31,919 research outputs found
Mining Pure, Strict Epistatic Interactions from High-Dimensional Datasets: Ameliorating the Curse of Dimensionality
Background: The interaction between loci to affect phenotype is called epistasis. It is strict epistasis if no proper subset of the interacting loci exhibits a marginal effect. For many diseases, it is likely that unknown epistatic interactions affect disease susceptibility. A difficulty when mining epistatic interactions from high-dimensional datasets concerns the curse of dimensionality. There are too many combinations of SNPs to perform an exhaustive search. A method that could locate strict epistasis without an exhaustive search can be considered the brass ring of methods for analyzing high-dimensional datasets. Methodology/Findings: A SNP pattern is a Bayesian network representing SNP-disease relationships. The Bayesian score for a SNP pattern is the probability of the data given the pattern, and has been used to learn SNP patterns. We identified a bound for the score of a SNP pattern. The bound provides an upper limit on the Bayesian score of any pattern that could be obtained by expanding a given pattern. We felt that the bound might enable the data to say something about the promise of expanding a 1-SNP pattern even when there are no marginal effects. We tested the bound using simulated datasets and semi-synthetic high-dimensional datasets obtained from GWAS datasets. We found that the bound was able to dramatically reduce the search time for strict epistasis. Using an Alzheimer's dataset, we showed that it is possible to discover an interaction involving the APOE gene based on its score because of its large marginal effect, but that the bound is most effective at discovering interactions without marginal effects. Conclusions/Significance: We conclude that the bound appears to ameliorate the curse of dimensionality in high-dimensional datasets. This is a very consequential result and could be pivotal in our efforts to reveal the dark matter of genetic disease risk from high-dimensional datasets. © 2012 Jiang, Neapolitan
Stopping Set Distributions of Some Linear Codes
Stopping sets and stopping set distribution of an low-density parity-check
code are used to determine the performance of this code under iterative
decoding over a binary erasure channel (BEC). Let be a binary
linear code with parity-check matrix , where the rows of may be
dependent. A stopping set of with parity-check matrix is a subset
of column indices of such that the restriction of to does not
contain a row of weight one. The stopping set distribution
enumerates the number of stopping sets with size of with parity-check
matrix . Note that stopping sets and stopping set distribution are related
to the parity-check matrix of . Let be the parity-check matrix
of which is formed by all the non-zero codewords of its dual code
. A parity-check matrix is called BEC-optimal if
and has the smallest number of rows. On the
BEC, iterative decoder of with BEC-optimal parity-check matrix is an
optimal decoder with much lower decoding complexity than the exhaustive
decoder. In this paper, we study stopping sets, stopping set distributions and
BEC-optimal parity-check matrices of binary linear codes. Using finite geometry
in combinatorics, we obtain BEC-optimal parity-check matrices and then
determine the stopping set distributions for the Simplex codes, the Hamming
codes, the first order Reed-Muller codes and the extended Hamming codes.Comment: 33 pages, submitted to IEEE Trans. Inform. Theory, Feb. 201
Probing anisotropic superfluidity of rashbons in atomic Fermi gases
Motivated by the prospect of realizing a Fermi gas of K atoms with a
synthetic non-Abelian gauge field, we investigate theoretically a strongly
interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the
two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with
mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to
an anisotropic superfluid. We show that this anisotropic superfluidity can be
probed via measuring the momentum distribution and single-particle spectral
function in a trapped atomic K cloud near a Feshbach resonance.Comment: 4 pages, 5 figure
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