Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields

Let K be a finite field with q elements and let X be a subset of a projective space P^{s-1}, over the field K, which is parameterized by Laurent monomials. Let I(X) be the vanishing ideal of X. Some of the main contributions of this paper are in determining the structure of I(X) and some of their invariants. It is shown that I(X) is a lattice ideal. We introduce the notion of a parameterized code arising from X and present algebraic methods to compute and study its dimension, length and minimum distance. For a parameterized code arising from a connected graph we are able to compute its length and to make our results more precise. If the graph is non-bipartite, we show an upper bound for the minimum distance. We also study the underlying geometric structure of X.Comment: Finite Fields Appl., to appea

Systems with the integer rounding property in normal monomial subrings

Let C be a clutter and let A be its incidence matrix. If the linear system x>=0;xA<=1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.Comment: Major revisio

Evaluación de dosis de biofertilizante y sanialgas en la producción de maíz (Zea mays L.) forrajero en la Comarca Lagunera

The Comarca Lagunera is one of the most important milk basins nationwide. The magnitude of this production system raises the need to implement strategies for the production of forage for their maintenance. The objective of the present study was to identify the doses and effect of biofertilizer (FerbiliQ®) and sanialgas® on growth, development and yield in forage corn. An experiment was established in Random Blocks with three repetitions in arrangement of Divided Plots, where the large parcels were the mycorrhizal doses (600 mL (100%), 300 mL (50%) and the control (0%) and the plots girls were the doses of sanialgas (with and without) 0 and 100% respectively, plant height (cm), root volume (cm3) and fresh forage yield (ton ha-1) were measured. the application of the biofertilizer in the plant growth (height) or the root volume, the yield was negatively affected when the seed was inoculated 100%, however, when sanialgas® was applied, the plant had greater development and resulted in an increase a significant 10% in the production of green forage, with respect to when the bioproduct was not applied.La Comarca Lagunera es una de las cuencas lecheras más importantes a nivel nacional. La magnitud de este sistema de producción plantea la necesidad de implementar estrategias para la producción de forraje para su manutención. El objetivo del presente estudio fue identificar las dosis y efecto del biofertilizante (FerbiliQ®) y sanialgas® sobre el crecimiento, desarrollo y rendimiento en maíz forrajero. Se estableció un experimento en Bloques al Azar con tres repeticiones en arreglo de Parcelas Divididas, donde las parcelas grandes fueron las dosis de micorrizas (600 mL (100 %), 300 mL (50 %) y el testigo (0 %) y las parcelas chicas fueron las dosis de sanialgas (con y sin) 0 y 100% respectivamente.&nbsp; Se midió la altura de planta (cm), volumen de raíz (cm3) y rendimiento de forraje fresco (ton ha-1). No hubo ningún efecto por la aplicación del biofertilizante en el crecimiento de la planta (altura) ni para el volumen de raíz; el rendimiento se afectó negativamente al inocular al 100 % la semilla. Sin embargo, cuando se aplicó sanialgas® la planta tuvo mayor desarrollo y repercutió en un incremento significativo del 10 % en la producción de forraje verde, respecto a cuándo no se aplicó el bioproducto

Seeing the Forest for the Trees: Mapping Cover and Counting Trees from Aerial Images of a Mangrove Forest Using Artificial Intelligence

Mangrove forests provide valuable ecosystem services to coastal communities across tropical and subtropical regions. Current anthropogenic stressors threaten these ecosystems and urge researchers to create improved monitoring methods for better environmental management. Recent efforts that have focused on automatically quantifying the above-ground biomass using image analysis have found some success on high resolution imagery of mangrove forests that have sparse vegetation. In this study, we focus on stands of mangrove forests with dense vegetation consisting of the endemic Pelliciera rhizophorae and the more widespread Rhizophora mangle mangrove species located in the remote Utria National Park in the Colombian Pacific coast. Our developed workflow used consumer-grade Unoccupied Aerial System (UAS) imagery of the mangrove forests, from which large orthophoto mosaics and digital surface models are built. We apply convolutional neural networks (CNNs) for instance segmentation to accurately delineate (33% instance average precision) individual tree canopies for the Pelliciera rhizophorae species. We also apply CNNs for semantic segmentation to accurately identify (97% precision and 87% recall) the area coverage of the Rhizophora mangle mangrove tree species as well as the area coverage of surrounding mud and water land-cover classes. We provide a novel algorithm for merging predicted instance segmentation tiles of trees to recover tree shapes and sizes in overlapping border regions of tiles. Using the automatically segmented ground areas we interpolate their height from the digital surface model to generate a digital elevation model, significantly reducing the effort for ground pixel selection. Finally, we calculate a canopy height model from the digital surface and elevation models and combine it with the inventory of Pelliciera rhizophorae trees to derive the height of each individual mangrove tree. The resulting inventory of a mangrove forest, with individual P. rhizophorae tree height information, as well as crown shape and size descriptions, enables the use of allometric equations to calculate important monitoring metrics, such as above-ground biomass and carbon stocks