here are such that edges are attached to older vertices
proportional to the degree plus a constant, i.e., we consider affine PA-models.
There is a substantial amount of literature proving that, quite generally,
PA-graphs possess power-law degree sequences with a power-law exponent \tau>2.
We prove that the diameter of the PA-model is bounded above by a constant
times \log{t}, where t is the size of the graph. When the power-law exponent
\tau exceeds 3, then we prove that \log{t} is the right order, by proving a
lower bound of this order, both for the diameter as well as for the typical
distance. This shows that, for \tau>3, distances are of the order \log{t}. For
\tau\in (2,3), we improve the upper bound to a constant times \log\log{t}, and
prove a lower bound of the same order for the diameter. Unfortunately, this
proof does not extend to typical distances. These results do show that the
diameter is of order \log\log{t}.
These bounds partially prove predictions by physicists that the typical
distance in PA-graphs are similar to the ones in other scale-free random
graphs, such as the configuration model and various inhomogeneous random graph
models, where typical distances have been shown to be of order \log\log{t} when
\tau\in (2,3), and of order \log{t} when \tau>3
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