Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.Comment: This replacement is part I of the final version of the paper, which has been split into two parts. The second part is available from the arXiv under the title "Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation" arXiv:2001.0872

Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspectsPeer ReviewedPostprint (author's final draft

The Codazzi Equation for Surfaces

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms {\bb R}^3, {\bb S}^3 and {\bb H}^3. We give essentially sharp generalizations of some classical theorems of surface theory that mainly depend on the Codazzi equation, and we apply them to the study of Weingarten surfaces in space forms. In particular, we study existence of holomorphic quadratic differentials, uniqueness of immersed spheres in geometric problems, height estimates, and the geometry and uniqueness of complete or properly embedded Weingarten surfaces

Real-time Monocular Object SLAM

We present a real-time object-based SLAM system that leverages the largest object database to date. Our approach comprises two main components: 1) a monocular SLAM algorithm that exploits object rigidity constraints to improve the map and find its real scale, and 2) a novel object recognition algorithm based on bags of binary words, which provides live detections with a database of 500 3D objects. The two components work together and benefit each other: the SLAM algorithm accumulates information from the observations of the objects, anchors object features to especial map landmarks and sets constrains on the optimization. At the same time, objects partially or fully located within the map are used as a prior to guide the recognition algorithm, achieving higher recall. We evaluate our proposal on five real environments showing improvements on the accuracy of the map and efficiency with respect to other state-of-the-art techniques

Neuroimágenes en las alteraciones del sueño

ResumenLas imágenes médicas han representado un importante avance en el estudio de las enfermedades del sistema nervio cerebral. Sin embargo existe un importante grupo de enfermedades que se caracterizan por la ausencia o una muy leve alteración de la estructura cerebral que son muy difíciles de detectar utilizando imágenes convencionales, como las enfermedades psiquiátricas, algunos tipos de epilepsia y las alteraciones del sueño.Las alteraciones de la estructura se pueden estudiar más detalladamente utilizando imágenes de resonancia magnética volumétricas que permiten la cuantificación del volumen de las distintas estructuras cerebrales. Es posible estudiar el cerebro desde el punto de vista metabólico mediante espectroscopia, que cuantifica diversos metabolitos cerebrales normales y anormales.Las técnicas de resonancia magnética funcional corresponden a pruebas similares a los test clínicos pero realizados al interior del resonador que permiten una evaluación de las áreas funcionales cerebrales. El PET-CT que utiliza principalmente glucosa radiactiva (18 FDG) para visualizar el metabolismo cerebral. Este artículo revisa los principales hallazgos demostrados mediante imágenes estructurales y funcionales en los pacientes con Síndrome de Apnea Obstructiva del Sueño (SAOS), Narcolepsia e Insomnio idiopático.SummaryMedical Images have represented an important advance in the study of central nervous system diseases. Nevertheless there is an important group of illness that is characterized for absence or a subtle alteration of cerebral structures that are difficult to detect utilizing conventional images, as psychiatric diseases, some types of epilepsy and sleep disorders. Structural alterations can be studied, in more detail, utilizing volumetric magnetic resonance imaging that permit the quantification of volume of different cerebral structures. It is possible to study the brain from the metabolic point of view using spectroscopy that quantifies diverse normal and abnormal brain metabolites. The technique of functional magnetic resonance corresponds to a clinical test inside MRI scanner that allows the evaluation of cerebral functional areas. PET-CT utilizes radioactive glucose (18 FDG) to visualize the cerebral metabolism. This article revises the main findings utilizing functional and structural imaging in the patients with Obstructive Sleep Apnea Syndrome, Narcolepsy and Idiopathic Insomnia

Immune priming and pathogen resistance in ant queens.

Growing empirical evidence indicates that invertebrates become more resistant to a pathogen following initial exposure to a nonlethal dose; yet the generality, mechanisms, and adaptive value of such immune priming are still under debate. Because life-history theory predicts that immune priming and large investment in immunity should be more frequent in long-lived species, we here tested for immune priming and pathogen resistance in ant queens, which have extraordinarily long life span. We exposed virgin and mated queens of Lasius niger and Formica selysi to a low dose of the entomopathogenic fungus Beauveria bassiana, before challenging them with a high dose of the same pathogen. We found evidence for immune priming in naturally mated queens of L. niger. In contrast, we found no sign of priming in virgin queens of L. niger, nor in virgin or experimentally mated queens of F. selysi, which indicates that immune priming in ant queens varies according to mating status and mating conditions or species. In both ant species, mated queens showed higher pathogen resistance than virgin queens, which suggests that mating triggers an up-regulation of the immune system. Overall, mated ant queens combine high reproductive output, very long life span, and elevated investment in immune defense. Hence, ant queens are able to invest heavily in both reproduction and maintenance, which can be explained by the fact that mature queens will be protected and nourished by their worker offspring

Keeping up appearances. Ways of representing the local powers in the rural world of Cordoba in Modern Times

With this essay we try to go in depth into the knowledge of the lifestyle of the ruling classes in the rural communities from Cordoba in the Modern period. For this we analyze the ways of distinction of these groups in the various scenes where most of their daily life passed. We will realize how privileged classes lived surrounded by all kinds of luxuries and comforts, which allowed them to have a great social recognition. This lifestyle entailed a considerable economic expense that not all the families could face up; despite this, many of these families went on doing it, so far as to get themselves heavily into debt just to be recognized as one of the group members.Con en este trabajo pretendemos profundizar en el conocimiento del estilo de vida de las clases dirigentes de las comunidades rurales cordobesas en la época Moderna. Para ello abordamos el análisis de las formas de distinción de estos grupos en los distintos escenarios en los que discurrió la mayor parte de la vida cotidiana de los mismos . Comprobaremos cómo las clases privilegiadas vivían rodeadas de todo tipo de lujos y comodidades, lo que les permitió gozar de un gran reconocimiento social. Este estilo de vida conllevaba la realización de un importante gasto económico que no todas las familias podían afrontar, a pesar de lo cual muchas de ellas continuaron haciéndolo, llegando incluso a endeudarse fuertemente con tal de ser reconocidos como integrantes del grupo

A bibliometric study of the research area of videogames using Dimensions.ai database

Videogames are a very interesting area of research for fields as diverse as computer science, health, psychology or even social sciences. Every year a growing number of articles are published in different topics inside this field, so it is very convenient to study the different bibliometric data in order to consolidate the research efforts. Thus, the aim of this work is to conduct a study on the distribution of articles related to videogames in the different fields of research, as well as to measure their interest over time, to identify the sources, countries and authors with the highest scientific production. In order to carry out this analysis, the information system Dimensions.ai has been considered, since it covers a large number of documents and allows for easy downloading and analysis of datasets. According to the study, three countries are the most prolific in this area: USA, Canada and UK. The obtained results also indicate that the fields with the highest number of publications are Information and Computer Sciences, Medical and Health Sciences, and Psychology and Cognitive Sciences, in this order. With regard to the impact of the publications, differences between the number of citations, and the number of Altmetric Attention Score, have been found