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 $C$ be a binary $[n,k]$ linear code with parity-check matrix $H$, where the rows of $H$ may be dependent. A stopping set $S$ of $C$ with parity-check matrix $H$ is a subset of column indices of $H$ such that the restriction of $H$ to $S$ does not contain a row of weight one. The stopping set distribution $\{T_i(H)\}_{i=0}^n$ enumerates the number of stopping sets with size $i$ of $C$ with parity-check matrix $H$. Note that stopping sets and stopping set distribution are related to the parity-check matrix $H$ of $C$. Let $H^{*}$ be the parity-check matrix of $C$ which is formed by all the non-zero codewords of its dual code $C^{\perp}$. A parity-check matrix $H$ is called BEC-optimal if $T_i(H)=T_i(H^*), i=0,1,..., n$ and $H$ has the smallest number of rows. On the BEC, iterative decoder of $C$ 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

A Bayesian Network Model for Spatio-Temporal Event Surveillance

Event surveillance involves analyzing a region in order to detect patterns that are indicative of some event of interest. An example is the monitoring of information about emergency department visits to detect a disease outbreak. Spatial event surveillance involves analyzing spatial patterns of evidence that are indicative of the event of interest. A special case of spatial event surveillance is spatial cluster detection, which searches for subregions in which the count of an event of interest is higher than expected. Temporal event surveillance involves monitoring for emerging temporal patterns. Spatio-temporal event surveillance involves joint spatial and temporal monitoring.When the events observed are of direct interest, then analyzing counts of those events is generally the preferred approach. However, in event surveillance we often only observe events that are indirectly related to the events of interest. For example, during an influenza outbreak, we may only have information about the chief complaints of patients who visited emergency departments. In this situation, a better surveillance approach may be to model the relationships among the events of interest and those observed.I developed a high-level Bayesian network architecture that represents a class of spatial event surveillance models, which I call BayesNet-S. I also developed an architecture that represents a class of temporal event surveillance models called BayesNet-T. These Bayesian network architectures are combined into a single architecture that represents a class of spatio-temporal models called BayesNet-ST. Using these architectures, it is often possible to construct a temporal, spatial, or spatio-temporal model from an existing Bayesian network event-surveillance model that is non-spatial and non-temporal. My general hypothesis is that when an existing model is extended to incorporate space and time, event surveillance will be improved.PANDA-CDCA (PC) (Cooper et al., 2007) is a non-temporal, non-spatial disease outbreak detection system. I extended PC both spatially and temporally. My specific hypothesis is that each of the spatial and temporal extensions of PC will perform outbreak detection better than does PC, and that the combined use of the spatial and temporal extensions will perform better than either extension alone.The experimental results obtained in this research support this hypothesis

Probing anisotropic superfluidity of rashbons in atomic Fermi gases

Motivated by the prospect of realizing a Fermi gas of $^{40}$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 $^{40}$K cloud near a Feshbach resonance.Comment: 4 pages, 5 figure