Gauge-free cluster variational method by maximal messages and moment matching

We present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e., it guarantees that the resulting GBP is not gauge invariant. We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected belief propagation equations. The method allows for a straightforward generalization to disordered systems

Crustal Characteristics in the Subduction Zone of Mexico: Implication of the Tectonostratigraphic Terranes on Slab Tearing

During the past years, significant work has been done for studying the crustal anisotropy and state of stress of the Mexican subduction zone. At the same time, there is new evidence of the geometry of the subducted slab proposing subduction tearing. Here, we present a study of the Earth crust using three different methods: azimuthal anisotropy based on ambient noise, shear‐wave splitting of tectonic tremors, and moment tensor inversions of the earthquakes of 7 September 2017 M_w 8.2 Tehuantepec, Mexico. This earthquake initiated a seismic sequence that triggered shallow seismicity and aftershocks. The shallow earthquakes fall into a region where there were few published focal mechanism higher than M_w 4.5. Two slab tearings: in the Michoacán–Guerrero border and in central Oaxaca, best represent the slab geometry of the Mexican subduction zone. At the Michoacán–Guerrero, the subducted slab is subhorizontal, whereas in central Oaxaca the plate is characterized by northeast vergence. We interpret that the mantle’s flow in this part of the subducted slab produces multiple alignments in the crust and differentiates the tectonostratigraphic terranes of the southern region of Mexico

Digital Economy, Big Data and Competition Law

Big data has a very important role in the digital economy, because firms have accurate tools to collect, store, analyse, treat, monetise and disseminate voluminous amounts of data. Companies have been improving their revenues with information about the behaviour, preferences, needs, expectations, desires and evaluations of their consumers. In this sense, data could be considered as a productive input. The article focuses on the current discussion regarding the possible use of competition law and policy to address privacy concerns related to big data companies. The most traditional and powerful tool to deal with privacy concerns is personal data protection law. Notwithstanding, the article examines whether competition law should play an important role in data-driven markets where privacy is a key factor. The article suggests a new approach to the following antitrust concepts in cases related to big data platforms: assessment of market power, merger notification thresholds, measurement of merger effects on consumer privacy, and investigation of abuse of dominant position. In this context, the article analyses decisions of competition agencies which reviewed mergers in big data-driven markets, such as Google/DoubleClick, Facebook/ WhatsApp and Microsoft/LinkedIn. It also reviews investigations of alleged abuse of dominant position associated with big data, in particular the proceeding opened by the Bundeskartellamt against Facebook, in which the German antitrust authority prohibited the data processing policy imposed by Facebook on its users. The article concludes that it is important to harmonise the enforcement of competition, consumer and data protection polices in order to choose the proper way to protect the users of dominant platforms, maximising the benefits of the data-driven economy

The marriage problem: from the bar of appointments to the agency

We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that lead the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of the Nash equilibrium states of the system that agree very well with the results of Monte Carlo simulations. Finally, through large scale numerical simulations we compare the Global Optimum of the society with the stable marriage of lower energy. We showed that both states are strongly correlated and that the selffish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the Global Optimum of the society.Comment: 15 pages, 9 figures. To be published in Physica A (2005

Interactividad y atención a la diversidad en el aprendizaje de la estadística

El objetivo de nuestra investigación es construir, ejemplificar y analizar los beneficios de una herramienta metodológica pensada para mejorar el éxito escolar en el aprendizaje de la Estadística en la Educación Secundaria Obligatoria, trabajando con alumnos de diversificación curricular. En estos momentos hemos construido el sistema tutorial y hemos realizado una evaluación a través del test de BADYG renovado y una estadística de rendimientos mediante pruebas de control inicial y final para alumnos que han utilizado el sistema y alumnos con enseñanza tradicional. Hemos obtenido una clasificación de errores junto con una serie de indicadores para cada tipo.The aim of our research is to build, exemplify and analyze the benefits of a methodological tool thought for improving the success of the students when learning Statistics in the Compulsory Secondary Education, working with pupils belonging to a diversification group. For the time being we have built the tutorial system and achieved an assessment through the updated BADYG test and a statistical analysis of the students outputs based on initial and final control tests for students who have used our system and students with traditional teaching. We have got a classification of errors together with a series of indicators for each kind of error

Fuero penal militar y la problemática en su ámbito de aplicación

La legislación, jurisprudencia y casuística recientes nos permiten analizar que ha existido una indebida incursión de la Justicia Ordinaria en la competencia de la Justicia Penal Militar violándose de esta manera el Fuero Militar. Ejemplo de ello se evidencia en las investigaciones por bajas en combate, entre otros casos, que son remitidas por el funcionario de policía judicial a la Justicia Penal Ordinaria y que esta asume de manera inmediata, por considerar que pueden ser constitutivos de graves infracciones a los Derechos Humanos y al Derecho Internacional Humanitario

Aspectos epidemiológicos da cárie dental em escolares brancos e não brancos de ambos os sexos internos em sete orfanatos da cidade de São Paulo, Brasil, em 1972

It was realized an epidemiological investigation of dental caries in 860 male and female Brazilians school children, white and non-white from ages 7 to 12 years old, living in 7 orphanages in the city of S. Paulo, Brazil, was conducted to find out whether it was possible to establish, in children living in the same environmental condition, differences in the caries-experience between whites and non-whites. There were controlled very important variables related to the dental carie such as diets and a frequent ingestion of sugar foods during or between meals. There were studied relations among sexes, ages, races and the DMFT, scores as well as the number of the erupted permanent and the mean DMFT for each 100 erupted permanent teeth. Conclusions drawn from the data point out that there are no significant differences of caries-experience in permanent teeth between white and non-white children.Foi realizado um levantamento epidemiológico de cárie dental em 860 escolares de ambos os sexos, de 7 a 12 anos, de cor branca e não branca, internos em sete orfanatos da cidade de São Paulo, com o objetivo de verificar se em crianças brancas e não-brancas, vivendo nas mesmas condições ambientais, era possível detectar diferenças na experiência da cárie. Neste estudo, foram controladas variáveis de grande importância em relação à cárie dental, tais como dieta e freqüência da ingestão de substâncias açucaradas durante, ou entre as refeições. Foram estudadas relações entre idade, sexo e cor das crianças com os valores do índice CPO, com o número de dentes permanentes irrompidos e com os valores médios de dentes permanentes atacados por cárie por 100 dentes irrompidos. Os resultados obtidos mostram que os brancos não apresentam prevalência de cárie dental estatisticamente maior do que os não brancos, na dentição permanente

Orientação sobre saúde bucal em um Centro de Saúde

This paper deals with a study made with the purpose of observing dental health, education of patients coming for the first time to a Health Center. The study was carried out during two weeks and 25 patients were observed through "Participant Observation". Data for the "Educational Diagnosis" was collected in a card specially designed for it. Results showed that dental health orientation was not given by the staff to patients. An educational programme about dental health is suggested to be integrated with the activities of the various services, being the Dentist responsible for the staff programme coordination and evaluation. Finally the importance of the health center for the development of preventive, curative and educational integrated programmes is emphasized.Foi realizado estudo com o fim de verificar qual a orientação sobre saúde bucal dada aos clientes que pela primeira vez compareceram a um centro de saúde. Durante o período de 2 semanas foram observados 25 clientes; o método utilizado foi o da "observação participante''. Os dados necessários para o "diagnóstico educativo" foram colhidos com o auxílio de uma ficha. Da análise destes dados concluiu-se não haver uma adequada orientação com relação à saúde bucal, por parte do pessoal responsável. Sugere-se como "tratamento educativo" revisão das normas em relação à saúde da boca e desenvolvimento de um programa educativo, incidental e planejado, integrado às diferentes atividades realizadas pelo Centro. Propõe-se um conteúdo programático responsabilizando o dentista pelo adestramento do pessoal, execução e avaliação do programa. Ressalta-se a importância do centro de saúde para o desenvolvimento de programas integrados, preventivos, curativos e educativos