6,124 research outputs found
On the hard sphere model and sphere packings in high dimensions
We prove a lower bound on the entropy of sphere packings of of
density . The entropy measures how plentiful such
packings are, and our result is significantly stronger than the trivial lower
bound that can be obtained from the mere existence of a dense packing. Our
method also provides a new, statistical-physics-based proof of the lower bound on the maximum sphere packing density by showing
that the expected packing density of a random configuration from the hard
sphere model is at least when the
ratio of the fugacity parameter to the volume covered by a single sphere is at
least . Such a bound on the sphere packing density was first achieved
by Rogers, with subsequent improvements to the leading constant by Davenport
and Rogers, Ball, Vance, and Venkatesh
Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers
Single domain proteins are thought to be tightly packed. The introduction of
voids by mutations is often regarded as destabilizing. In this study we show
that packing density for single domain proteins decreases with chain length. We
find that the radius of gyration provides poor description of protein packing
but the alpha contact number we introduce here characterize proteins well. We
further demonstrate that protein-like scaling relationship between packing
density and chain length is observed in off-lattice self-avoiding walks. A key
problem in studying compact chain polymer is the attrition problem: It is
difficult to generate independent samples of compact long self-avoiding walks.
We develop an algorithm based on the framework of sequential Monte Carlo and
succeed in generating populations of compact long chain off-lattice polymers up
to length . Results based on analysis of these chain polymers suggest
that maintaining high packing density is only characteristic of short chain
proteins. We found that the scaling behavior of packing density with chain
length of proteins is a generic feature of random polymers satisfying loose
constraint in compactness. We conclude that proteins are not optimized by
evolution to eliminate packing voids.Comment: 9 pages, 10 figures. Accepted by J. Chem. Phy
Space Frequency Codes from Spherical Codes
A new design method for high rate, fully diverse ('spherical') space
frequency codes for MIMO-OFDM systems is proposed, which works for arbitrary
numbers of antennas and subcarriers. The construction exploits a differential
geometric connection between spherical codes and space time codes. The former
are well studied e.g. in the context of optimal sequence design in CDMA
systems, while the latter serve as basic building blocks for space frequency
codes. In addition a decoding algorithm with moderate complexity is presented.
This is achieved by a lattice based construction of spherical codes, which
permits lattice decoding algorithms and thus offers a substantial reduction of
complexity.Comment: 5 pages. Final version for the 2005 IEEE International Symposium on
Information Theor
Rotated sphere packing designs
We propose a new class of space-filling designs called rotated sphere packing
designs for computer experiments. The approach starts from the asymptotically
optimal positioning of identical balls that covers the unit cube. Properly
scaled, rotated, translated and extracted, such designs are excellent in
maximin distance criterion, low in discrepancy, good in projective uniformity
and thus useful in both prediction and numerical integration purposes. We
provide a fast algorithm to construct such designs for any numbers of
dimensions and points with R codes available online. Theoretical and numerical
results are also provided
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