22,945 research outputs found
Kolmogorov Random Graphs and the Incompressibility Method
We investigate topological, combinatorial, statistical, and enumeration
properties of finite graphs with high Kolmogorov complexity (almost all graphs)
using the novel incompressibility method. Example results are: (i) the mean and
variance of the number of (possibly overlapping) ordered labeled subgraphs of a
labeled graph as a function of its randomness deficiency (how far it falls
short of the maximum possible Kolmogorov complexity) and (ii) a new elementary
proof for the number of unlabeled graphs.Comment: LaTeX 9 page
Surface Incompressibility from Semiclassical Relativistic Mean Field Calculations
By using the scaling method and the Thomas-Fermi and Extended Thomas-Fermi
approaches to Relativistic Mean Field Theory the surface contribution to the
leptodermous expansion of the finite nuclei incompressibility has been
self-consistently computed. The validity of the simplest expansion, which
contains volume, volume-symmetry, surface and Coulomb terms, is examined by
comparing it with self-consistent results of the finite nuclei
incompressibility for some currently used non-linear sigma-omega parameter
sets. A numerical estimate of higher-order contributions to the leptodermous
expansion, namely the curvature and surface-symmetry terms, is made.Comment: 18 pages, REVTeX, 3 eps figures, changed conten
Analysis of the incompressibility constraint in the Smoothed Particle Hydrodynamics method
Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method
for fluid-flow simulations. In this work, fundamental concepts of the method
are first briefly recalled. Then, we present a thorough comparison of three
different incompressibility treatments in SPH: the weakly compressible
approach, where a suitably-chosen equation of state is used; and two truly
incompressible methods, where the velocity field projection onto a
divergence-free space is performed. A noteworthy aspect of the study is that,
in each incompressibility treatment, the same boundary conditions are used (and
further developed) which allows a direct comparison to be made. Problems
associated with implementation are also discussed and an optimal choice of the
computational parameters has been proposed and verified. Numerical results show
that the present state-of-the-art truly incompressible method (based on a
velocity correction) suffer from density accumulation errors. To address this
issue, an algorithm, based on a correction for both particle velocities and
positions, is presented. The usefulness of this density correction is examined
and demonstrated in the last part of the paper
Generator Coordinate Calculations for the Breathing-Mode Giant Monopole Resonance in Relativistic Mean Field Theory
The breathing-mode giant monopole resonance (GMR) is studied within the
framework of the relativistic mean-field theory using the Generator Coordinate
Method (GCM). The constrained incompressibility and the excitation energy of
isoscalar giant monopole states are obtained for finite nuclei with various
sets of Lagrangian parameters. A comparison is made with the results of
nonrelativistic constrained Skyrme Hartree-Fock calculations and with those
from Skyrme RPA calculations. In the RMF theory the GCM calculations give a
transition density for the breathing mode, which resembles much that obtained
from the Skyrme HF+RPA approach and also that from the scaling mode of the GMR.
From the systematic study of the breathing-mode as a function of the
incompressibility in GCM, it is shown that the GCM succeeds in describing the
GMR energies in nuclei and that the empirical breathing-mode energies of heavy
nuclei can be reproduced by forces with an incompressibility close to
MeV in the RMF theory.Comment: 27 pages (Revtex) and 5 figures (available upon request), Preprint
MPA-793 (March 1994
Using the Incompressibility Method to obtain Local Lemma results for Ramsey-type Problems
We reveal a connection between the incompressibility method and the Lovasz
local lemma in the context of Ramsey theory. We obtain bounds by repeatedly
encoding objects of interest and thereby compressing strings. The method is
demonstrated on the example of van der Waerden numbers. It applies to lower
bounds of Ramsey numbers, large transitive subtournaments and other Ramsey
phenomena as well.Comment: 8 pages, 1 figur
Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method
We use the incompressibility method based on Kolmogorov complexity to
determine the total number of bits of routing information for almost all
network topologies. In most models for routing, for almost all labeled graphs
bits are necessary and sufficient for shortest path routing. By
`almost all graphs' we mean the Kolmogorov random graphs which constitute a
fraction of of all graphs on nodes, where is an arbitrary
fixed constant. There is a model for which the average case lower bound rises
to and another model where the average case upper bound
drops to . This clearly exposes the sensitivity of such bounds
to the model under consideration. If paths have to be short, but need not be
shortest (if the stretch factor may be larger than 1), then much less space is
needed on average, even in the more demanding models. Full-information routing
requires bits on average. For worst-case static networks we
prove a lower bound for shortest path routing and all
stretch factors in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea
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