Euclidean position in Euclidean 2-orbifolds

Intuitively, a set of sites on a surface is in Euclidean position if points are so close to each other that planar algorithms can be easily adapted in order to solve most of the classical problems in Computational Geometry. In this work we formalize a definition of the term “Euclidean position” for a relevant class of metric spaces, the Euclidean 2-orbifolds, and present methods to compute whether a set of sites has this property. We also show the relation between the convex hull of a point set in Euclidean position on a Euclidean 2-orbifold and the planar convex hull of the inverse image (via the quotient map) of the set

Quadrangulations and 2-Colorations

Any metric quadrangulation (made by segments of straight line) of a point set in the plane determines a 2-coloration of the set, such that edges of the quadrangulation can only join points with different colors. In this work we focus in 2-colorations and study whether they admit a quadrangulation or not, and whether, given two quadrangulations of the same 2-coloration, it is possible to carry one into the other using some local operations, called diagonal slides and diagonal rotation. Although the answer is negative in general, we can show a very wide family of 2-colorations, called onions 2-coloration, that are quadrangulable and which graph of quadrangulations is always connected

The Possibilities of Kinect as an Access Device for People with Cerebral Palsy A Preliminary Study

Cerebral palsy (CP) is a general term for a group of permanent, nonprogressive movement disorders that cause physical disability in development, mainly in the areas of body movement but it might also affect intellectual capabilities. Among all this diversity of profiles, we find that, for some of them, access to a computer application is almost impossible in spite of the great variety of commercial devices based of different technologies. Kinect might be a viable possibility in order to facilitate access to games and computer applications that help users improve their skills or communication

Transforming Triangulations on Nonplanar Surfaces

We consider whether any two triangulations of a polygon or a point set on a nonplanar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder

Transforming triangulations on non planar-surfaces

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinde

K-Factores en nubes bicromáticas

Consideramos una colección de puntos bicromática y nos preguntamos cuántos puntos adicionales son necesarios considerar para asegurar la existencia de un k {factor. Dos tipos de puntos adicionales serán tratados: puntos de Steiner y puntos blancos (con posición prefijada pero no así su color

Ascomycetes from the tropical cloud forest of Honey, Puebla de los Angeles, Mexico

Antecedentes y Objetivos: Los ascomicetos son un grupo de hongos que se caracteriza por la formación de ascosporas dentro de ascas; se localizan en todos los ecosistemas terrestres y marinos. Los estudios de este grupo en el bosque mesófilo en México se han ido incrementando y en esta ocasión se presenta un inventario micoflorístico del municipio Honey, localizado en la Sierra Norte de Puebla, el cual conserva 50% de su vegetación original. Métodos: Los hongos fueron recolectados en seis localidades del municipio Honey, durante los años 2016 al 2018. Los especímenes fueron estudiados y determinados de acuerdo con las técnicas tradicionales en micología y se depositaron en las colecciones de hongos de los herbarios ENCB y FEZA.Resultados clave: Se determinaron 52 especies de ascomicetos para el municipio Honey, de los cuales 39 son nuevos registros para el estado, mientras que Adelphella babingtonii, Cudoniella acicularis, Lachnum fuscescens, Ophioceras leptosporum, Orbilia curvatispora y Unguiculariopsis acerina lo son para México. Además, Hymenoscyphus herrerae se describe como especie nueva para la ciencia. De tal forma que con el presente estudio se tiene un total de 93 especies para la entidad y 141 para los bosques mesófilos del país. La familia Xylariaceae presentó la mayor riqueza taxonómica con 16 especies, siendo Xylaria con 14, el género mejor representado (27%) de los ascomicetos del bosque mesófilo de Honey.Conclusiones: Los ascomicetos son el grupo de hongos mejor estudiados en los bosques mesófilos de Puebla; no obstante, es necesario incrementar los esfuerzos para inventariar y describir la riqueza fúngica y de otros organismos de este ecosistema amenazadoBackground and Aims: Ascomycetes are a group of fungi that are characterized by the formation of ascospores within ascas, they occur in all terrestrial and marine ecosystems. The studies of this group in the cloud forest in Mexico have been increasing and a mycofloristic inventory of the municipality of Honey in the Sierra Norte in Puebla, which preserves 50% of its original vegetation, is presented here.Methods: The specimens were collected in six locations in the municipality of Honey, during the years 2016 to 2018. The specimens were studied and determined according to traditional techniques in mycology and were deposited in the fungus collections of the herbaria ENCB and FEZA.Key results: Fifty-two species of ascomycetes were determined for the municipality of Honey, of which 39 are new records for the state, while Adelphella babingtonii, Cudoniella acicularis, Lachnum fuscescens, Ophioceras leptosporum, Orbilia curvatispora and Unguiculariopsis acerina are new records for Mexico. Additionally, Hymenoscyphus herrerae is described as a new species for science. Hence, with this study there are a total of 93 species for the entity and 141 for the cloud forest from Mexico. The family Xylariaceae presented the highest taxonomic richness with 16 species, Xylaria with 14 being the best represented genus (27%) of ascomycetes from the cloud forest of Honey.Conclusions: The Ascomycetes are the best studied group of fungi in the cloud forest from Puebla; however, it is necessary to increase efforts to inventory and describe the richness of fungi and other organisms in this endangered ecosystem

Compact Grid Representation of Graphs

A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some graph families

Reporting Bichromatic Segment Intersections from Point Sets

In this paper, we introduce a natural variation of the problem of computing all bichromatic intersections between two sets of segments. Given two sets R and B of n points in the plane defining two sets of segments, say red and blue, we present an O(n2) time and space algorithm for solving the problem of reporting the set of segments of each color intersected by segments of the other color. We also prove that this problem is 3-Sum hard and provide some illustrative examples of several point configurations

Monochromatic geometric k-factors for bicolored point sets with auxiliary points

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S