Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption expressing a natural relationship between the lower semicontinuous envelopes of the data functions in the domain of the sum function. We also provide a new rule for the subdifferential of the sum of two convex functions, which uses a strategy of augmenting the involved functions. The main feature of our analysis is that no continuity-type condition is required. Our approach allows us to unify, recover, and extend different results in the recent literature.Research of the first and the second authors is supported by CONICYT grants, Fondecyt 1150909 and 1151003, Basal PFB-03, and Basal FB003. Research of the second and third authors is supported by MINECO of Spain and FEDER of EU, grant MTM2014-59179-C2-1-P. Research of the third author is also supported by the Australian Research Council: Project DP160100854

Subdifferential of the supremum function: moving back and forth between continuous and non-continuous settings

In this paper we establish general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the non-continuous to the continuous setting, we proceed by a compactification-based approach which leads us to problems having compact index sets and upper semi-continuously indexed mappings, giving rise to new characterizations of the subdifferential of the supremum by means of upper semicontinuous regularized functions and an enlarged compact index set. In the opposite sense, we rewrite the subdifferential of these new regularized functions by using the original data, also leading us to new results on the subdifferential of the supremum. We give two applications in the last section, the first one concerning the nonconvex Fenchel duality, and the second one establishing Fritz-John and KKT conditions in convex semi-infinite programming.Research supported by CONICYT (Fondecyt 1190012 and 1190110), Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Grant Beatriz Galindo BEAGAL 18/00205), and Research Project PGC2018-097960-B-C21 from MICINN, Spain. The research of the third author is also supported by the Australian ARC - Discovery Projects DP 180100602

Necessary and Sufficient Optimality Conditions in DC Semi-infinite Programming

This paper deals with particular families of DC optimization problems involving suprema of convex functions. We show that the specific structure of this type of function allows us to cover a variety of problems in nonconvex programming. Necessary and sufficient optimality conditions for these families of DC optimization problems are established, where some of these structural features are conveniently exploited. More precisely, we derive necessary and sufficient conditions for (global and local) optimality in DC semi-infinite programming and DC cone-constrained optimization, under natural constraint qualifications. Finally, a penalty approach to DC abstract programming problems is developed in the last section.The first author was partially supported by ANID Chile under grant Fondecyt Regular 1190110. The second author is supported by Research Project PGC2018-097960-B-C21 from MICINN Spain, and Australian ARC–Discovery Projects DP 180100602. The third author was partially supported by ANID Chile under grants Fondecyt regular 1190110, Fondecyt regular 1200283, and Programa Regional Mathamsud 20-Math-08 CODE: MATH190003

Evaluation of the Sportsmanship-Aggression Continuum in Youth Football

Given the importance of sport in modern society, it is essential that appropriate instruments are available for the assessment of both fair play and unfair play in the sport of football, particularly in the context of youth football. This research study presents the findings from the implementation of a protocol intended to assess fair play during football matches across three seasons. The study included 64 teams, 1192 players, 64 coaches and 292 referees all of whom were involved in the First Cadet category of the Football Federation of Alava (FFA). The measurement instrument employed was the Record of Football Match Evaluations (RFME) developed by Gimeno, Saenz, Arino and Aznar (2007). The results revealed that there was a high level of fair play at this level of play which extended to referees, coaches and players across the seasons of interest; there was a greater frequency of fair play attitudes relative to unfair play attitudes; home teams that were victorious were judged to have the most favorable fair play attitudes; and there was a negative correlation between perceived fair play and the number of cards shown by referees. The instrument 1) allowed for the effective utilization of a tool to assess fair play in youth football; 2) was effective for use over the course of the season; and 3) provided knowledge about the social agents who initiate inappropriate and unsportsmanlike acts during football matches for of school age youth, which enables consideration of appropriate counter measures. Dada la trascendencia que tiene en nuestra sociedad el deporte, en especial el fútbol desde edades muy tempranas, se hace necesario que los gestores de las competiciones dispongan de herramientas que permitan evaluar los comportamientos de deportividad y no deportividad que se observan en contextos deportivos de fútbol. En la presente investigación, se muestra la implementación de un protocolo de evaluación continua de la deportividad en los partidos de fútbol, durante tres temporadas deportivas. Participaron 64 equipos; 1192 futbolistas, 64 entrenadores y 292 árbitros, de la categoría primera cadete de la Federación Alavesa de Fútbol (F.A.F.). El instrumento de recogida de información utilizado fue el “Registro de Evaluación de Partidos de Fútbol” (REPF) (Gimeno, Sáenz, Ariño y Aznar, 2007). Los resultados re"ejan: puntuaciones positivas, en relación a la deportividad de árbitros, entrenadores y jugadores en cada una de las temporadas evaluadas; una mayor frecuencia de actitudes y conductas deportivas en comparación con las no-deportivas; una mayor percepción de deportividad en aquellos partidos en los que el equipo local es el ganador; y una correlación negativa entre la percepción de deportividad de un partido y el número de tarjetas mostradas por los árbitros. Como conclusión, se puede afirmar que el instrumento que se presenta permite: 1. Utilizar una herramienta de evaluación específica de la deportividad para la disciplina del fútbol en edad escolar; 2. Evaluar la deportividad a lo largo de toda la temporada; 3. Identificar los agentes que presentan comportamientos inadecuados durante la práctica deportiva de los jóvenes deportistas, pudiendo proponer las mejores medidas de intervenció

Recuento histórico del Herbario de la Universidad de la Amazonia (HUAZ)

Los herbarios son centros en donde se almacenan sistemáticamente colecciones de plantas secas, lo que permite certificar y corroborar la identidad de los especimenes en cuestión. El Herbario Amazónico Colombiano (COAH) se encuentra ubicado en la ciudad de Bogotá, por lo que se ha hecho necesario implementar una colección de referencia para la región amazónica, con fines de apoyar investigaciones locales y labores de docencia. Esto ha generado confianza en el desarrollo de proyectos, los cuales se han apoyado desde el herbario de la Universidad de la Amazonía - HUAZ

Aporte de hojarasca en la estación de monitoreo de biodiversidad, Centro de Investigaciones Amazónicas Macagual.

Se estimó la producción de hojarasca total, en la estación de monitoreo de biodiversidad del Centro de Investigaciones Amazónicas Macagual (CIAM), la cual abarca diferentes tipos de cobertura. Se utilizaron 20 trampas de 1m2 para colectar el material caído, se cuantificó mensualmente entre abril y septiembre de 2008. La hojarasca se llevó al laboratorio del herbario HUAZ, se separó en hojas, ramas, flores y material no identificado, se pesó en fresco y seco. Se tomaron además datos climáticos como precipitación, temperatura y humedad relativa. La producción de hojarasca fue de 4.8 Mg/ha/año; representadas en hojas 70%, ramas 13.5%, flores 0.27% y material no determinado 16.25%. Las hojas se determinaron hasta el nivel de familia, género y morfoespecies para las no determinadas. No se encontró una diferencia significativa en la producción de hojarasca en las diferentes coberturas durante el periodo de estudio. A las 6 especies con mayor aporte de hojarasca se le analizaron los macronutrientes como N, P, K y C

Moreau-Rockafellar-Type Formulas for the Subdifferential of the Supremum Function

We characterize the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions. The main contribution of this paper consists of providing formulas for such a subdifferential under weak continuity assumptions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the reference point, and not at nearby points as in [Valadier, C. R. Math. Acad. Sci. Paris, 268 (1969), pp. 39--42]. We also derive new Fritz John- and KKT-type optimality conditions for semi-infinite convex optimization, omitting the continuity/closedness assumptions in [Dinh et al., ESAIM Control Optim. Calc. Var., 13 (2007), pp. 580--597]. When the family of functions is finite, we use continuity conditions concerning only the active functions, and not all the data functions as in [Rockafellar, Proc. Lond. Math. Soc. (3), 39 (1979), pp. 331--355; Volle, Acta Math. Vietnam., 19 (1994), pp. 137--148].Research of the first and second authors is supported by CONICYT grants, Fondecyt 1150909 and 1151003, and Proyecto grant PIA AFB-170001. Research of the second and third authors is supported by MINECO of Spain and FEDER of EU, grant MTM2014-59179-C2-1-P. Research of the third author is also supported by the Australian Research Council, Project DP160100854

PSICOFARMACOGENÉTICA

Psychiatric disorders are chronic, recurrent and are responsible for huge social and individual costs. Psychopharmacology is a growing field with and an increasing number and quality of drugs, which have improved treatment efficacy and decreased adverse effects. Pharmacogenetics is a relatively recent science that study genetics influence on drug response and adverse effects. In these review, we point to the major findings in psycopharmacogenetics and comment on the perspectives for the scientific community and clinicians in Brazil.Doenças psiquiátricas são patologias crônicas, recorrentes e promotoras de desarranjo e custo social extenso. A psicofarmacologia apresenta um número crescente de medicações eficazes e sua evolução acontece no sentido de aumentar a eficácia do tratamento de pacientes refratários, assim como reduzir os freqüentes efeitos colaterais associados com as medicações tradicionais. A farmacogenética é uma ciência relativamente recente que estuda as influências genéticas na resposta a droga e que pode vir a ser ferramenta essencial para o entendimento do funcionamento de drogas, assim como dos efeitos colaterais de medicações. Nessa revisão foram levantados os principais achados farmacogenéticos com antipsicóticos e antidepressivos e comentadas as perspectivas da farmacogenética na comunidade científica e clínica no Brasil

Phosphorylation-dependent regulation of the NOTCH1 intracellular domain by dual-specificity tyrosine-regulated kinase 2

NOTCH proteins constitute a receptor family with a widely conserved role in cell cycle, growing and development regulation. NOTCH1, the best characterised member of this family, regulates the expression of key genes in cell growth and angiogenesis, playing an essential role in cancer development. These observations provide a relevant rationale to propose the inhibition of the intracellular domain of NOTCH1 (Notch1-IC) as a strategy for treating various types of cancer. Notch1-IC stability is mainly controlled by post-translational modifications. FBXW7 ubiquitin E3 ligase-mediated degradation is considered one of the most relevant, being the previous phosphorylation at Thr-2512 residue required. In the present study, we describe for the first time a new regulation mechanism of the NOTCH1 signalling pathway mediated by DYRK2. We demonstrate that DYRK2 phosphorylates Notch1-IC in response to chemotherapeutic agents and facilitates its proteasomal degradation by FBXW7 ubiquitin ligase through a Thr-2512 phosphorylation-dependent mechanism. We show that DYRK2 regulation by chemotherapeutic agents has a relevant effect on the viability, motility and invasion capacity of cancer cells expressing NOTCH1. In summary, we reveal a novel mechanism of regulation for NOTCH1 which might help us to better understand its role in cancer biology