2,738 research outputs found
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
Low-Temperature Excitations of Dilute Lattice Spin Glasses
A new approach to exploring low-temperature excitations in finite-dimensional
lattice spin glasses is proposed. By focusing on bond-diluted lattices just
above the percolation threshold, large system sizes can be obtained which
lead to enhanced scaling regimes and more accurate exponents. Furthermore, this
method in principle remains practical for any dimension, yielding exponents
that so far have been elusive. This approach is demonstrated by determining the
stiffness exponent for dimensions , (the upper critical dimension),
and . Key is the application of an exact reduction algorithm, which
eliminates a large fraction of spins, so that the reduced lattices never exceed
variables for sizes as large as L=30 in , L=9 in , or L=8
in . Finite size scaling analysis gives for ,
significantly improving on previous work. The results for and ,
and , are entirely new and are compared with
mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in
d=7, as to appear in Europhysics Letters (see
http://www.physics.emory.edu/faculty/boettcher/ for related information
d_c=4 is the upper critical dimension for the Bak-Sneppen model
Numerical results are presented indicating d_c=4 as the upper critical
dimension for the Bak-Sneppen evolution model. This finding agrees with
previous theoretical arguments, but contradicts a recent Letter [Phys. Rev.
Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we
find that avalanches are compact for all dimensions d<=4, and are fractal for
d>4. Under those conditions, scaling arguments predict a d_c=4, where
hyperscaling relations hold for d<=4. Other properties of avalanches, studied
for 1<=d<=6, corroborate this result. To this end, an improved numerical
algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers
available at http://userwww.service.emory.edu/~sboettc
Extremal Optimization for Graph Partitioning
Extremal optimization is a new general-purpose method for approximating
solutions to hard optimization problems. We study the method in detail by way
of the NP-hard graph partitioning problem. We discuss the scaling behavior of
extremal optimization, focusing on the convergence of the average run as a
function of runtime and system size. The method has a single free parameter,
which we determine numerically and justify using a simple argument. Our
numerical results demonstrate that on random graphs, extremal optimization
maintains consistent accuracy for increasing system sizes, with an
approximation error decreasing over runtime roughly as a power law t^(-0.4). On
geometrically structured graphs, the scaling of results from the average run
suggests that these are far from optimal, with large fluctuations between
individual trials. But when only the best runs are considered, results
consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers
available at http://www.physics.emory.edu/faculty/boettcher
SALT Spectropolarimetry and Self-Consistent SED and Polarization Modeling of Blazars
We report on recent results from a target-of-opportunity program to obtain
spectropolarimetry observations with the Southern African Large Telescope
(SALT) on flaring gamma-ray blazars. SALT spectropolarimetry and
contemporaneous multi-wavelength spectral energy distribution (SED) data are
being modelled self-consistently with a leptonic single-zone model. Such
modeling provides an accurate estimate of the degree of order of the magnetic
field in the emission region and the thermal contributions (from the host
galaxy and the accretion disk) to the SED, thus putting strong constraints on
the physical parameters of the gamma-ray emitting region. For the specific case
of the -ray blazar 4C+01.02, we demonstrate that the combined SED and
spectropolarimetry modeling constrains the mass of the central black hole in
this blazar to .Comment: Submitted to Galaxies - Proceedings of "Polarized Emission from
Astrophysical Jets", Ierapetra, Crete, June 12 - 16, 201
Continuous extremal optimization for Lennard-Jones Clusters
In this paper, we explore a general-purpose heuristic algorithm for finding
high-quality solutions to continuous optimization problems. The method, called
continuous extremal optimization(CEO), can be considered as an extension of
extremal optimization(EO) and is consisted of two components, one is with
responsibility for global searching and the other is with responsibility for
local searching. With only one adjustable parameter, the CEO's performance
proves competitive with more elaborate stochastic optimization procedures. We
demonstrate it on a well known continuous optimization problem: the
Lennerd-Jones clusters optimization problem.Comment: 5 pages and 3 figure
Current definitions of âtransdiagnosticâ in treatment development: A search for consensus
Research in psychopathology has identified psychological processes that are relevant across a range of Diagnostic and Statistical Manual (DSM) mental disorders, and these efforts have begun to produce treatment principles and protocols that can be applied transdiagnostically. However, review of recent work suggests that there has been great variability in conceptions of the term âtransdiagnosticâ in the treatment development literature. We believe that there is value in arriving at a common understanding of the term âtransdiagnostic.â The purpose of the current manuscript is to outline three principal ways in which the term âtransdiagnosticâ is currently used, to delineate treatment approaches that fall into these three categories, and to consider potential advantages and disadvantages of each approachFirst author draf
Reduction of Dilute Ising Spin Glasses
The recently proposed reduction method for diluted spin glasses is
investigated in depth. In particular, the Edwards-Anderson model with \pm J and
Gaussian bond disorder on hyper-cubic lattices in d=2, 3, and 4 is studied for
a range of bond dilutions. The results demonstrate the effectiveness of using
bond dilution to elucidate low-temperature properties of Ising spin glasses,
and provide a starting point to enhance the methods used in reduction. Based on
that, a greedy heuristic call ``Dominant Bond Reduction'' is introduced and
explored.Comment: 10 pages, revtex, final version, find related material at
http://www.physics.emory.edu/faculty/boettcher
Hysteretic Optimization For Spin Glasses
The recently proposed Hysteretic Optimization (HO) procedure is applied to
the 1D Ising spin chain with long range interactions. To study its
effectiveness, the quality of ground state energies found as a function of the
distance dependence exponent, , is assessed. It is found that the
transition from an infinite-range to a long-range interaction at
is accompanied by a sharp decrease in the performance . The transition is
signaled by a change in the scaling behavior of the average avalanche size
observed during the hysteresis process. This indicates that HO requires the
system to be infinite-range, with a high degree of interconnectivity between
variables leading to large avalanches, in order to function properly. An
analysis of the way auto-correlations evolve during the optimization procedure
confirm that the search of phase space is less efficient, with the system
becoming effectively stuck in suboptimal configurations much earlier. These
observations explain the poor performance that HO obtained for the
Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that
its usefulness might be limited in many combinatorial optimization problems.Comment: 6 pages, 9 figures. To appear in JSTAT. Author website:
http://www.bgoncalves.co
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