Admixture Correction in the Outgroup-f3 Statistic

Genetic inheritance can be studied within a purely genetic scope. However, this eliminates part of the picture. The field of genetics is often thought of as a natural science with little in common with fields of social science. However, in human genetics and the genetics of the organisms which humans impact, the role of cultural and societal forces cannot be ignored. For instance, lactase is an enzyme used to digest lactose in milk. As such, it is an enzyme whose activity reduces significantly after weaning. Nonetheless, as humans have begun to ingest more dairy products into adulthood, lactase persistence has evolved to enable humans to digest these dairy products. My research involves mathematically representing the genetic similarity of two populations accurately via the f3 statistic. The outgroup-f3 statistic is useful in understanding a population’s genetic history and how genetically related two populations are. It shows how close two populations are compared to a third population that is equally distant genetically from the first two. However, if two populations share a recent genetic interaction with another population, the outgroup-f3 statistic could show those two populations as being closer together than they truly are. This genetic interaction of two or more previously isolated populations interbreeding is referred to as admixture. Admixture skews, or even inhibits, an understanding of those populations’ genetic histories. To avoid this problem, I have attempted to devise a modified version of the outgroup-f3 statistic to ensure an accurate representation of genetic relatedness. For my project, artificial admixture was introduced in six unadmixed human populations. Depending on the relationship between increased contamination and the f3 statistic, we proposed and adjusted solutions for a corrected f3 accordingly. I tested my proposed corrections by applying it to populations that contain individuals with and without recent histories of genetic admixture. After correcting for the proportion of admixture in the population, I compared this corrected outgroup-f3 statistic to the outgroup-f3 value calculated for the original unadmixed population. The goal of this work is to have a corrected statistic that one can apply to two populations, independent of admixture proportions. Ultimately, this will help us to better understand the evolutionary histories of populations. Moreover, a corrected statistic will aid other researchers as they analyse demographic histories further in the past.MathematicsAnthropolog

Impact of radiative corrections on sterile neutrino scenarios

In sterile neutrino scenarios, radiative corrections induce mass splittings proportional to the top Yukawa coupling, in contrast to the three active neutrino case where the induced splittings are proportional to the tau Yukawa coupling. In view of this, we have analyzed the stability of the four-neutrino schemes favored by oscillation experiments, consisting in two pairs of nearly degenerate neutrinos separated by the LSND gap. Requiring compatibility with the measurements of the abundances of primordial elements produced in Big Bang Nucleosynthesis, we find that when the heaviest pair corresponds to the solar neutrinos (mainly an admixture of nu_e - nu_s) the natural mass splitting is 3-5 orders of magnitude larger than the observed one, discrediting the scenario from a theoretical point of view. On the contrary, the scheme where the heaviest pair corresponds to the atmospheric neutrinos (mainly an admixture of nu_mu - nu_tau) is safe from radiative corrections due to the small sterile component of these mass eigenstates.Comment: 14 pages, LaTeX, 2 figures. Discussion enlarged, references added and typos correcte

Intersecting Faces: Non-negative Matrix Factorization With New Guarantees

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where provably correct algorithms have been developed. In this paper, we propose the notion of subset-separable NMF, which substantially generalizes the property of separability. We show that subset-separability is a natural necessary condition for the factorization to be unique or to have minimum volume. We developed the Face-Intersect algorithm which provably and efficiently solves subset-separable NMF under natural conditions, and we prove that our algorithm is robust to small noise. We explored the performance of Face-Intersect on simulations and discuss settings where it empirically outperformed the state-of-art methods. Our work is a step towards finding provably correct algorithms that solve large classes of NMF problems

Sbottoms of Natural NMSSM at the LHC

Search for the bottom squarks (sbottoms) at the Large Hadron Collider (LHC) has recently assumed a heightened focus in the hunt for Supersymmetry (SUSY). The popular framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) could conceive a naturally light sbottom which could easily be consistent with available constraints from the experiments at the LHC. Phenomenology of such sbottoms could in principle be as striking as that for a light top squark (stop) thanks to a rather nontrivial neutralino sector (with appreciable mixing among the neutral higgsinos and the singlino) that the scenario gives rise to. Nonetheless, finding such sbottoms might require a moderately large amount of data ($\sim 300$ $\text{fb}^{-1}$) at the 13 TeV run of the LHC. A multi-channel analysis establishing a generic depletion of events in the usual $2b$-$jets$ +\text{\sout{E}}_T final state while registering, in conjunction, characteristically significant rates in various multi-lepton final states accompanied by $b$-$jets$ might point not only to the presence of light sbottom(s) but could also shed crucial light on their compositions and the (singlino) nature of the lightest SUSY particle (LSP).Comment: 30 pages, 6 figures, 5 tables; matches with published versio

The behaviour of a two-component backfilling grout used in a Tunnel-Boring Machine

The instantaneous filling of the annulus that is created behind the segment lining at the end of the tail during the TBM advance is an operation of paramount importance. Its main goal is to minimize the surface settlements due to any over-excavation generated by the passage of the TBM. To correctly achieve the goals, a simultaneous backfilling system and the injected material should satisfy the technical, operational and performance characteristics. A two-component system injection for the back-filling is progressively substituting the use of traditional mortars. In this paper different systems of back-filling grout and in particular the two-component system are analyzed and the results of laboratory tests are presented and discusse

The Drosophila genome nexus: a population genomic resource of 623 Drosophila melanogaster genomes, including 197 from a single ancestral range population.

Hundreds of wild-derived Drosophila melanogaster genomes have been published, but rigorous comparisons across data sets are precluded by differences in alignment methodology. The most common approach to reference-based genome assembly is a single round of alignment followed by quality filtering and variant detection. We evaluated variations and extensions of this approach and settled on an assembly strategy that utilizes two alignment programs and incorporates both substitutions and short indels to construct an updated reference for a second round of mapping prior to final variant detection. Utilizing this approach, we reassembled published D. melanogaster population genomic data sets and added unpublished genomes from several sub-Saharan populations. Most notably, we present aligned data from phase 3 of the Drosophila Population Genomics Project (DPGP3), which provides 197 genomes from a single ancestral range population of D. melanogaster (from Zambia). The large sample size, high genetic diversity, and potentially simpler demographic history of the DPGP3 sample will make this a highly valuable resource for fundamental population genetic research. The complete set of assemblies described here, termed the Drosophila Genome Nexus, presently comprises 623 consistently aligned genomes and is publicly available in multiple formats with supporting documentation and bioinformatic tools. This resource will greatly facilitate population genomic analysis in this model species by reducing the methodological differences between data sets