33,344 research outputs found
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
We construct a braided version of Thompson's group V.Comment: 27 page
The first-mover advantage in scientific publication
Mathematical models of the scientific citation process predict a strong
"first-mover" effect under which the first papers in a field will, essentially
regardless of content, receive citations at a rate enormously higher than
papers published later. Moreover papers are expected to retain this advantage
in perpetuity -- they should receive more citations indefinitely, no matter how
many other papers are published after them. We test this conjecture against
data from a selection of fields and in several cases find a first-mover effect
of a magnitude similar to that predicted by the theory. Were we wearing our
cynical hat today, we might say that the scientist who wants to become famous
is better off -- by a wide margin -- writing a modest paper in next year's
hottest field than an outstanding paper in this year's. On the other hand,
there are some papers, albeit only a small fraction, that buck the trend and
attract significantly more citations than theory predicts despite having
relatively late publication dates. We suggest that papers of this kind, though
they often receive comparatively few citations overall, are probably worthy of
our attention.Comment: 7 pages, 3 figure
Realistic spin glasses below eight dimensions: a highly disordered view
By connecting realistic spin glass models at low temperature to the highly
disordered model at zero temperature, we argue that ordinary Edwards-Anderson
spin glasses below eight dimensions have at most a single pair of physically
relevant pure states at nonzero low temperature. Less likely scenarios that
evade this conclusion are also discussed.Comment: 18 pages (RevTeX; 1 figure; to appear in Physical Review E
Characterizing the structure of small-world networks
We give exact relations which are valid for small-world networks (SWN's) with
a general `degree distribution', i.e the distribution of nearest-neighbor
connections. For the original SWN model, we illustrate how these exact
relations can be used to obtain approximations for the corresponding basic
probability distribution. In the limit of large system sizes and small
disorder, we use numerical studies to obtain a functional fit for this
distribution. Finally, we obtain the scaling properties for the mean-square
displacement of a random walker, which are determined by the scaling behavior
of the underlying SWN
Clustering and preferential attachment in growing networks
We study empirically the time evolution of scientific collaboration networks
in physics and biology. In these networks, two scientists are considered
connected if they have coauthored one or more papers together. We show that the
probability of scientists collaborating increases with the number of other
collaborators they have in common, and that the probability of a particular
scientist acquiring new collaborators increases with the number of his or her
past collaborators. These results provide experimental evidence in favor of
previously conjectured mechanisms for clustering and power-law degree
distributions in networks.Comment: 13 pages, 2 figure
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
Universality and Crossover of Directed Polymers and Growing Surfaces
We study KPZ surfaces on Euclidean lattices and directed polymers on
hierarchical lattices subject to different distributions of disorder, showing
that universality holds, at odds with recent results on Euclidean lattices.
Moreover, we find the presence of a slow (power-law) crossover toward the
universal values of the exponents and verify that the exponent governing such
crossover is universal too. In the limit of a 1+epsilon dimensional system we
obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let
A statistical network analysis of the HIV/AIDS epidemics in Cuba
The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks
Matching Kasteleyn Cities for Spin Glass Ground States
As spin glass materials have extremely slow dynamics, devious numerical
methods are needed to study low-temperature states. A simple and fast
optimization version of the classical Kasteleyn treatment of the Ising model is
described and applied to two-dimensional Ising spin glasses. The algorithm
combines the Pfaffian and matching approaches to directly strip droplet
excitations from an excited state. Extended ground states in Ising spin glasses
on a torus, which are optimized over all boundary conditions, are used to
compute precise values for ground state energy densities.Comment: 4 pages, 2 figures; minor clarification
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