356 research outputs found
Multistep greedy algorithm identifies community structure in real-world and computer-generated networks
We have recently introduced a multistep extension of the greedy algorithm for
modularity optimization. The extension is based on the idea that merging l
pairs of communities (l>1) at each iteration prevents premature condensation
into few large communities. Here, an empirical formula is presented for the
choice of the step width l that generates partitions with (close to) optimal
modularity for 17 real-world and 1100 computer-generated networks. Furthermore,
an in-depth analysis of the communities of two real-world networks (the
metabolic network of the bacterium E. coli and the graph of coappearing words
in the titles of papers coauthored by Martin Karplus) provides evidence that
the partition obtained by the multistep greedy algorithm is superior to the one
generated by the original greedy algorithm not only with respect to modularity
but also according to objective criteria. In other words, the multistep
extension of the greedy algorithm reduces the danger of getting trapped in
local optima of modularity and generates more reasonable partitions.Comment: 17 pages, 2 figure
Religion et cours de natation
Sommaire:
1. INTRODUCTION.
2. LâAFFAIRE OSMANOÄLU: FAITS ET PROCEDURE.
3. LA PRATIQUE DES ETATS MEMBRES DU CONSEIL DE LâEUROPE.
4. LE JUGEMENT DE LA COUR DE STRASBOURG. a) GĂ©nĂ©ralitĂ©s. b) Existence dâune ingĂ©rence. c) Justification de lâingĂ©rence. i) Base lĂ©gale. ii) But lĂ©gitime. iii) Mesure nĂ©cessaire dans une sociĂ©tĂ© dĂ©mocratique?. La thĂšse des requĂ©rants. Les arguments du Gouvernement. Le jugement de la Cour.
5. COMMENTAIRE
Level Set Approach to Reversible Epitaxial Growth
We generalize the level set approach to model epitaxial growth to include
thermal detachment of atoms from island edges. This means that islands do not
always grow and island dissociation can occur. We make no assumptions about a
critical nucleus. Excellent quantitative agreement is obtained with kinetic
Monte Carlo simulations for island densities and island size distributions in
the submonolayer regime.Comment: 7 pages, 9 figure
Motion of a vortex sheet on a sphere with pole vortices
We cons i der the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices xed on north and south poles.Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties.First,the vortex sheet is linearly unstable due to Kelvin-Helmholtz instability.Second,the curvature of the vortex sheet diverges in nite time.Last,the vortex sheet evolves into a rolling-up doubly branched spiral,when the equation of motion is regularized by the vortex method.The purpose of this article is to investigate how the curvature of the sphere and the presence of the pole vortices
On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials
The paper concerns - convergence to equilibrium for weak solutions of
the spatially homogeneous Boltzmann Equation for soft potentials (-4\le
\gm<0), with and without angular cutoff. We prove the time-averaged
-convergence to equilibrium for all weak solutions whose initial data have
finite entropy and finite moments up to order greater than 2+|\gm|. For the
usual -convergence we prove that the convergence rate can be controlled
from below by the initial energy tails, and hence, for initial data with long
energy tails, the convergence can be arbitrarily slow. We also show that under
the integrable angular cutoff on the collision kernel with -1\le \gm<0, there
are algebraic upper and lower bounds on the rate of -convergence to
equilibrium. Our methods of proof are based on entropy inequalities and moment
estimates.Comment: This version contains a strengthened theorem 3, on rate of
convergence, considerably relaxing the hypotheses on the initial data, and
introducing a new method for avoiding use of poitwise lower bounds in
applications of entropy production to convergence problem
Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement
Identifying strongly connected substructures in large networks provides
insight into their coarse-grained organization. Several approaches based on the
optimization of a quality function, e.g., the modularity, have been proposed.
We present here a multistep extension of the greedy algorithm (MSG) that allows
the merging of more than one pair of communities at each iteration step. The
essential idea is to prevent the premature condensation into few large
communities. Upon convergence of the MSG a simple refinement procedure called
"vertex mover" (VM) is used for reassigning vertices to neighboring communities
to improve the final modularity value. With an appropriate choice of the step
width, the combined MSG-VM algorithm is able to find solutions of higher
modularity than those reported previously. The multistep extension does not
alter the scaling of computational cost of the greedy algorithm.Comment: 7 pages, parts of text rewritten, illustrations and pseudocode
representation of algorithms adde
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