Efficient Generation of Rectangulations via Permutation Languages

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a large variety of different classes of generic rectangulations. Our algorithms work under very mild assumptions, and apply to a large number of rectangulation classes known from the literature, such as generic rectangulations, diagonal rectangulations, 1-sided/area-universal, block-aligned rectangulations, and their guillotine variants. They also apply to classes of rectangulations that are characterized by avoiding certain patterns, and in this work we initiate a systematic investigation of pattern avoidance in rectangulations. Our generation algorithms are efficient, in some cases even loopless or constant amortized time, i.e., each new rectangulation is generated in constant time in the worst case or on average, respectively. Moreover, the Gray codes we obtain are cyclic, and sometimes provably optimal, in the sense that they correspond to a Hamilton cycle on the skeleton of an underlying polytope. These results are obtained by encoding rectangulations as permutations, and by applying our recently developed permutation language framework

The Minimum Cost Query Problem on Matroids with Uncertainty Areas

We study the minimum weight basis problem on matroid when elements\u27 weights are uncertain. For each element we only know a set of possible values (an uncertainty area) that contains its real weight. In some cases there exist bases that are uniformly optimal, that is, they are minimum weight bases for every possible weight function obeying the uncertainty areas. In other cases, computing such a basis is not possible unless we perform some queries for the exact value of some elements. Our main result is a polynomial time algorithm for the following problem. Given a matroid with uncertainty areas and a query cost function on its elements, find the set of elements of minimum total cost that we need to simultaneously query such that, no matter their revelation, the resulting instance admits a uniformly optimal base. We also provide combinatorial characterizations of all uniformly optimal bases, when one exists; and of all sets of queries that can be performed so that after revealing the corresponding weights the resulting instance admits a uniformly optimal base

On the Two-Dimensional Knapsack Problem for Convex Polygons

We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the knapsack. We allow to rotate the polygons by arbitrary angles. We present a quasi-polynomial time O(1)-approximation algorithm for the general case and a polynomial time O(1)-approximation algorithm if all input polygons are triangles, both assuming polynomially bounded integral input data. Also, we give a quasi-polynomial time algorithm that computes a solution of optimal weight under resource augmentation, i.e., we allow to increase the size of the knapsack by a factor of 1+? for some ? > 0 but compare ourselves with the optimal solution for the original knapsack. To the best of our knowledge, these are the first results for two-dimensional geometric knapsack in which the input objects are more general than axis-parallel rectangles or circles and in which the input polygons can be rotated by arbitrary angles

Efficient generation of rectangulations via permutation languages

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a large variety of different classes of generic rectangulations. Our algorithms work under very mild assumptions, and apply to a large number of rectangulation classes known from the literature, such as generic rectangulations, diagonal rectangulations, 1-sided/area-universal, block-aligned rectangulations, and their guillotine variants. They also apply to classes of rectangulations that are characterized by avoiding certain patterns, and in this work we initiate a systematic investigation of pattern avoidance in rectangulations. Our generation algorithms are efficient, in some cases even loopless or constant amortized time, i.e., each new rectangulation is generated in constant time in the worst case or on average, respectively. Moreover, the Gray codes we obtain are cyclic, and sometimes provably optimal, in the sense that they correspond to a Hamilton cycle on the skeleton of an underlying polytope. These results are obtained by encoding rectangulations as permutations, and by applying our recently developed permutation language framework

Grafito sobre sigillata hispánica con el hapax lavapenis

En el transcurso de la excavación arqueológica realizada en el acueducto de la ciudad romana de Uxama Argaela (Osma, Soria), se recuperó un plato de terra sigillata de la forma hispánica 15/17, que repite todas las características propias de ésta en cuanto a dimensiones, pasta o barniz. Sin embargo, tiene algo que lo hace peculiar y es un grafito con un substantivo sin paralelo epigráfico y de naturaleza inusual en latín. Su contexto estratigráfico se relaciona con el final del funcionamiento del acueducto.A terra sigillata plate, hispanic 15/17 form, was found during the archaeological excavations in the aqueduct of the roman town Uxama Argaela (Osma, Soria). As far as material, form, size, and slip there is nothing remarkable in this vessel. However, a graffiti, a latin substantive, quite unusual and without known epigraphic analogue, makes this dish quite a peculiar object. Stratigraphic context relates this finding with the final stages of aqueduct usage

Traversing combinatorial 0/1-polytopes via optimization

In this paper, we present a new framework that exploits combinatorial optimization for efficiently generating a large variety of combinatorial objects based on graphs, matroids, posets and polytopes. Our method relies on a simple and versatile algorithm for computing a Hamilton path on the skeleton of any 0/1-polytope \conv(X), where X\seq \{0,1\}^n. The algorithm uses as a black box any algorithm that solves a variant of the classical linear optimization problem~$\min\{w\cdot x\mid x\in X\}$, and the resulting delay, i.e., the running time per visited vertex on the Hamilton path, is only by a factor of $\log n$ larger than the running time of the optimization algorithm. When $X$ encodes a particular class of combinatorial objects, then traversing the skeleton of the polytope~\conv(X) along a Hamilton path corresponds to listing the combinatorial objects by local change operations, i.e., we obtain Gray code listings. As concrete results of our general framework, we obtain efficient algorithms for generating all ($c$-optimal) bases and independent sets in a matroid; ($c$-optimal) spanning trees, forests, matchings, maximum matchings, and $c$-optimal matchings in a general graph; vertex covers, minimum vertex covers, $c$-optimal vertex covers, stable sets, maximum stable sets and $c$-optimal stable sets in a bipartite graph; as well as antichains, maximum antichains, $c$-optimal antichains, and $c$-optimal ideals of a poset. Specifically, the delay and space required by these algorithms are polynomial in the size of the matroid ground set, graph, or poset, respectively. Furthermore, all of these listings correspond to Hamilton paths on the corresponding combinatorial polytopes, namely the base polytope, matching polytope, vertex cover polytope, stable set polytope, chain polytope and order polytope, respectively. As another corollary from our framework, we obtain an \cO(t_{\upright{LP}} \log n) delay algorithm for the vertex enumeration problem on 0/1-polytopes $\{x\in\mathbb{R}^n\mid Ax\leq b\}$, where $A\in \mathbb{R}^{m\times n}$ and~$b\in\mathbb{R}^m$, and t_{\upright{LP}} is the time needed to solve the linear program $\min\{w\cdot x\mid Ax\leq b\}$. This improves upon the 25-year old \cO(t_{\upright{LP}}\,n) delay algorithm due to Bussieck and L\"ubbecke

Texto: Contaminación y alteración microbiana de los alimentos

En actual perspectiva de vida en el planeta, los microorganismos tienen como principal función la reciclar toda la materia orgánica en general de esta manera cumplen su rol biológico con mucha eficiencia dentro de todo ecosistema en nuestro planeta. Durante la producción, elaboración, transformación y almacenamiento de los productos vegetales y animales tiene lugar un incremento o una reducción de la flora contaminante original y la adquirida durante el transporte, por contactar con aparatos, a partir de los manipuladores de I alimentos o por la adición de productos complementarios. Permanentemente para el especialista en alimentos, debe evitar la suciedad y la contaminación mediante medidas higiénicas, teniendo en cuenta que el aire, la temperatura y el agua constituyen normalmente los principales factores en el proceso de contaminación alimentaria. Como consecuencia de la actividad de los microrganismos se producen en los alimentos diferentes transformaciones químicas y a veces físicas, que generalmente determinan una pérdida de calidad, del sabor y de consistencia y que en ocasiones alteran totalmente al alimento dejándolo no apto para el consumo humano y animal. Es por ello la importancia que tiene el estudio a profundidad; referente a los principios de la contaminación y la alteración dentro de la formación profesional del ingeniero alimentario.Trabado de investigacio

Manejo de estiércol y purines y sostenibilidad

Optimizar la gestión de deyecciones en las explotaciones es un reto del sector que contribuye a dar respuesta a desafíos ambientales, favoreciendo, por tanto, su sostenibilidad tanto en aspectos ambientales como sociales y económicos. Dada la variedad de sistemas productivos y entornos en que estos se ubican, no es posible proponer una única solución, por lo que resulta necesario para cada caso identificar aquellas estrategias y manejos que, adaptándose a sus características, permitan reducir su impacto ambiental y conservar en lo posible los nutrientes para su uso posterior dentro de un plan de fertilización de cultivos. En este capítulo se detalla una selección de estrategias y manejos de purines y estiércoles, describiendo los principios en los que se basa su capacidad de minimizar la pérdida de nutrientes e incluso revalorizarlo para su posterior utilización como fertilizantePublishe