A Linear Algebra Approach to Fast DNA Mixture Analysis Using GPUs

Analysis of DNA samples is an important step in forensics, and the speed of analysis can impact investigations. Comparison of DNA sequences is based on the analysis of short tandem repeats (STRs), which are short DNA sequences of 2-5 base pairs. Current forensics approaches use 20 STR loci for analysis. The use of single nucleotide polymorphisms (SNPs) has utility for analysis of complex DNA mixtures. The use of tens of thousands of SNPs loci for analysis poses significant computational challenges because the forensic analysis scales by the product of the loci count and number of DNA samples to be analyzed. In this paper, we discuss the implementation of a DNA sequence comparison algorithm by re-casting the algorithm in terms of linear algebra primitives. By developing an overloaded matrix multiplication approach to DNA comparisons, we can leverage advances in GPU hardware and algoithms for Dense Generalized Matrix-Multiply (DGEMM) to speed up DNA sample comparisons. We show that it is possible to compare 2048 unknown DNA samples with 20 million known samples in under 6 seconds using a NVIDIA K80 GPU.Comment: Accepted for publication at the 2017 IEEE High Performance Extreme Computing conferenc

Supersymmetric Spin Networks and Quantum Supergravity

We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative quantization of supergravity. The supersymmetric extension of the area operator is defined and partly diagonalized. The spectrum is discrete as in quantum general relativity, and the two cases could be distinguished by measurements of quantum geometry.Comment: 21 pages, LaTex, 22 figures, typos corrected and references complete

Geometry over composition algebras : projective geometry

The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in correspondance with Jordan algebras and that the points of a projective space correspond to rank one matrices in the Jordan algebra. A second part thus studies properties of rank one matrices. Finally, subvarieties of projective spaces are discussed.Comment: 24 page

Inelastic Dark Matter and the SABRE Experiment

We present here the sensitivity of the SABRE (Sodium iodide with Active Background REjection) experiment to benchmark proto-philic, spin dependent, Inelastic Dark Matter models previously proposed due to their lowered tension with existing experimental results. We perform fits to cross section, mass, and mass splitting values to find the best fit to DAMA/LIBRA data for these models. In this analysis, we consider the Standard Halo Model (SHM), as well as an interesting extension upon it, the SHM+Stream distribution, to investigate the influence of the Dark Matter velocity distribution upon experimental sensitivity and whether or not its consideration may be able to help relieve the present experimental tension. Based on our analysis, SABRE should be sensitive to all the three benchmark models within 3-5 years of data taking.Comment: Adjusted for full DAMA run 1+2 efficiency. Updated to match published versio

SMARANDACHE FUNCTION JOURNAL, 4-5

This journal is yearly published (in the Spring or Fall) in a 300-400 pages volume, and 800-1000 copies. SNJ is a referred journal: reviewed, indexed, cited, concerning any of Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc

A nonparametric Bayesian approach to the rare type match problem

The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) is based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles, that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions, and discards the information about the names of the different DNA profiles. This fits very well the data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes approach.Comment: arXiv admin note: text overlap with arXiv:1506.0844