Grothendieck categories as a bilocalization of linear sites

We prove that the 2-category Grt of Grothendieck abelian categories with colimit preserving functors and natural transformations is a bicategory of fractions in the sense of Pronk of the 2-category Site of linear sites with continuous morphisms of sites and natural transformations. This result can potentially be used to make the tensor product of Grothendieck categories from earlier work by Lowen, Shoikhet and the author into a bi-monoidal structure on Grt

Gabriel-Ulmer duality for topoi and its relation with site presentations

Let $\kappa$ be a regular cardinal. We study Gabriel-Ulmer duality when one restricts the 2-category of locally $\kappa$-presentable categories with $\kappa$-accessible right adjoints to its locally full sub-2-category of $\kappa$-presentable Grothendieck topoi with geometric $\kappa$-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category of the 2-category of $\kappa$-small cocomplete categories with $\kappa$-colimit preserving functors arising as the corresponding 2-category of presentations via the restriction. We analyse the relation of these presentations of Grothendieck topoi with site presentations and we show that the 2-category of locally $\kappa$-presentable Grothendieck topoi with geometric $\kappa$-accessible morphisms is a reflective sub-bicategory of the full sub-2-category of the 2-category of sites with morphisms of sites genearated by the weakly $\kappa$-ary sites in the sense of Shulman [37].Comment: 25 page

On the tensor product of linear sites and Grothendieck categories

We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves. We show that our tensor product is a special case of the tensor product of locally presentable linear categories, and that the tensor product of locally coherent Grothendieck categories is locally coherent if and only if the Deligne tensor product of their abelian categories of finitely presented objects exists. We describe the tensor product of non-commutative projective schemes in terms of Z-algebras, and show that for projective schemes our tensor product corresponds to the usual product scheme.Comment: New sections 5.3 on the alpha-Deligne tensor product and 5.4 on future prospect

Company-university collaboration in applying gamification to learning about insurance

Incorporating gamification into training–learning at universities is hampered by a shortage of quality, adapted educational video games. Large companies are leading in the creation of educational video games for their internal training or to enhance their public image and universities can benefit from collaborating. The aim of this research is to evaluate, both objectively and subjectively, the potential of the simulation game BugaMAP (developed by the MAPFRE Foundation) for university teaching about insurance. To this end, we have assessed both the game itself and the experience of using the game as perceived by 142 economics students from various degree plans and courses at the University of Seville during the 2017–2018 academic year. As a methodology, a checklist of gamification components is used for the objective evaluation, and an opinion questionnaire on the game experience is used for the subjective evaluation. Among the results several findings stand out. One is the high satisfaction of the students with the knowledge acquired using fun and social interaction. Another is that the role of the university professors and the company monitors turns out to be very active and necessary during the game-learning sessions. Finally, in addition to the benefits to the university of occasionally available quality games to accelerate student skills training, the company–university collaboration serves as a trial and refinement of innovative tools for game-based learning

Axially Symmetric Post-Newtonian Stellar Systems

We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations of classical ones. By introducing in the field equations provided by the 1PN approximation a known distribution function (DF) corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained, which are solved using the Hunter method. The rotation curves of the 1PN-corrected models differs from the classical ones and, for the generalized Kalnajs discs, the 1PN corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models.Comment: 13 pages, 4 figures, to be published at Rev.Integr.Temas Ma

Distribution functions for a family of axially symmetric galaxy models

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in Rev. Acad. Colomb. Cienc. Ex. Fis. Na

A Comparison of Machine-Learning Methods to Select Socioeconomic Indicators in Cultural Landscapes

Cultural landscapes are regarded to be complex socioecological systems that originated as a result of the interaction between humanity and nature across time. Cultural landscapes present complex-system properties, including nonlinear dynamics among their components. There is a close relationship between socioeconomy and landscape in cultural landscapes, so that changes in the socioeconomic dynamic have an effect on the structure and functionality of the landscape. Several numerical analyses have been carried out to study this relationship, with linear regression models being widely used. However, cultural landscapes comprise a considerable amount of elements and processes, whose interactions might not be properly captured by a linear model. In recent years, machine-learning techniques have increasingly been applied to the field of ecology to solve regression tasks. These techniques provide sound methods and algorithms for dealing with complex systems under uncertainty. The term ‘machine learning’ includes a wide variety of methods to learn models from data. In this paper, we study the relationship between socioeconomy and cultural landscape (in Andalusia, Spain) at two different spatial scales aiming at comparing different regression models from a predictive-accuracy point of view, including model trees and neural or Bayesian networks