Implicitization of surfaces via geometric tropicalization

In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula for tropical multiplicities of regular points in arbitrary dimension and we prove a conjecture of Sturmfels and Tevelev regarding sufficient combinatorial conditions to compute tropical varieties via geometric tropicalization. Using these two results, we extend previous work of Sturmfels, Tevelev and Yu for tropical implicitization of generic surfaces, and we provide methods for approaching the non-generic cases.Comment: 20 pages, 6 figures. Mayor reorganization and exposition improved. The results on geometric tropicalization have been extended to any dimension. In particular, Conjecture 2.8 is now Theorem 2.

Cambios estacionales en los ensambles de aves en un ecotono bosque-estepa del norte de Patagonia

Estudiamos las variaciones estacionales en una comunidad de aves que habitan el ecotono bosque-estepa del norte de Patagonia. Analizamos los cambios en la riqueza de especies, la composición de especies y la abundancia total, y a nivel de las especies, evaluamos las diferencias en la estacionalidad reproductiva y de muda. El ensamble de aves mostró pocas variaciones estacionales en la riqueza y abundancia total, pero un notable cambio en la composición de especies entre la primavera–verano y el otoño–invierno. El cambio en la composición de especies no promovió variaciones estacionales en la riqueza y la abundancia total, debido a la presencia de especies abundantes que visitan el área en las diferentes estaciones. A nivel de las especies, las aves residentes y migrantes de corta distancia tendieron a comenzar la reproducción antes que las migrantes de larga distancia, y aquellas especies de aves comenzaron la muda de plumas del cuerpo y del ala al finalizar la reproducción. Por lo cual encontramos una baja superposición de estas dos demandantes actividades. Elaenia albiceps, la única especie migradora de larga distancia, no presentó muda corporal o del plumaje de vuelo en nuestra área de estudio. Nuestros resultados remarcan la importancia del movimiento de las aves en respuesta a las variaciones en la disponibilidad de recursos, que promueven la migración o el desplazamiento local de las aves.We studied seasonal variation in a community of birds inhabiting a forest?steppe ecotone of north Patagonia. We analyzed changesin species richness, species composition and total abundance, and, at the species level, we evaluated differences in breeding and moltingseasonality. The bird assemblage showed a low seasonal variation in richness and total abundance, but a great change in species compositionbetween spring?summer and fall?winter. The change in species composition did not lead to changes in richness and total abundance, due tothe presence of abundant species that visit the area in different seasons. At the species level, resident birds and short distance migrantstended to begin breeding earlier than long distance migrants, and those bird species began to molt body and flight feathers after breeding.Therefore, we found a low overlap between these two energetically demanding activities. Elaenia albiceps, the only long-distance migrantspecies, did not molt body and flight feathers in our study area. Our results highlight the importance of bird movements in response to seasonalvariations in the availability of resources, which promote migration or local displacements of birds.Fil: Cueto, Víctor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Centro de Investigación Esquel de Montaña y Estepa Patagóica. Universidad Nacional de la Patagonia "San Juan Bosco". Facultad de Ciencias Naturales - Sede Esquel. Centro de Investigación Esquel de Montaña y Estepa Patagónica; ArgentinaFil: Gorosito, Cristian Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Centro de Investigación Esquel de Montaña y Estepa Patagóica. Universidad Nacional de la Patagonia "San Juan Bosco". Facultad de Ciencias Naturales - Sede Esquel. Centro de Investigación Esquel de Montaña y Estepa Patagónica; Argentin

Tropical secant graphs of monomial curves

The first secant variety of a projective monomial curve is a threefold with an action by a one-dimensional torus. Its tropicalization is a three-dimensional fan with a one-dimensional lineality space, so the tropical threefold is represented by a balanced graph. Our main result is an explicit construction of that graph. As a consequence, we obtain algorithms to effectively compute the multidegree and Chow polytope of an arbitrary projective monomial curve. This generalizes an earlier degree formula due to Ranestad. The combinatorics underlying our construction is rather delicate, and it is based on a refinement of the theory of geometric tropicalization due to Hacking, Keel and Tevelev.Comment: 30 pages, 8 figures. Major revision of the exposition. In particular, old Sections 4 and 5 are merged into a single section. Also, added Figure 3 and discussed Chow polytopes of rational normal curves in Section

The singular kernel coagulation equation with multifragmentation

In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak $L^1$ compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also given.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1210.150

Transcultural adaptation of the who oral health questionnaire and its validation in chilean children

Indexación: Scopus.Introduction: The last edition of the WHO "Oral Health Questionnaire for Children" was published in 2013. This is an only-English version, and as such it requires linguistic adaptation and validation to be applied in the Chilean population. Objectives: To translate and adapt the WHO Oral Health Questionnaire for Children to Spanish and validate it in a Chilean population. Methods: A translation and back translation of the original instrument from English to Spanish was carried out by four translators. The questionnaire was self-reported as a pilot test in ten individuals. A sample was subsequently selected for convenience taking into account the population distribution, resulting in a final sample of 103 individuals. The internal consistency was calculated with Cronbach's alpha, criterion validity with Pearson's correlation coefficient and construct validity with Exploratory Factor Analysis. Results: A conceptual and semantic equivalence of the instrument was obtained. Women and men accounted for 43.69% and 56.31% of the sample, respectively. Cronbach's alpha coefficient was 0.62, while criterion validity was slightly positive between the total dimensions and the DMFT (r=0.13, p-value= 0.20). The Exploratory Factor Analysis yielded a total of 11 factors that explain 70% of the variability in the data. Conclusions: The oral health questionnaire has been appropriately adapted to Spanish, having conceptual as well as semantic equivalence to the original version, being reliable and valid to be used in a population of 12-year-old Chilean children. © 2018, Universidad de Concepcion. All rights reserved.http://joralres.com/index.php/JOR/article/view/432/43