Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Sampling and learning the Mallows and Generalized Mallows models under the Cayley distance

[EN]The Mallows and Generalized Mallows models are compact yet powerful and natural ways of representing a probability distribution over the space of permutations. In this paper we deal with the problems of sampling and learning (estimating) such distributions when the metric on permutations is the Cayley distance. We propose new methods for both operations, whose performance is shown through several experiments. We also introduce novel procedures to count and randomly generate permutations at a given Cayley distance both with and without certain structural restrictions. An application in the field of biology is given to motivate the interest of this model.

An R package for permutations, Mallows and Generalized Mallows models

[EN]Probability models on permutations associate a probability value to each of the permutations on n items. This paper considers two popular probability models, the Mallows model and the Generalized Mallows model. We describe methods for making inference, sampling and learning such distributions, some of which are novel in the literature. This paper also describes operations for permutations, with special attention in those related with the Kendall and Cayley distances and the random generation of permutations. These operations are of key importance for the efficient computation of the operations on distributions. These algorithms are implemented in the associated R package. Moreover, the internal code is written in C++.

Effective and Robust Generalized Predictive Speed Control of Induction Motor

14 p.

Construcción de un modelo predictivo de tipo Gradient boosting para ventas online

En este proyecto se describirá como construir un modelo predictivo de tipo gradient boosting para predecir el número de ventas online de un producto X del cual solo sabremos su número de identificación, teniendo en cuenta las campañas publicitarias y las características tanto cualitativas y cuantitativas de éste. Para ello se utilizarán y se explicarán las diferentes técnicas utilizadas, como son: la técnica de la validación cruzada y el Blending. El objetivo del proyecto es implementar el modelo así como explicar con exactitud cada técnica y herramienta utilizada y obtener un resultado válido para la competición propuesta en Kaggle con el nombre de Online Product Sales.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Photosynthetic responses of trees in high-elevation forests: comparing evergreen species along an elevation gradient in the Central Andes

Plant growth at extremely high elevations is constrained by high daily thermal amplitude, strong solar radiation and water scarcity. These conditions are particularly harsh in the tropics, where the highest elevation treelines occur. In this environment, the maintenance of a positive carbon balance involves protecting the photosynthetic apparatus and taking advantage of any climatically favourable periods. To characterize photoprotective mechanisms at such high elevations, and particularly to address the question of whether these mechanisms are the same as those previously described in woody plants along extratropical treelines, we have studied photosynthetic responses in Polylepis tarapacana Philippi in the central Andes (18 degrees S) along an elevational gradient from 4300 to 4900 m. For comparative purposes, this gradient has been complemented with a lower elevation site (3700 m) where another Polylepis species (P. rugulosa Bitter) occurs. During the daily cycle, two periods of photosynthetic activity were observed: one during the morning when, despite low temperatures, assimilation was high; and the second starting at noon when the stomata closed because of a rise in the vapour pressure deficit and thermal dissipation is prevalent over photosynthesis. From dawn to noon there was a decrease in the content of antenna pigments (chlorophyll b and neoxanthin), together with an increase in the content of xanthophyll cycle carotenoids. These results could be caused by a reduction in the antenna size along with an increase in photoprotection. Additionally, photoprotection was enhanced by a partial overnight retention of de-epoxized xanthophylls. The unique combination of all of these mechanisms made possible the efficient use of the favourable conditions during the morning while still providing enough protection for the rest of the day. This strategy differs completely from that of extratropical mountain trees, which uncouple light-harvesting and energy-use during long periods of unfavourable, winter conditions.