4,998 research outputs found
Approximate Capacities of Two-Dimensional Codes by Spatial Mixing
We apply several state-of-the-art techniques developed in recent advances of
counting algorithms and statistical physics to study the spatial mixing
property of the two-dimensional codes arising from local hard (independent set)
constraints, including: hard-square, hard-hexagon, read/write isolated memory
(RWIM), and non-attacking kings (NAK). For these constraints, the strong
spatial mixing would imply the existence of polynomial-time approximation
scheme (PTAS) for computing the capacity. It was previously known for the
hard-square constraint the existence of strong spatial mixing and PTAS. We show
the existence of strong spatial mixing for hard-hexagon and RWIM constraints by
establishing the strong spatial mixing along self-avoiding walks, and
consequently we give PTAS for computing the capacities of these codes. We also
show that for the NAK constraint, the strong spatial mixing does not hold along
self-avoiding walks
Detecting gravitational waves from highly eccentric compact binaries
In dense stellar regions, highly eccentric binaries of black holes and
neutron stars can form through various n-body interactions. Such a binary could
emit a significant fraction of its binding energy in a sequence of largely
isolated gravitational wave bursts prior to merger. Given expected black hole
and neutron star masses, many such systems will emit these repeated bursts at
frequencies within the sensitive band of contemporary ground-based
gravitational wave detectors. Unfortunately, existing gravitational wave
searches are ill-suited to detect these signals. In this work, we adapt a
"power stacking" method to the detection of gravitational wave signals from
highly eccentric binaries. We implement this method as an extension of the
Q-transform, a projection onto a multiresolution basis of windowed complex
exponentials that has previously been used to analyze data from the network of
LIGO/Virgo detectors. Our method searches for excess power over an ensemble of
time-frequency tiles. We characterize the performance of our method using Monte
Carlo experiments with signals injected in simulated detector noise. Our
results indicate that the power stacking method achieves substantially better
sensitivity to eccentric binary signals than existing localized burst searches.Comment: 17 pages, 20 figure
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