On Gruenhage spaces, separating σ-isolated families, and their relatives

We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage.This work has been partially supported by the Generalitat Valenciana project GV/2014/072 and Universidad de Alicante project GRE11-08

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.Research partially supported by the University of Alicante, project GRE11-08

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.This work has been partially supported by the Generalitat Valenciana project GV/2014/072 and Universidad de Alicante project GRE11-08

On dentability and cones with a large dual

In this paper we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone C if and only if it is a point of continuity for such a cone and C∗ − C∗ = X∗; x is a denting point of a convex set A if and only if x is a point of continuity and a weakly strongly extreme point of A. We also analize how our results help us to shed some light on several open problems in the literature.M. A. Melguizo Padial has been supported by project MTM2017-86182-P (AEI/FEDER, UE). Fernando García-Castaño has been partially supported by MINECO and FEDER (MTM2014-54182), by Fundación Séneca—Región de Murcia (19275/PI/14), and by MTM2017-86182-P (AEI/FEDER, UE)

A set-valued Lagrange theorem based on a process for convex vector programming

In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base.The authors have been supported by project MTM2017-86182-P (AEI, Spain and ERDF/FEDER, EU). The author Fernando García-Castaño has also been supported by MINECO and FEDER (MTM2014-54182)

Algoritmos de planificación de robots usando fast marching

El objeto de este proyecto es conseguir que el robot LEGO NXT Mindstorm siga lo más fielmente posible una ruta que le es planificada mediante un algoritmo planificador (ya desarrollado por el Departamento de Sistemas y Automática de la Universidad Carlos III) basado en la metodología Fast Marching (marcha rápida) Para el seguimiento de la ruta por el robot vamos a necesitar por una parte un software desarrollado mediante la aplicación informática Matlab (2007b) y un sistema de relocalización mediante el cual podemos conocer con una gran precisión donde se encuentra el robot dentro del mapa que hemos cargado. El sistema de relocalización se basa en el uso del algoritmo “Differential Evolution” ya implementado en un proyecto anterior. Se trata de una especie de algoritmo genético mejorado, se parte de una población inicial en la que se introduce una perturbación (diferencia de dos vectores) y dicha perturbación se suma a un tercer vector para obtener un vector de prueba. Cada uno de los vectores correspondientes a los puntos de la población inicial, competirá con el vector de prueba que tenga su mismo índice pasando a la siguiente generación los individuos más aptos. Por cada una de las sucesivas generaciones se repetirá el proceso de introducción de perturbación, crear vector de prueba y el proceso de competición o selección de los individuos que habrán de pasar a la siguiente generación. Cuando el algoritmo ha convergido totalmente (tras el paso de sucesivas generaciones) obtenemos la solución con mejor valor de la función de Fitness o función de salud. La función del algoritmo “Differential Evolution” es obtener la mejor función de salud (Fitness) o minimizar la función de coste (Cost). En lo referente a este proyecto, el algoritmo “Differential evolution” se encarga de minimizar la diferencia entre los vectores V0 y V1, siendo V0 el vector que contiene las mediciones realizadas por el sensor de ultrasonidos del entorno que rodea al robot y V1 el vector que contiene las medidas estimadas que se obtendrían si el robot se encontrara donde nosotros creemos que está. El cuadrado de la diferencia entre V0 y V1 se denomina error cuadrático. El sistema de relocalización nos permite hacer las correcciones necesarias en la ruta para que solventando el inconveniente de la acumulación de errores en un seguimiento de ruta odométrico se llegue hasta el punto de destino convenido. __________________________________________________________________________________________________The purpose of this proyect Is to make the LEGO NXT Mindstorm robot follow as closely as possible a route that is planned by a scheduler algorithm (already developed by the Department of Systems and Automation, at Carlos III University in Madrid) based on the Fast Marching method (quick start). In order for the robot to monitor the route, we will need the following. On the one hand, we will need software developed using the Matlab IT (information Technology) application (2007b). On the other hand, we will need a relocation system to achieve the maximum precision about it’s location in the map. The relocation system is based on the use of the algorithm “Differential Evolution”. This has been already implemented in a previous draft. It is a kind of improved genetic algorithm. It starts from an initial population in which a disturbance (difference between two vectors) is introduced. This disturbance is added to a third vector in order to get a test vector. Each one of the vectors corresponding to the initial population points will compete with the test vector with the same index. The most skilled individuals will move into the next generation. When the algorithm has completely converged (after the passage of consecutive generations) we can get the best value solution of the fitness function (or health function). The function of the algorithm “Differential Evolution” is to get the best health function (Fitness) or to minimize the cost function (cost). With regard to this proyect, the algorithm “Differential Evolution” makes sure the minimization of the difference between vectors V0 and V1. Vector V0 contains the measurements of the robot environment, taken by the ultrasonic sensor. Vector V1 contains the estimated measurements if the robot were located where we think it is. The difference between V0 and V1 squared is called the quadratic error. The relocation system allows us to make the necessary corrections to the route so that it is possible to get to the agreed point of destination by solving the problem of error accumulation in an odometric route tracking.Ingeniería Técnica en Electrónic

Determinación del estado de madurez del aguacate mediante procesamiento de imágenes con la Raspberry PI

Este proyecto se basa en el procesamiento de imágenes para determinar el estado de madurez de frutas, en este caso se utilizará el aguacate, la determinación se hará mediante la captura de una imagen, de la cual se analizarán diferentes características que posee la fruta, de la cuales se tomará como principal su color promedio. Posteriormente, la clasificación se hará mediante el uso del algoritmo de máquinas de vectores de soporte (SVM) con la ayuda de la librería de OpenCV en Python y la Raspberry Pi como sistema embebido. Los sistemas de control de calidad en la industria agro tienen grandes avances gracias a las técnicas de procesamiento digital de imágenes, la idea que se permite entrar en contexto se basa en el análisis realizado sobre las capturas tomadas bajo un ambiente controlado, este se emplea para la captura de la imagen del aguacate, y analizando aspectos de la fruta como lo son la forma, tamaño y color, mostrando su estado de maduración por medio del método de visión artificial

Las sociedades ribereñas prehispánicas del Bajo Magdalena y su uso de la navegación fluvial

This article studies the origins of the way of life known as an amphibian culture on the Colombian Atlantic coast, its expression in forms of mixed subsistence associated with the indigenous tradition around the use of aquatic ecosystems and especially in the river navigation of the lower Magdalena. For this purpose, we have used documents and primary sources such as chronicles of the Indies, files from the General Archive of the Indies in Seville (AGI), archaeological field research, and compilations of historical documents on the Caribbean coast made by historians. We note that pre-Hispanic navigation was widely spread in this area since, besides the hostile terrestrial roads, nature offered fluvial paths, representing a travel alternative with significant advantages in different areas. This produced an eventual use and appropriation of this knowledge by the European colonizers of the XVI century, as in an environment where the ships and the knowledge of the western world did not seem to be enough, the canoes together with the indigenous labor force were more useful than the European ships, with disastrous consequences for a way of life that, nevertheless, still survives nowadaysEste artículo estudia los orígenes de la forma de vida denominada como cultura anfibia en la costa atlántica colombiana, su expresión en formas de subsistencia mixta asociadas con la tradición indígena en torno al aprovechamiento de los ecosistemas acuáticos y especialmente en la navegación fluvial del Bajo Magdalena. Para ello, se han consultado documentos y fuentes primarias tales como crónicas de Indias, legajos provenientes del Archivo General de Indias en Sevilla (AGI), investigaciones arqueológicas de campo y recopilaciones de documentos históricos sobre la costa Caribe realizadas por historiadores. Observamos que la navegación prehispánica se encontraba bastante extendida en esta zona, pues además de los hostiles caminos terrestres la naturaleza aquí ofrecía caminos fluviales los cuales representaron una alternativa de desplazamiento con ventajas nada desdeñables en diferentes ámbitos. Esto produjo una eventual instrumentalización de estos saberes por parte de los colonizadores europeos del siglo XVI, pues en un medio en donde las naves y los conocimientos de occidente no parecían ser suficientes, las canoas junto con la fuerza de trabajo indígena resultaron más útiles que las embarcaciones europeas, con consecuencias nefastas para una forma de vida que, sin embargo, pervive en la actualidad

Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

We show that under a separation property, a Q-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Fernando García-Castaño and Miguel Ángel Melguizo-Padial acknowledge the financial support from the Spanish Ministry of Science, Innovation and Universities (MCIN/AEI) under grant PID2021-122126NB-C32, co-funded by the European Regional Development Fund (ERDF) under the slogan “A way of making Europe”

On the Increasing Convex Order of Relative Spacings of Order Statistics

Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of the expected proportional shortfall order. As an application, we compare relative deprivation within some parametric families of income distributions