Cartier and Weil Divisors on Varieties with Quotient Singularities

The main goal of this paper is to show that the notions of Weil and Cartier $\mathbb{Q}$-divisors coincide for $V$-manifolds and give a procedure to express a rational Weil divisor as a rational Cartier divisor. The theory is illustrated on weighted projective spaces and weighted blow-ups.Comment: 16 page

Race/ethnicity and gender differences in drug use and abuse among college students

This study examines race/ethnicity and gender differences in drug use and abuse for substances other than alcohol among undergraduate college students. A probability-based sample of 4,580 undergraduate students at a Midwestern research university completed a cross-sectional Web-based questionnaire that included demographic information and several substance use measures. Male students were generally more likely to report drug use and abuse than female students. Hispanic and White students were more likely to report drug use and abuse than Asian and African American students prior to coming to college and during college. The findings of the present study reveal several important racial/ethnic differences in drug use and abuse that need to be considered when developing collegiate drug prevention and intervention efforts.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2377408/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2377408/Accepted manuscrip

A Mathematical Assessment of the Isolation Tree Method for Outliers Detection in Big Data

In this paper, the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection is presented. We show that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved using the Law of Large Numbers. A couple of counterexamples are presented to show that the original method is inconclusive and no quality certificate can be given, when using it as a means to detect anomalies. Hence, an alternative version of IRF is proposed, whose mathematical foundation, as well as its limitations, are fully justified. Finally, numerical experiments are presented to compare the performance of the classic IRF with the proposed one.Comment: 21 pages, 14 figures, 3 table

Universal temporal features of rankings in competitive sports and games

Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the wealth distribution worldwide. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are universal mechanisms of stratification common to many systems. Human sports and games, with their (varied but simplified) rules of competition and measures of performance, serve as an ideal test bed to look for universal features of hierarchy formation. With this goal in mind, we analyse here the behaviour of players and team rankings over time for several sports and games. Even though, for a given time, the distribution of performance ranks varies across activities, we find statistical regularities in the dynamics of ranks. Specifically the rank diversity, a measure of the number of elements occupying a given rank over a length of time, has the same functional form in sports and games as in languages, another system where competition is determined by the use or disuse of grammatical structures. Our results support the notion that hierarchical phenomena may be driven by the same underlying mechanisms of rank formation, regardless of the nature of their components. Moreover, such regularities can in principle be used to predict lifetimes of rank occupancy, thus increasing our ability to forecast stratification in the presence of competition

Crónica de la participación de los Colectivos de Docencia en el Tercer Coloquio. Tronco General

3er Coloquio Fortalecimiento de los Colectivos de Docencia.Conclusiones de la participación de los Colectivos de Docencia del Tronco General, donde conceptos como: recepción; orientación; introducción e incorporación, pareciera que están presentes de manera reiterada. Y que en los escenarios de enseñanza remota y en la etapa de prefiguración de un modelo de enseñanza híbrido, forman parte ya de las posibles rutas, en el reconocimiento de lo hasta ahora conseguido, por una comunidad atenta, responsable y propositiva

Exploring Water Radiolysis in Proton Cancer Therapy: Time-Dependent, Non-Adiabatic Simulations of H\u3csup\u3e+\u3c/sup\u3e + (H2O)1-6

© 2017 Privett et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. To elucidate microscopic details of proton cancer therapy (PCT), we apply the simplest-level electron nuclear dynamics (SLEND) method to H+ + (H2O)1-6 at ELab = 100 keV. These systems are computationally tractable prototypes to simulate water radiolysis reactions - i.e. the PCT processes that generate the DNA-damaging species against cancerous cells. To capture incipient bulk-water effects, ten (H2O)1-6 isomers are considered, ranging from quasi-planar/ multiplanar (H2O)1-6 to smallest-drop prism and cage (H2O)6 structures. SLEND is a time-dependent, variational, non-adiabatic and direct method that adopts a nuclear classicalmechanics description and an electronic single-determinantal wavefunction in the Thouless representation. Short-time SLEND/6-31G∗ (n = 1-6) and /6-31G∗ ∗ (n = 1-5) simulations render cluster-to-projectile 1-electron-transfer (1-ET) total integral cross sections (ICSs) and 1- ET probabilities. In absolute quantitative terms, SLEND/6-31G∗ 1-ET ICS compares satisfactorily with alternative experimental and theoretical results only available for n = 1 and exhibits almost the same accuracy of the best alternative theoretical result. SLEND/6-31G∗ ∗ overestimates 1-ET ICS for n = 1, but a comparable overestimation is also observed with another theoretical method. An investigation on H+ + H indicates that electron direct ionization (DI) becomes significant with the large virtual-space quasi-continuum in large basis sets; thus, SLEND/6-31G∗ 1-ET ICS is overestimated by DI contributions. The solution to this problem is discussed. In relative quantitative terms, both SLEND/6-31∗ and /6-31G∗ ∗ 1-ET ICSs precisely fit into physically justified scaling formulae as a function of the cluster size; this indicates SLEND\u27s suitability for predicting properties of water clusters with varying size. Longtime SLEND/6-31G∗ (n = 1-4) simulations predict the formation of the DNA-damaging radicals H, OH, O and H3O. While smallest-drop isomers are included, no early manifestations of bulk water PCT properties are observed and simulations with larger water clusters will be needed to capture those effects. This study is the largest SLEND investigation on water radiolysis to date

Cosmological simulations using a static scalar-tensor theory

We present $\Lambda$CDM $N$-body cosmological simulations in the framework of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.Comment: 4 pages, 6 figures, to appear in Journal of Physics: Conference Series: VII Mexican School on Gravitation and Mathematical Physics. 26 November to 1 December 2006, Playa del Carmen, Quintana Roo, Mexic