Cusp Disruption in Minor Mergers

We present 0.55 x 10^6 particle simulations of the accretion of high-density dwarf galaxies by low-density giant galaxies, using models that contain both power-law central density cusps and point masses representing supermassive black holes. The cusp of the dwarf galaxy is disrupted during the merger, producing a remnant with a central density that is only slightly higher than that of the giant galaxy initially. Removing the black hole from the giant galaxy allows the dwarf galaxy to remain intact and leads to a remnant with a high central density, contrary to what is observed. Our results support the hypothesis that the persistence of low-density cores in giant galaxies is a consequence of supermassive black holes.Comment: 5 pages, 2 postscript figures, uses emulateapj.sty. Accepted for publication in The Astrophysical Journal Letter

Las hipótesis de Fisher en Latinoamérica: un análisis de cointegración

En este artículo se evalúan las hipótesis de Fisher y de integración de los mercados latinoamericanos mediante pruebas de cointegración y de cambio estructural endógeno. Los hallazgos sugieren varias conclusiones: a) el efecto Fisher se valida principalmente en Costa Rica; b) el efecto internacional de Fisher se valida débilmente entre Chile y Costa Rica y entre Colombia y México; c) la integración de los países y mercados es heterogénea, y d) únicamente Chile no tuvo cambios estructurales. En el estudio se usan series mensuales de Brasil, Chile, Colombia, Costa Rica, México y Perú durante el periodo comprendido entre enero de 1997 y diciembre de 2014.Neste artigo, avaliam-se as hipóteses de Fisher e de integração dos mercados latino-americanos mediante testes de cointegração e de mudança estrutural endógena. Os achados sugerem várias conclusões: a) o efeito Fisher é validado principalmente na Costa Rica; b) o efeito internacional de Fisher é validado debilmente entre o Chile e a Costa Rica, e entre a Colômbia e o México; c) a integração dos países e mercados é heterogênea; d) unicamente o Chile não teve mudanças estruturais. Além disso, usam-se séries mensais do Brasil, Chile, Colômbia, Costa Rica, México e do Peru durante o período compreendido entre janeiro de 1997 e dezembro de 2014.This article evaluates the Fisher hypothesis and the hypothesis of the integration of Latin American markets through co-integration and endogenous structural change tests. The findings suggest a number of conclusions: a) the Fisher effect is validated mainly in Costa Rica; b) the international Fisher effect is validated weakly between Chile and Costa Rica and between Colombia and Mexico; c) the integration of counties and markets is heterogeneous, and d) only Chile did not present structural changes. The study uses monthly series for Brazil, Chile, Colombia, Costa Rica, Mexico and Peru during the January 1997 to December 2014 period

Morphing Planar Graph Drawings with Unidirectional Moves

Alamdari et al. showed that given two straight-line planar drawings of a graph, there is a morph between them that preserves planarity and consists of a polynomial number of steps where each step is a \emph{linear morph} that moves each vertex at constant speed along a straight line. An important step in their proof consists of converting a \emph{pseudo-morph} (in which contractions are allowed) to a true morph. Here we introduce the notion of \emph{unidirectional morphing} step, where the vertices move along lines that all have the same direction. Our main result is to show that any planarity preserving pseudo-morph consisting of unidirectional steps and contraction of low degree vertices can be turned into a true morph without increasing the number of steps. Using this, we strengthen Alamdari et al.'s result to use only unidirectional morphs, and in the process we simplify the proof.Comment: 13 pages, 9 figure

Diseño y Validación de un Instrumento para Evaluar el Perfil Competencial Innovador del Docente Universitario.

Existen escasas investigaciones que traten de definir, diseñar propuestas metodológicas y validar herramientas para el estudio del perfil competencial innovador del docente universitario. El presente trabajo tiene como objetivo preparar un cuestionario técnica y teóricamente sólido para evaluarlo, que incluyera las características técnicas necesarias para cualquier buen instrumento de medición, especialmente la validación del constructo. En este sentido, después de diseñar y desarrollar la validez de contenido a través de juicio de expertos, se aplicó a 1.404 profesores de universidades de Bolivia, España y México. Posteriormente se analizó su fiabilidad y la validez de constructo a través de Modelos de Ecuaciones Estructurales. Los resultados obtenidos permiten encontrar una fiabilidad excelente, tanto en el cuestionario total como en sus dimensiones (alfa de Cronbach=0,982) y un AFE (oblicua/Promax) de 9 factores consistentes, unipolares y robustos, con un 70,265% de varianza total explicada. Finalmente, el AFC dio un modelo de medición final bastante parsimonioso y altamente satisfactorio (CFI=0,910; RMSEA=0,053; Hoelter=305; PRATIO=0,937). En conclusión, se puede afirmar que se ha contribuido al campo de la ciencia con un cuestionario válido y fiable para medir el perfil competencial innovador del docente universitario.post-print1112 K

On Schnyder's Theorm

The central topic of this thesis is Schnyder's Theorem. Schnyder's Theorem provides a characterization of planar graphs in terms of their poset dimension, as follows: a graph G is planar if and only if the dimension of the incidence poset of G is at most three. One of the implications of the theorem is proved by giving an explicit mapping of the vertices to R^2 that defines a straightline embedding of the graph. The other implication is proved by introducing the concept of normal labelling. Normal labellings of plane triangulations can be used to obtain a realizer of the incidence poset. We present an exposition of Schnyder’s theorem with his original proof, using normal labellings. An alternate proof of Schnyder’s Theorem is also presented. This alternate proof does not use normal labellings, instead we use some structural properties of a realizer of the incidence poset to deduce the result. Some applications and a generalization of one implication of Schnyder’s Theorem are also presented in this work. Normal labellings of plane triangulations can be used to obtain a barycentric embedding of a plane triangulation, and they also induce a partition of the edge set of a plane triangulation into edge disjoint trees. These two applications of Schnyder’s Theorem and a third one, relating realizers of the incidence poset and canonical orderings to obtain a compact drawing of a graph, are also presented. A generalization, to abstract simplicial complexes, of one of the implications of Schnyder’s Theorem was proved by Ossona de Mendez. This generalization is also presented in this work. The concept of order labelling is also introduced and we show some similarities of the order labelling and the normal labelling. Finally, we conclude this work by showing the source code of some implementations done in Sage

Morphing planar triangulations

A morph between two drawings of the same graph can be thought of as a continuous deformation between the two given drawings. A morph is linear if every vertex moves along a straight line segment from its initial position to its final position. In this thesis we study algorithms for morphing, in which the morphs are given by sequences of linear morphing steps. In 1944, Cairns proved that it is possible to morph between any two planar drawings of a planar triangulation while preserving planarity during the morph. However this morph may require exponentially many steps. It was not until 2013 that Alamdari et al. proved that the morphing problem for planar triangulations can be solved using polynomially many steps. In 1990 it was shown by Schnyder that using special drawings that we call Schnyder drawings it is possible to draw a planar graph on a O(n)×O(n) grid, and moreover such drawings can be found in O(n) time (here n denotes the number of vertices of the graph). It still remains unknown whether there is an efficient algorithm for morphing in which all drawings are on a polynomially sized grid. In this thesis we give two different new solutions to the morphing problem for planar triangulations. Our first solution gives a strengthening of the result of Alamdari et al. where each step is a unidirectional morph. This also leads to a simpler proof of their result. Our second morphing algorithm finds a planar morph consisting of O(n²) steps between any two Schnyder drawings while remaining in an O(n)×O(n) grid. However, there are drawings of planar triangulations which are not Schnyder drawings, and for these drawings we show that a unidirectional morph consisting of O(n) steps that ends at a Schnyder drawing can be found. We conclude this work by showing that the basic steps from our morphs can be implemented using a Schnyder wood and weight shifts on the set of interior faces