The 2+12+1 convex hull of a finite set

We study $\mathbb{R}^2\oplus\mathbb{R}$-separately convex hulls of finite sets of points in $\mathbb{R}^3$, as introduced in \cite{KirchheimMullerSverak2003}. When $\mathbb{R}^3$ is considered as a certain subset of $3\times 2$ matrices, this notion of convexity corresponds to rank-one convex convexity $K^{rc}$. If $\mathbb{R}^3$ is identified instead with a subset of $2\times 3$ matrices, it actually agrees with the quasiconvex hull, due to a recent result \cite{HarrisKirchheimLin18}. We introduce "$2+1$ complexes", which generalize $T_n$ constructions. For a finite set $K$, a "$2+1$ $K$-complex" is a $2+1$ complex whose extremal points belong to $K$. The "$2+1$-complex convex hull of $K$", $K^{cc}$, is the union of all $2+1$ $K$-complexes. We prove that $K^{cc}$ is contained in the $2+1$ convex hull $K^{rc}$. We also consider outer approximations to $2+1$ convexity based in the locality theorem \cite[4.7]{Kirchheim2003}. Starting with a crude outer approximation we iteratively chop off "$D$-prisms". For the examples in \cite{KirchheimMullerSverak2003}, and many others, this procedure reaches a "$2+1$ $K$-complex" in a finite number of steps, and thus computes the $2+1$ convex hull. We show examples of finite sets for which this procedure does not reach the $2+1$ convex hull in finite time, but we show that a sequence of outer approximations built with $D$-prisms converges to a $2+1$ $K$-complex. We conclude that $K^{rc}$ is always a "$2+1$ $K$-complex", which has interesting consequences

El trabajo colaborativo en la educación en línea: dos experiencias académicas

1 archivo PDF (14 páginas)El vinculo entre computadoras y acceso a internet en el sector educativo son medios a los cuales se recurre actualmente para generar una estrategia de mayor aprovechamiento en función de los planes y programas de estudio de las instituciones. Sin embargo, el salto entre lo presencial y lo virtual, no es tan fácil de realizar por lo que los modelos pedagógicos deben ser retroalimentados con actividades de tipo mixto (a distancia y presenciales), pues la brecha digital en ocasiones se deriva por aspectos culturales. De esta manera, el trabajo colaborativo en la virtualidad se ha usado por muchos responsables de curso (Profesores y/o Facilitadores de contenidos a distancia) como una estrategia de aprendizaje, con la finalidad de compartir formas de pensamiento para la generación de conocimiento, sin embargo para poder tener un orden en este tipo de participación en cursos a distancia, se necesita establecer reglas y/o formas de trabajo para que este sea ordenado y que cada participante de las dinámicas grupales cumplan con un papel o rol para ser cumplido con disposición y compromiso para la realización de actividades, es decir Deslindar responsabilidades y hacer participes a los estudiantes en la construcción de su propio conocimiento. Este trabajo se basa en la presentación de una estrategia de trabajo colaborativa aprendida en diferentes cursos de educación a distancia tomados por un servidor y canalizados directamente a mi trabajo docente apoyado en gran medida de Aulas Virtuales en la UAM- Azcapotzalco, con la experiencia de la versatilidad de cada grupo atendido en diferentes trimestres el UEA´s tales como presentación de proyectos, Estructuración del Proyecto I y cursos de aprendizaje de modelado tridimensional como es el caso de la UEA Temas de Opción Terminal I todas ellas en la licenciatura de Diseño Industrial

The implementation of the European portfolio for student teachers Of languages as a self assessment guide in a pre service english Language teaching program

El Portafolio Europeo para Maestros Estudiantes de Lenguas (EPOSTL, por sus siglas en inglés) es un documento desarrollado para ayudar a los profesores en formación a reflexionar sobre sus conocimientos didácticos, evaluar sus propias competencias didácticas y mantener un registro de su progreso y experiencias a lo largo de la enseñanza de idiomas. Este documento se enfoca en dos de las seis secciones del EPOSTL original. Una primera sección de declaración personal que invita a reflexionar sobre preguntas generales con respecto a la experiencia de enseñanza. Y una segunda sección de autoevaluación que comprenden 154 descriptores sobre competencias y conocimientos relacionados con la enseñanza de lenguas. Con respecto a los resultados obtenidos del desarrollo de los descriptores, se encuentran algunas conclusiones sobre cómo influyó este portafolio reflexivo al docente en formación en términos de su crecimiento profesional y personal

Extending the halo mass resolution of NN-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.Comment: 11 pages, 7 Figure

Bioactive Compounds from Marine Heterobranchs

The natural products of heterobranch molluscs display a huge variability both in structure and in their bioactivity. Despite the considerable lack of information, it can be observed from the recent literature that this group of animals possesses an astonishing arsenal of molecules from different origins that provide the molluscs with potent chemicals that are ecologically and pharmacologically relevant. In this review, we analyze the bioactivity of more than 450 compounds from ca. 400 species of heterobranch molluscs that are useful for the snails to protect themselves in different ways and/or that may be useful to us because of their pharmacological activities. Their ecological activities include predator avoidance, toxicity, antimicrobials, antifouling, trail-following and alarm pheromones, sunscreens and UV protection, tissue regeneration, and others. The most studied ecological activity is predation avoidance, followed by toxicity. Their pharmacological activities consist of cytotoxicity and antitumoral activity; antibiotic, antiparasitic, antiviral, and anti-inflammatory activity; and activity against neurodegenerative diseases and others. The most studied pharmacological activities are cytotoxicity and anticancer activities, followed by antibiotic activity. Overall, it can be observed that heterobranch molluscs are extremely interesting in regard to the study of marine natural products in terms of both chemical ecology and biotechnology studies, providing many leads for further detailed research in these fields in the near future