27,276 research outputs found
Deterministic Modularity Optimization
We study community structure of networks. We have developed a scheme for
maximizing the modularity Q based on mean field methods. Further, we have
defined a simple family of random networks with community structure; we
understand the behavior of these networks analytically. Using these networks,
we show how the mean field methods display better performance than previously
known deterministic methods for optimization of Q.Comment: 7 pages, 4 figures, minor change
Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
We consider the Edwards-Anderson Ising spin glass model on the half-plane with zero external field and a wide range of choices, including
mean zero Gaussian, for the common distribution of the collection J of i.i.d.
nearest neighbor couplings. The infinite-volume joint distribution
of couplings J and ground state pairs with periodic
(respectively, free) boundary conditions in the horizontal (respectively,
vertical) coordinate is shown to exist without need for subsequence limits. Our
main result is that for almost every J, the conditional distribution
is supported on a single ground state pair.Comment: 20 pages, 3 figure
The Brownian Web: Characterization and Convergence
The Brownian Web (BW) is the random network formally consisting of the paths
of coalescing one-dimensional Brownian motions starting from every space-time
point in . We extend the earlier work of Arratia
and of T\'oth and Werner by providing characterization and convergence results
for the BW distribution, including convergence of the system of all coalescing
random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under
diffusive space-time scaling. We also provide characterization and convergence
results for the Double Brownian Web, which combines the BW with its dual
process of coalescing Brownian motions moving backwards in time, with forward
and backward paths ``reflecting'' off each other. For the BW, deterministic
space-time points are almost surely of ``type'' -- {\em zero} paths
into the point from the past and exactly {\em one} path out of the point to the
future; we determine the Hausdorff dimension for all types that actually occur:
dimension 2 for type , 3/2 for and , 1 for , and 0
for and .Comment: 52 pages with 4 figure
Deterministic creation, pinning, and manipulation of quantized vortices in a Bose-Einstein condensate
We experimentally and numerically demonstrate deterministic creation and
manipulation of a pair of oppositely charged singly quantized vortices in a
highly oblate Bose-Einstein condensate (BEC). Two identical blue-detuned,
focused Gaussian laser beams that pierce the BEC serve as repulsive obstacles
for the superfluid atomic gas; by controlling the positions of the beams within
the plane of the BEC, superfluid flow is deterministically established around
each beam such that two vortices of opposite circulation are generated by the
motion of the beams, with each vortex pinned to the \emph{in situ} position of
a laser beam. We study the vortex creation process, and show that the vortices
can be moved about within the BEC by translating the positions of the laser
beams. This technique can serve as a building block in future experimental
techniques to create, on-demand, deterministic arrangements of few or many
vortices within a BEC for precise studies of vortex dynamics and vortex
interactions.Comment: 9 pages, 7 figure
Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
Communication networks show the small-world property of short paths, but the
spreading dynamics in them turns out slow. We follow the time evolution of
information propagation through communication networks by using the SI model
with empirical data on contact sequences. We introduce null models where the
sequences are randomly shuffled in different ways, enabling us to distinguish
between the contributions of different impeding effects. The slowing down of
spreading is found to be caused mostly by weight-topology correlations and the
bursty activity patterns of individuals
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