Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

Tele-repaso: repasa la lección con tu profesor por internet

TELE-REPASO es un servicio del IES Duques de Nájera de Logroño para que los alumnos y alumnas puedan realizar test de repaso de sus lecciones por internet. Las preguntas de los test han sido propuestas por los profesores y profesoras de cada asignatura. El sistema se encarga de corregir cada test y llevar cuenta de los test realizados, notas obtenidas, etc.Eje: Educación secundaria y profesional: Uso de las NTICRed de Universidades con Carreras en Informática (RedUNCI

Tele-repaso: repasa la lección con tu profesor por internet

TELE-REPASO es un servicio del IES Duques de Nájera de Logroño para que los alumnos y alumnas puedan realizar test de repaso de sus lecciones por internet. Las preguntas de los test han sido propuestas por los profesores y profesoras de cada asignatura. El sistema se encarga de corregir cada test y llevar cuenta de los test realizados, notas obtenidas, etc.Eje: Educación secundaria y profesional: Uso de las NTICRed de Universidades con Carreras en Informática (RedUNCI

Complexity and algorithms for Euler characteristic of simplicial complexes

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatorial commutative algebra and we also give a second description of them that requires no algebra. We present experiments showing that the two new algorithms can be implemented to be faster than previous Euler characteristic implementations by a large margin. © 2012 Elsevier B.V

Types of signature analysis in reliability based on Hilbert series

The present paper studies multiple failure and signature analysis of coherent systems using the theory of monomial ideals. While system reliability has been studied using Hilbert series of monomial ideals, this is not enough to understand in a deeper sense the ideal structure features that reflect the behavior of the system under multiple simultaneous failures. Therefore, we introduce the lcm-filtration of a monomial ideal, and we study the Hilbert series and resolutions of the corresponding ideals. Given a monomial ideal, we explicitly compute the resolutions for all ideals in the associated lcm-filtration, and we apply this to study coherent systems. Some computational results are shown in examples to demonstrate the usefulness of this approach and the computational issues that arise. We also study the failure distribution from a statistical point of view by means of the algebraic tools described. © 2016 Elsevier Lt

Efecto de una exposición subletal de Tetranychus urticae Koch (Acari: Tetranychidae) al triflumurón sobre sus parámetros biológicos

Effects of sublethal exposure to triflumuron on the biological performance of the two-spotted spider mite Tetranychus urticae Koch were analysed under laboratory conditions. Survivorship was affected by the compound. Triflumuron caused a reduction both in the percentage of eggs that developed to adults and in the survival of adult stage. Triflumuron also affected the fecundity. The net reproductive rate (R0), the intrinsic rate of increase (rm), and the finite rate of increase (lambda) of treated females were lower than in those non treated, resulting in a reduction of population growth. These results suggest that triflumuron could be a valuable addition in integrated pest management programs of T. urticae, although more laboratory, semi-field and field testing is required.Se analizaron, bajo condiciones de laboratorio, los efectos de una exposición subletal al triflumurón sobre los parámetros biológicos de la araña amarilla Tetranychus urticae Koch. La supervivencia fue afectada por el compuesto. El triflumurón causó una reducción tanto en el porcentaje de huevos que llegaron a adultos como en la supervivencia de los imagos y en la fecundidad. La tasa reproductiva neta (R0), el coeficiente de incremento intrínseco (rm), y el coeficiente de incremento finito (lamda) de las hembras tratadas fueron más bajos que en las no tratadas, dando como resultado la reducción del crecimiento de la población. Estos resultados sugieren que el triflumurón podría ser una incorporación interesante en programas de manejo integrado de T. urticae, aunque es preciso desarrollar más experimentos tanto de laboratorio como de semicampo y campo

A computer implementation of the partition of the unity procedure and its application to arthropod population dynamics. A case study on the European grape berry moth

This paper presents a new procedure to construct families of spatial approximation-prediction functions which depend on several parameters. The method is based on partitions of the unity. In order to find optimal functions in these families we introduce a Vietoris simplicial set associated to an influence radius. We consider error estimators induced by these Vietoris simplicial sets. A computational implementation of these mathematical models has been developed to be applied to any kind of finite discrete data. Our methods provide a useful tool for the analysis of the spatial distribution of species, which is imperative for developing accurate and efficient management of endangered and invasive species, biological conservation programs, etc. We demonstrate the application of our method to the analysis of the spatial distribution of the grape moth Lobesia botrana (Lepidoptera Tortricidae) in the vineyards of La Rioja obtaining useful results for the management of this pest. © 2010 IMACS. Published by Elsevier B.V. All rights reserved

On the free resolution induced by a pommaret basis

We combine the theory of Pommaret bases with a (slight generalisation of a) recent construction by Sköldberg based on discrete Morse theory. This combination allows us the explicit determination of a (generally non-minimal) free resolution for a graded polynomial module with the computation of only one Pommaret basis. If only the Betti numbers are needed, one can considerably simplify the computations by determining only the constant part of the differential. For the special case of a quasi-stable monomial ideal, we show that the induced resolution is a mapping cone resolution. We present an implementation within the CoCoALib and test it with some common benchmark ideals

Alexander duality in experimental designs

If F is a full factorial design and D is a fraction of F, then for a given monomial ordering, the algebraic method gives a saturated polynomial basis for D which can be used for regression. Consider now an algebraic basis for the complementary fraction of D in F, built under the same monomial ordering. We show that the basis for the complementary fraction is the Alexander dual of the first basis, constructed by shifting monomial exponents. For designs with two levels, the Alexander dual uses the traditional definition for simplicial complexes, while for designs with more than two levels, the dual is constructed with respect to the basis for the design F. This yields various new constructions for designs, where the basis and linear aberration can easily be read from the duality