On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation

In the framework of toroidal Pseudodifferential operators on the flat torus $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$ we begin by proving the closure under composition for the class of Weyl operators $\mathrm{Op}^w_\hbar(b)$ with simbols $b \in S^m (\mathbb{T}^n \times \mathbb{R}^n)$. Subsequently, we consider $\mathrm{Op}^w_\hbar(H)$ when $H=\frac{1}{2} |\eta|^2 + V(x)$ where $V \in C^\infty (\Bbb T^n;\Bbb R)$ and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schr\"odinger equation. Moreover, we prove the convergence (in a weak sense) of the Wigner transform of the solution of the Schr\"odinger equation to the solution of the Liouville equation on $\Bbb T^n \times \Bbb R^n$ written in the measure sense. These results are applied to the study of some WKB type wave functions in the Sobolev space $H^{1} (\mathbb{T}^n; \Bbb C)$ with phase functions in the class of Lipschitz continuous weak KAM solutions (of positive and negative type) of the Hamilton-Jacobi equation $\frac{1}{2} |P+ \nabla_x v_\pm (P,x)|^2 + V(x) = \bar{H}(P)$ for $P \in \ell \Bbb Z^n$ with $\ell >0$, and to the study of the backward and forward time propagation of the related Wigner measures supported on the graph of $P+ \nabla_x v_\pm$

PRNP P39L variant is a rare cause of frontotemporal dementia in Iialian population

The missense P39L variant in the prion protein gene (PRNP) has recently been associated with frontotemporal dementia (FTD). Here, we analyzed the presence of the P39L variant in 761 patients with FTD and 719 controls and found a single carrier among patients. The patient was a 67-year-old male, with a positive family history for dementia, who developed apathy, short term memory deficit, and postural instability at 66. Clinical and instrumental workup excluded prion disease. At MRI, bilateral frontal lobe atrophy was present. A diagnosis of FTD was made, with a mainly apathetic phenotype. The PRNP P39L mutation may be an extremely rare cause of FTD (0.13%)

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Benchmarking of human Y-chromosomal haplogroup classifiers with whole-genome and whole-exome sequence data

In anthropological, medical, and forensic studies, the nonrecombinant region of the human Y chromosome (NRY) enables accurate reconstruction of pedigree relationships and retrieval of ancestral information. Using high-throughput sequencing (HTS) data, we present a benchmarking analysis of command-line tools for NRY haplogroup classification. The evaluation was performed using paired Illumina data from whole-genome sequencing (WGS) and whole-exome sequencing (WES) experiments from 50 unrelated donors. Additionally, as a validation, we also used paired WGS/WES datasets of 54 individuals from the 1000 Genomes Project. Finally, we evaluated the tools on data from third-generation HTS obtained from a subset of donors and one reference sample. Our results show that WES, despite typically offering less genealogical resolution than WGS, is an effective method for determining the NRY haplogroup. Y-LineageTracker and Yleaf showed the highest accuracy for WGS data, classifying precisely 98% and 96% of the samples, respectively. Yleaf outperforms all benchmarked tools in the WES data, classifying approximately 90% of the samples. Yleaf, Y-LineageTracker, and pathPhynder can correctly classify most samples (88%) sequenced with third-generation HTS. As a result, Yleaf provides the best performance for applications that use WGS and WES. Overall, our study offers researchers with a guide that allows them to select the most appropriate tool to analyze the NRY region using both second- and third-generation HTS data

Two-loop Yang-Mills diagrams from superstring amplitudes

Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams. A key ingredient in the string construction is represented by the twisted (Prym) super differentials, as their periods encode the information about the background field. We provide an efficient method to calculate perturbatively the determinant of the twisted period matrix in terms of sets of super-moduli appropriate to the degeneration limits. Using this result we show that there is a precise one-to-one correspondence between the degeneration of different factors in the superstring amplitudes and one-particle irreducible Feynman diagrams capturing the gauge theory effective action at the two-loop level.Comment: 42 pages plus appendices, 10 figure

The search for transient astrophysical neutrino emission with IceCube-DeepCore

We present the results of a search for astrophysical sources of brief transient neutrino emission using IceCube and DeepCore data acquired between 2012 May 15 and 2013 April 30. While the search methods employed in this analysis are similar to those used in previous IceCube point source searches, the data set being examined consists of a sample of predominantly sub-TeV muon-neutrinos from the Northern Sky (-5 degrees < delta < 90 degrees) obtained through a novel event selection method. This search represents a first attempt by IceCube to identify astrophysical neutrino sources in this relatively unexplored energy range. The reconstructed direction and time of arrival of neutrino events are used to search for any significant self-correlation in the data set. The data revealed no significant source of transient neutrino emission. This result has been used to construct limits at timescales ranging from roughly 1 s to 10 days for generic soft-spectra transients. We also present limits on a specific model of neutrino emission from soft jets in core-collapse supernovae