6,536 research outputs found
Rapid Mixing for Lattice Colorings with Fewer Colors
We provide an optimally mixing Markov chain for 6-colorings of the square
lattice on rectangular regions with free, fixed, or toroidal boundary
conditions. This implies that the uniform distribution on the set of such
colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet
has a finite correlation length and a unique Gibbs measure at zero temperature.
Four and five are now the only remaining values of q for which it is not known
whether there exists a rapidly mixing Markov chain for q-colorings of the
square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA
Spatial Mixing of Coloring Random Graphs
We study the strong spatial mixing (decay of correlation) property of proper
-colorings of random graph with a fixed . The strong spatial
mixing of coloring and related models have been extensively studied on graphs
with bounded maximum degree. However, for typical classes of graphs with
bounded average degree, such as , an easy counterexample shows that
colorings do not exhibit strong spatial mixing with high probability.
Nevertheless, we show that for with and
sufficiently large , with high probability proper -colorings of
random graph exhibit strong spatial mixing with respect to an
arbitrarily fixed vertex. This is the first strong spatial mixing result for
colorings of graphs with unbounded maximum degree. Our analysis of strong
spatial mixing establishes a block-wise correlation decay instead of the
standard point-wise decay, which may be of interest by itself, especially for
graphs with unbounded degree
Ablation debris control by means of closed thick film filtered water immersion
The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types
Quantum speedup of classical mixing processes
Most approximation algorithms for #P-complete problems (e.g., evaluating the
permanent of a matrix or the volume of a polytope) work by reduction to the
problem of approximate sampling from a distribution over a large set
. This problem is solved using the {\em Markov chain Monte Carlo} method: a
sparse, reversible Markov chain on with stationary distribution
is run to near equilibrium. The running time of this random walk algorithm, the
so-called {\em mixing time} of , is as shown
by Aldous, where is the spectral gap of and is the minimum
value of . A natural question is whether a speedup of this classical
method to , the diameter of the graph
underlying , is possible using {\em quantum walks}.
We provide evidence for this possibility using quantum walks that {\em
decohere} under repeated randomized measurements. We show: (a) decoherent
quantum walks always mix, just like their classical counterparts, (b) the
mixing time is a robust quantity, essentially invariant under any smooth form
of decoherence, and (c) the mixing time of the decoherent quantum walk on a
periodic lattice is , which is indeed
and is asymptotically no worse than the
diameter of (the obvious lower bound) up to at most a logarithmic
factor.Comment: 13 pages; v2 revised several part
Gravitational lens optical scalars in terms of energy-momentum distributions
This is a general work on gravitational lensing. We present new expressions
for the optical scalars and the deflection angle in terms of the
energy-momentum tensor components of matter distributions. Our work generalizes
standard references in the literature where normally stringent assumptions are
made on the sources. The new expressions are manifestly gauge invariant, since
they are presented in terms of curvature components. We also present a method
of approximation for solving the lens equations, that can be applied to any
order.Comment: 17 pages, 2 figures. Titled changed. Small improvements. References
added. Final version published in Phys.Rev.
Two-divisibility of the coefficients of certain weakly holomorphic modular forms
We study a canonical basis for spaces of weakly holomorphic modular forms of
weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a
relation between the Fourier coefficients of modular forms in this canonical
basis and a generalized Ramanujan tau-function, and use this to prove that
these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa
X-Ray Synchrotron Emitting Fe-Rich Ejecta in SNR RCW 86
Supernova remnants may exhibit both thermal and nonthermal X-ray emission. We
present Chandra observations of RCW 86. Striking differences in the morphology
of X-rays below 1 keV and above 2 keV point to a different physical origin.
Hard X-ray emission is correlated fairly well with the edges of regions of
radio emission, suggesting that these are the locations of shock waves at which
both short-lived X-ray emitting electrons, and longer-lived radio-emitting
electrons, are accelerated. Soft X-rays are spatially well-correlated with
optical emission from nonradiative shocks, which are almost certainly portions
of the outer blast wave. These soft X-rays are well fit with simple thermal
plane-shock models. Harder X-rays show Fe K alpha emission and are well
described with a similar soft thermal component, but a much stronger
synchrotron continuum dominating above 2 keV, and a strong Fe K alpha line.
Quantitative analysis of this line and the surrounding continuum shows that it
cannot be produced by thermal emission from a cosmic-abundance plasma; the
ionization time is too short, as shown both by the low centroid energy (6.4
keV) and the absence of oxygen lines below 1 keV. Instead, a model of a plane
shock into Fe-rich ejecta, with a synchrotron continuum, provides a natural
explanation. This requires that reverse shocks into ejecta be accelerating
electrons to energies of order 50 TeV. We show that maximum energies of this
order can be produced by radiation-limited diffusive shock acceleration at the
reverse shocks.Comment: ApJ, accepted; full resolution images in
http://spider.ipac.caltech.edu/staff/rho/rcw86chandra.p
Generalized Swiss-cheese cosmologies: Mass scales
We generalize the Swiss-cheese cosmologies so as to include nonzero linear
momenta of the associated boundary surfaces. The evolution of mass scales in
these generalized cosmologies is studied for a variety of models for the
background without having to specify any details within the local
inhomogeneities. We find that the final effective gravitational mass and size
of the evolving inhomogeneities depends on their linear momenta but these
properties are essentially unaffected by the details of the background model.Comment: 10 pages, 14 figures, 1 table, revtex4, Published form (with minor
corrections
Visual search in ecological and non-ecological displays: Evidence for a non-monotonic effect of complexity on performance
Copyright @ 2013 PLoSThis article has been made available through the Brunel Open Access Publishing Fund.Considerable research has been carried out on visual search, with single or multiple targets. However, most studies have used artificial stimuli with low ecological validity. In addition, little is known about the effects of target complexity and expertise in visual search. Here, we investigate visual search in three conditions of complexity (detecting a king, detecting a check, and detecting a checkmate) with chess players of two levels of expertise (novices and club players). Results show that the influence of target complexity depends on level of structure of the visual display. Different functional relationships were found between artificial (random chess positions) and ecologically valid (game positions) stimuli: With artificial, but not with ecologically valid stimuli, a “pop out” effect was present when a target was visually more complex than distractors but could be captured by a memory chunk. This suggests that caution should be exercised when generalising from experiments using artificial stimuli with low ecological validity to real-life stimuli.This study is funded by Brunel University and the article is made available through the Brunel Open Access Publishing Fund
- …