A forest simulation approach using weighted Voronoi diagrams. An application to Mediterranean fir Abies pinsapo Boiss stands

Aim of study: a) To present a new version of the forest simulator Vorest, an individual-based spatially explicit model that uses weighted Voronoi diagrams to simulate the natural dynamics of forest stands with closed canopies. b) To apply the model to the current dynamics of a Grazalema pinsapo stand to identify the nature of its competition regime and the stagnation risks it is currently facing.Area of study: Sierra del Pinar de Grazalema (S Spain)Material and methods: Two large plots representative of Grazalema pinsapo stands were used to fit and validate the model (plus 6 accesory plots to increase the availability of mortality data). Two inventories were carried out in 1998 and 2007 producing tree size and location data. We developed a forest simulator based on three submodels: growth, competition and mortality. The model was fitted, evaluated and validated for Grazalema plots. The simulation outputs were used to infer the expected evolution of structural diversity of  forest stands.Main results: Vorest has proved to be a good tool for simulating dynamics of natural closed stands. The application to Grazalema pinsapo stands has allowed assessing the nature of the main processes that are driving its development pathway. We have found that the prevailing size-asymmetric competition dominates the self-thinning process in small-sized trees. At the same time, there is an active tree-size differentiation process.Research highlights:Vorest has proved to be a good tool for simulating natural stands with closed canopies.The Grazalema pinsapo stand under consideration is currently undergoing a natural process of differentiation, avoiding long-term stagnation.Keywords: Vorest; stand dynamics; individual-based forest model; spatially explicit forest model; pinsapo

La Geometría en la Informática

La Geometría Algorítmica trata problemas geométricos de forma constructiva. Actualmente ha cobrado un gran interés debido a las numerosas aplicaciones que tiene en la Informática. En este trabajo se hace una introducción a la disciplina indicando su interés en Informática y aportando enlaces de interés para la docencia y la investigación en la materia

New bound for incremental constructing arrangements of curves

Let A(Γ) be the arrangement induced by a set Γ of n unbounded Jordan curves in the plane that intersect each other in at most two points. The upper bound for constructing those arrangements by an incremental method is, up to now, O(nλ4(n)). In this paper we improve this bound to O(nλ3(n)).Ministerio de Ciencia y Tecnologí

Point set stratification and minimum weight structures

Three different concepts of depth in a point set are considered and compared: Convex depth, location depth and Delaunay depth. As a notion of weight is naturally associated to each depth definition, we also present results on minimum weight structures (like spanning trees, poligonizations and triangulations) with respect to the three variations.DURSYMinisterio de Ciencia y Tecnologí

Searching for equilibrium positions in a game of political competition with restrictions

This paper considers a problem of political economy in which a Nash equilibrium study is performed in a proposed game with restrictions where the two major parties in a country vary their position within a politically flexible framework to increase their number of voters. The model as presented fits the reality of many countries. Moreover, it avoids the uniqueness of equilibrium positions. The problem is stated and solved from a geometric point of view

Caminos de desviación mínima local

Un camino que conecta dos puntos s y t en el plano es de desviación mínima respecto de un conjunto de puntos S si la mayor de las distancias entre un punto del camino y S es la menor posible entre todos los caminos que conectan s y t. En este trabajo estudiamos los caminos de desviación mínima que satisfacen además que todo subcamino es también de desviación mínima, a los que llamamos caminos de desviación mínima local.Postprint (published version

Moving coins

AbstractWe consider combinatorial and computational issues that are related to the problem of moving coins from one configuration to another. Coins are defined as non-overlapping discs, and moves are defined as collision free translations, all in the Euclidean plane. We obtain combinatorial bounds on the number of moves that are necessary and/or sufficient to move coins from one configuration to another. We also consider several decision problems related to coin moving, and obtain some results regarding their computational complexity

Connecting red cells in a bichromatic Voronoi diagram

Let S be a set of n + m sites, of which n are red and have weight wR, and m are blue and weigh wB. The objective of this paper is to calculate the minimum value of wR such that the union of the red Voronoi cells in the weighted Voronoi diagram of S is a connected set. The problem is solved for the multiplicatively-weighted Voronoi diagram in O((n+m)^2 log(nm)) time and for the additively-weighted Voronoi diagram in O(nmlog(nm)) time

DVALon: una herramienta para diagramas de Voronoi y grafos de proximidad de alcance limitado

Presentamos un estudio de los diagramas de Voronoi de alcance limitado de un conjunto finito de puntos del plano y DVALon, una herramienta para la manipulaci´on de dichos diagramas, los grafos de proximidad de alcance limitado y su aplicación a los caminos de desviación mínima y de separación máxima.Postprint (published version