A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

Risk and protective factors in the mental health of adolescents living with HIV in Namibia

"Introducción": A pesar de que el 90% de los adolescentes con VIH en el mundo viven en África subsahariana, pocos estudios han examinado el impacto que tiene el hecho de estar infectados por VIH sobre su salud mental en este región. Además, los adolescentes con VIH en contextos de escasos recursos se enfrentan con factores de riesgo adicionales, como la pobreza, la falta de apoyo social y el estigma relacionado con el VIH. Este estudio examina la salud mental de los adolescentes que viven con el VIH en Namibia, un país con una de las prevalencias de VIH más altas del mundo. El estudio examina si estos adolescentes muestran mayores problemas de salud mental respecto a un grupo de comparación de la comunidad. Asimismo, el estudio evalúa los factores que predicen problemas de salud mental con el fin de identificar las potenciales áreas de intervención que permitan mejorar dichos problemas. Métodos: En una fase piloto, se organizan grupos de discusión con 34 adolescentes y entrevistas con ocho informantes clave para explorar las percepciones locales sobre los problemas de salud mental, así como sus factores de riesgo y factores de proteccion. Dado que las propiedades psicométricas del instrumento seleccionado para medir salud mental, el cuestionario Strengths and Difficulties Questionnaire/ Cuestionario de Capacidades y Dificultades (SDQ), nunca habían sido exploradas antes en Namibia, se decidió administrarlo a 236 participantes con edades comprendidas entre 12 y 18 años en una fase piloto cuantitativa...

Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.