Moderate deviations for the determinant of Wigner matrices

We establish a moderate deviations principle (MDP) for the log-determinant $\log | \det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.Comment: 20 pages, one missing reference added; Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics and Statistics, 201

On the Representation Theory of an Algebra of Braids and Ties

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic Combinatorics

Modeling focal epileptic activity in the Wilson-Cowan model with depolarization block

Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures

Evolution of Black Holes in the Galaxy

In this article we consider the formation and evolution of black holes, especially those in binary stars where radiation from the matter falling on them can be seen. We consider a number of effects introduced by some of us, which are not traditionally included in binary evolution of massive stars. These are (i) hypercritical accretion, which allows neutron stars to accrete enough matter to collapse to a black hole during their spiral-in into another star. (ii) the strong mass loss of helium stars, which causes their evolution to differ from that of the helium core of a massive star. (iii) The direct formation of low-mass black holes (M\sim2\msun) from single stars, a consequence of a significant strange-matter content of the nuclear-matter equation of state at high density. We discuss these processes here, and then review how they affect various populations of binaries with black holes and neutron stars.Comment: 46 pages, 1 figure, to be published in Physics Repor

The Role of Color Neutrality in Nuclear Physics--Modifications of Nucleonic Wave Functions

The influence of the nuclear medium upon the internal structure of a composite nucleon is examined. The interaction with the medium is assumed to depend on the relative distances between the quarks in the nucleon consistent with the notion of color neutrality, and to be proportional to the nucleon density. In the resulting description the nucleon in matter is a superposition of the ground state (free nucleon) and radial excitations. The effects of the nuclear medium on the electromagnetic and weak nucleon form factors, and the nucleon structure function are computed using a light-front constituent quark model. Further experimental consequences are examined by considering the electromagnetic nuclear response functions. The effects of color neutrality supply small but significant corrections to predictions of observables.Comment: 37 pages, postscript figures available on request to [email protected]

Milagro limits and HAWC sensitivity for the rate-density of evaporating Primordial Black Holes

postprin

Iam hiQ—a novel pair of accuracy indices for imputed genotypes

Background Imputation of untyped markers is a standard tool in genome-wide association studies to close the gap between directly genotyped and other known DNA variants. However, high accuracy with which genotypes are imputed is fundamental. Several accuracy measures have been proposed and some are implemented in imputation software, unfortunately diversely across platforms. In the present paper, we introduce Iam hiQ, an independent pair of accuracy measures that can be applied to dosage files, the output of all imputation software. Iam (imputation accuracy measure) quantifies the average amount of individual-specific versus population-specific genotype information in a linear manner. hiQ (heterogeneity in quantities of dosages) addresses the inter-individual heterogeneity between dosages of a marker across the sample at hand. Results Applying both measures to a large case–control sample of the International Lung Cancer Consortium (ILCCO), comprising 27,065 individuals, we found meaningful thresholds for Iam and hiQ suitable to classify markers of poor accuracy. We demonstrate how Manhattan-like plots and moving averages of Iam and hiQ can be useful to identify regions enriched with less accurate imputed markers, whereas these regions would by missed when applying the accuracy measure info (implemented in IMPUTE2). Conclusion We recommend using Iam hiQ additional to other accuracy scores for variant filtering before stepping into the analysis of imputed GWAS data

The Physics of Star Cluster Formation and Evolution

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe

Mendelian randomization and mediation analysis of leukocyte telomere length and risk of lung and head and neck cancers

Background: Evidence from observational studies of telomere length (TL) has been conflicting regarding its direction of association with cancer risk. We investigated the causal relevance of TL for lung and head and neck cancers using Mendelian Randomization (MR) and mediation analyses. Methods: We developed a novel genetic instrument for TL in chromosome 5p15.33, using variants identified through deep-sequencing, that were genotyped in 2051 cancer-free subjects. Next, we conducted an MR analysis of lung (16 396 cases, 13 013 controls) and head and neck cancer (4415 cases, 5013 controls) using eight genetic instruments for TL. Lastly, the 5p15.33 instrument and distinct 5p15.33 lung cancer risk loci were evaluated using two-sample mediation analysis, to quantify their direct and indirect, telomere-mediated, effects. Results: The multi-allelic 5p15.33 instrument explained 1.49-2.00% of TL variation in our data (p = 2.6 × 10-9). The MR analysis estimated that a 1000 base-pair increase in TL increases risk of lung cancer [odds ratio (OR) = 1.41, 95% confidence interval (CI): 1.20-1.65] and lung adenocarcinoma (OR = 1.92, 95% CI: 1.51-2.22), but not squamous lung carcinoma (OR = 1.04, 95% CI: 0.83-1.29) or head and neck cancers (OR = 0.90, 95% CI: 0.70-1.05). Mediation analysis of the 5p15.33 instrument indicated an absence of direct effects on lung cancer risk (OR = 1.00, 95% CI: 0.95-1.04). Analysis of distinct 5p15.33 susceptibility variants estimated that TL mediates up to 40% of the observed associations with lung cancer risk. Conclusions: Our findings support a causal role for long telomeres in lung cancer aetiology, particularly for adenocarcinoma, and demonstrate that telomere maintenance partially mediates the lung cancer susceptibility conferred by 5p15.33 loci