Étale Covers and Fundamental Groups of Schematic Finite Spaces

[EN] We introduce the category of finite étale covers of an arbitraryschematic space X and show that, equipped with an appropriate naturalfiber functor, it is a Galois Category. This allows us to define the étale fundamental group of schematic spaces. If X is a finite model of a schemeS, we show that the resulting Galois theory on X coincides with theclassical theory of finite étale covers on S, and therefore, we recover the classical étale fundamental group introduced by Grothendieck. Toprove these results, it is crucial to find a suitable geometric notion ofconnectedness for schematic spaces and also to study their geometric points. We achieve these goals by means of the strong cohomologicalconstraints enjoyed by schematic spaces.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

Las imágenes de la historia en la obra de Stanley Kubrick.

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Chemical abundances of stars with brown-dwarf companions

It is well-known that stars with giant planets are on average more metal-rich than stars without giant planets, whereas stars with detected low-mass planets do not need to be metal-rich. With the aim of studying the weak boundary that separates giant planets and brown dwarfs (BDs) and their formation mechanism, we analyze the spectra of a sample of stars with already confirmed BD companions both by radial velocity and astrometry. We employ standard and automatic tools to perform an EW-based analysis and to derive chemical abundances from CORALIE spectra of stars with BD companions. We compare these abundances with those of stars without detected planets and with low-mass and giant-mass planets. We find that stars with BDs do not have metallicities and chemical abundances similar to those of giant-planet hosts but they resemble the composition of stars with low-mass planets. The distribution of mean abundances of $\alpha$-elements and iron peak elements of stars with BDs exhibit a peak at about solar abundance whereas for stars with low-mass and high-mass planets the [X$_\alpha$/H] and [X$_{\rm Fe}$/H] peak abundances remain at $\sim -0.1$~dex and $\sim +0.15$~dex, respectively. We display these element abundances for stars with low-mass and high-mass planets, and BDs versus the minimum mass, $m_C \sin i$, of the most-massive substellar companion in each system, and we find a maximum in $\alpha$-element as well as Fe-peak abundances at $m_C \sin i \sim 1.35\pm 0.20$ jupiter masses. We discuss the implication of these results in the context of the formation scenario of BDs in comparison with that of giant planets.Comment: Accepted for publication in Astronomy & Astrophysic

Machine Learning in Business Intelligence 4.0: Cost Control in a Destination Hotel

Cost control is a recurring problem in companies where studies have provided different solutions. The main objective of this research is to propose and validate an alternative to cost control using data science to support decision-making using the business intelligence 4.0 paradigm. The work uses Machine Learning (ML) to support decision-making in company cost-control management. Specifically, we used the ability of hierarchical agglomerative clustering (HAC) algorithms to generate clusters and suggest possible candidate products that could be substituted for other, more cost-effective ones. These candidate products were analyzed by a panel of company experts, facilitating decisions based on business costs. We needed to analyze and modify the company's ecosystem and its associated variables to obtain an adequate data warehouse during the study, which was developed over three years and validated HAC as a support to decision-making in cost control

Assessing math anxiety in elementary schoolchildren through a Spanish version of the Scale for Early Mathematics Anxiety (SEMA)

Math anxiety (MA) affects students of all age groups. Because of its effects on children’s academic development, the need to recognize its early manifestations has been highlighted. We designed a European-Spanish version of the Scale for Early Mathematics Anxiety (SEMA; Wu et al. (2012)), and assessed its psychometric properties in a sample of children aged 7 to 12 years. The participants (967 typically developing children) were elementary school students recruited from ten schools. Children reported their general and math anxiety levels in an individual session and performed nonverbal IQ and math abilities subtests in a group session. Teachers reported the final math grades. The psychometric indices obtained, and the resulting factor structure revealed that the European-Spanish version of the SEMA developed in this study is a reliable and valid measure to evaluate MA in children from 3rd to 6th grade. Moreover, we explored gender differences, that resulted in small effect sizes, which disappeared when controlling for trait anxiety. Differences across grades were found for both global MA and the numerical processing anxiety factor but not for the situational and performance anxiety factor. Finally, MA was negatively associated with students’ math achievement, although the strength of the associations varied with the MA measure selected, the kind of math achievement analyzed, and the school stage considered. Our findings highlight the relevance of MA in elementary school and highlight the need for an early identification of students at risk of suffering MA to palliate the negative consequences of MA in children’s cognitive and academic development

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.