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[EN] Artificial intelligence is present in the usual environment of all high school students. However, the general population—and students in particular—do not know how these algorithmic techniques work, which often have very simple mechanisms and can be explained at an elementary level in mathematics or technology classes in the Secondary Education. Possibly these contents will take many years to form part of the curricula of these subjects, but they can be introduced as part of the algebra contents that are explained in mathematics, or those related to the algorithms, in the computer lectures. Especially if they are proposed in the form of a game, in which different groups of students can compete, as we propose in this article. Thus, we present a very simple example of an algorithm of teaching of reinforcement (Machine Learning-Reinforcement Learning), that synthesizes in a playful activity the fundamental elements that constitute an algorithm of artificial intelligence., [ES] La inteligencia artificial está presente en el entorno habitual de todos los estudiantes de secundaria. Sin embargo, la población general -y los alumnos en particular- no conocen cómo funcionan estas técnicas algorítmicas, que muchas veces tienen mecanismos muy sencillos y que pueden explicarse a nivel elemental en las clases de matemáticas o de tecnología en los Institutos de Enseñanza Secundaria (IES). Posiblemente estos contenidos tardarán muchos años en formar parte de los currículos de estas asignaturas, pero se pueden introducir como parte de los contenidos de álgebra que se explican en matemáticas, o de los relacionados con los algoritmos, en las clases de informática. Sobre todo si se plantean en forma de juego, en los que pueden competir diferentes grupos de estudiantes, tal y como proponemos en este artículo. Así, presentamos un ejemplo muy simple de un algoritmo de aprendizaje por refuerzo (Machine Learning-Reinforcement Learning), que sintetiza en una actividad lúdica los elementos fundamentales que constituyen un algoritmo de inteligencia artificial.

[EN] We present a McShane-Whitney extension theorem for real-valued fuzzy Lipschitz maps defined between fuzzy metric spaces. Motivated by the potential applications of the obtained results, we generalize the mathematical theory of extensions of Lipschitz maps to the fuzzy context. We develop the problem in its full generality, explaining the similarities and differences with the classical case of extensions on metric spaces.

[EN] A new stochastic approach is presented to understand general spectral type problems for (not necessarily linear) functions between topological spaces. In order to show its potential applications, we construct the theory for the case of bilinear forms acting in couples of a Banach space and its dual. Our method consists of using integral representations of bilinear maps that satisfy particular domination properties, which is shown to be equivalent to having a certain spectral structure. Thus, we develop a measure-based technique for the characterization of bilinear operators having a spectral representation, introducing the notion of eigenmeasure, which will become the central tool of our formalism. Specific applications are provided for operators between finite and infinite dimensional linear spaces.

[EN] Using some representation results for Kothe-Bochner spaces of vector valued functions by means of vector measures, we analyze the maximal extension for some classes of linear operators acting in these spaces. A factorization result is provided, and a specific representation of the biggest vector valued function space to which the operator can be extended is given. Thus, we present a generalization of the optimal domain theorem for some types of operators on Banach function spaces involving domination inequalities and compactness. In particular, we show that an operator acting in Bochner spaces of p-integrable functions for any 1

[EN] Countries are recording health information on the global spread of COVID-19 using different methods, sometimes changing the rules after a few days. All of them are publishing the number of new individuals infected, recovered and dead individuals, along with some supplementary material. These data are often recorded in a non-uniform manner and do not conform the standard definitions of these variables. In this paper we show that, using data from the first wave of the epidemic (February-June), Kaplan-Meier curves calculated with them could provide useful information on the dynamics of the disease in different countries. We developed our scheme based on the cumulative total number of infected, recovered and dead individuals provided by the countries. We present a robust and simple model to show certain characteristics of the evolution of the dynamic process, showing that the differences in evolution between countries are reflected in the corresponding Kaplan-Meier-type curves. We compare the curves obtained for the most affected countries at that time, with the corresponding interpretation of the properties that distinguish them. The model is revealed as a practical tool for countries in the management of the Healthcare System.

Using the representation of the real interpolation of spaces of p-integrable functions with respect to a vector measure, we show new factorization theorems for p th power factorable operators acting in interpolation couples of Banach function spaces. The recently introduced Lorentz spaces of the semivariation of vector mea sures play a central role in the resulting factorization theorems. We apply our results to analyze extension of operators from classical weighted Lebesgue L p -spaces — in general with different weights — that can be extended to their q-th powers. This is the case, for example, of the convolution operators defined by L p -improving mea-sures acting in Lebesgue L p -spaces or Lorentz spaces. A new representation theorem for Banach lattices with a special lattice geometric property, as a space of vector measure integrable functions, is also proved.

This is the peer reviewed version of the following article: Manzano, A, Rueda, P, Sánchez-Pérez, EA. Closed injective ideals of multilinear operators, related measures and interpolation. Mathematische Nachrichten. 2020; 293: 510-532, which has been published in final form at https://doi.org/10.1002/mana.201800415. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving., [EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.

[EN] We consider a quasi-metric topological structure for the construction of a new reinforcement learning model in the framework of financial markets. It is based on a Lipschitz type extension of reward functions defined in metric spaces. Specifically, the McShane and Whitney extensions are considered for a reward function which is defined by the total evaluation of the benefits produced by the investment decision at a given time. We define the metric as a linear combination of a Euclidean distance and an angular metric component. All information about the evolution of the system from the beginning of the time interval is used to support the extension of the reward function, but in addition this data set is enriched by adding some artificially produced states. Thus, the main novelty of our method is the way we produce more states-which we call "dreams"-to enrich learning. Using some known states of the dynamical system that represents the evolution of the financial market, we use our technique to simulate new states by interpolating real states and introducing some random variables. These new states are used to feed a learning algorithm designed to improve the investment strategy by following a typical reinforcement learning scheme. (C) 2020 Elsevier B.V. All rights reserved.

[EN] Using the representation of the real interpolation of spaces of p-integrable functions with respect to a vector measure, we show new factorization theorems for p-th power factorable operators acting in interpolation couples of Banach function spaces. The recently introduced Lorentz spaces of the semivariation of vector measures play a central role in the resulting factorization theorems. We apply our results to analyze extension of operators from classical weighted Lebesgue Lp-spaces ¿ in general with di¿erent weights ¿ that can be extended to their q-th powers. This is the case, for example, of the convolution operators defined by Lp-improving measures acting in Lebesgue Lp-spaces or Lorentz spaces. A new representation theorem for Banach lattices with a special lattice geometric property, as a space of vector measure integrable functions, is also proved.

[EN] Let (Omega,sigma,mu) be a finite measure space and consider a Banach function space Y(mu). We say that a Banach space E is representable by Y(mu) if there is a continuous bijection I:Y(mu)-> E. In this case, it is possible to define an order and, consequently, a lattice structure for E in such a way that we can identify it as a Banach function space, at least regarding some local properties. General and concrete applications are shown, including the study of the notion of the pth power of a Banach space, the characterization of spaces of operators that are isomorphic to Banach lattices of multiplication operators, and the representation of certain spaces of homogeneous polynomials on Banach spaces as operators acting in function spaces.

[EN] University rankings are now relevant decision-making tools for both institutional and private purposes in the management of higher education and research. However, they are often computed only for a small set of institutions using some sophisticated parameters. In this paper we present a new and simple algorithm to calculate an approximation of these indices using some standard bibliometric variables, such as the number of citations from the scientific output of universities and the number of articles per quartile. To show our technique, some results for the ARWU index are presented. From a technical point of view, our technique, which follows a standard machine learning scheme, is based on the interpolation of two classical extrapolation formulas for Lipschitz functions defined in metric spaces-the so-called McShane and Whitney formulae-. In the model, the elements of the metric space are the universities, the distances are measured using some data that can be extracted from the Incites database, and the Lipschitz function is the ARWU index.

[EN] We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context of the generalized Orlicz spaces associated to an N-function Phi and a (quasi-) Banach function space X over a positive finite measure mu. We show that the Orlicz and the Luxemburg spaces do not coincide in general, and also that under mild requirements (sigma-Fatou property, strictly monotone renorming) the coincidence holds. We use as a technical tool the classes L-omega(Phi)(m), L-Phi(m) and L-Phi(parallel to m parallel to) of Orlicz spaces of scalar integrable functions with respect to a Banachspace-valued countably additive vector measure m, providing also some new results on these spaces. (C) 2020 Elsevier Inc. All rights reserved.

[EN] Comments and information appearing on the internet and on different social media sway opinion concerning potential remedies for diagnosing and curing diseases. In many cases, this has an impact on citizens' health and affects medical professionals, who find themselves having to defend their diagnoses as well as the treatments they propose against ill-informed patients. The propagation of these opinions follows the same pattern as the dissemination of fake news about other important topics, such as the environment, via social media networks, which we use as a testing ground for checking our procedure. In this article, we present an algorithm to analyse the behaviour of users of Twitter, the most important social network with respect to this issue, as well as a dynamic knowledge graph construction method based on information gathered from Twitter and other open data sources such as web pages. To show our methodology, we present a concrete example of how the associated graph structure of the tweets related to World Environment Day 2019 is used to develop a heuristic analysis of the validity of the information. The proposed analytical scheme is based on the interaction between the computer tool-a database implemented with Neo4j-and the analyst, who must ask the right questions to the tool, allowing to follow the line of any doubtful data. We also show how this method can be used. We also present some methodological guidelines on how our system could allow, in the future, an automation of the procedures for the construction of an autonomous algorithm for the detection of false news on the internet related to health.

[ES] El objetivo de la investigación es presentar un procedimiento que permita conocer el desarrollo económico y social de una entidad local a partir de iniciativas de gobierno abierto y apertura de la información. Se propone una metodología que facilite esta acción mediante la incorporación de plataformas analíticas a disposición del ciudadano. Para mostrar la aplicación de esta metodología, se explica la creación de la plataforma COMUNDA, que utiliza datos disponibles del Ayuntamiento de la Pobla de Vallbona (Valencia) sobre los gastos municipales para analizar aspectos de la contratación pública. Estos instrumentos de segundo nivel, creados a partir de datos publicados por los ayuntamientos, pueden constituir herramientas analíticas para detectar irregularidades y para publicitar el tejido empresarial del municipio que pueden permitir a los ayuntamientos articular políticas adecuadas, ya las empresas y los particulares conocer mejor las características socioeconómicas de la población. Se ha comprobado la utilidad del protocolo de actuación y análisis propuesto, extrapolable a otros casos, sobre el caso concreto de la plataforma citada. En este caso, la métrica MELODA da una calificación de 48,3% de calidad en la reutilización y se ha podido comprobar que la utilización de nuestro procedimiento constata un incremento de la contratación pública en el municipio en el año 2011, uno de los peores años de la crisis económica, y que la contratación a empresas externas al municipio es de dos a tres millones de euros superior a la contratación local., [Otros] L'objectiu de la investigació és presentar un procediment que permeti conèixer el desenvolupament econòmic i social d'una entitat local a partir d'iniciatives de govern obert i obertura de la informació. Es proposa una metodologia que faciliti aquesta acció mitjançant la incorporació de plataformes analítiques a disposició del ciutadà. Per mostrar l'aplicació d'aquesta metodologia, s'explica la creació de la plataforma COMUNDA, que utilitza dades disponibles de l'Ajuntament de la Pobla de Vallbona (València) sobre les despeses municipals per analitzar aspectes de la contractació pública. Aquests instruments de segon nivell, creats a partir de dades publicades pels ajuntaments, poden constituir eines analítiques per detectar irregularitats i per publicitar el teixit empresarial del municipi que poden permetre als ajuntaments articular polítiques adequades, i a les empreses i als particulars conèixer millor les característiques socioeconòmiques de la població. S'ha comprovat la utilitat del protocol d'actuació i anàlisi proposat, extrapolable a altres casos, sobre el cas concret de la plataforma citada. En aquest cas, la mètrica MELODA dona una qualificació de 48,3% de qualitat en la reutilització i s'ha pogut comprovar que la utilització del nostre procediment constata un increment de la contractació pública al municipi l'any 2011, un dels pitjors anys de la crisi econòmica, i que la contractació a empreses externes al municipi és de dos a tres milions d'euros superior a la contractació local., [EN] This study describes a procedure that can trackthe economic and social development of a local government body, based on open government initiatives and openness of information. A methodology is proposed that incorporates analytical platforms available to the general public. To illustrateits application, the creation of the COMUNDA platform is described. The COMUNDA platform uses data provided from the Town Council of La Pobla de Vallbona (Valencia) on municipal spending in order to analyse aspects of public procurement. These second-level instruments, created from data published by the councils, can be useful analytical tools for detecting irregularities and for focusing attention on the business fabric of the municipality. The information obtained can help councils to design appropriate policies and help companies and individuals to understand the socioeconomic characteristics of the population. The article confirms the usefulness of the action and analysis protocolproposed for the platform mentioned, and the results suggest that it can be extrapolated to other scenarios. In this case, the MELODA metric gives a data reusabilityrating of 48.3%. Our procedure shows an increase in public procurement in the municipality in 2011, one of the worst years of the economic crisis, and also finds that outsourcing to external companies in the municipality accounts for 2 to 3 million € more than local contracting.

"This is the peer reviewed version of the following article: Peset, F, F Garzón-Farinós, LM González, X García-Massó, A Ferrer-Sapena, JL Toca-Herrera, and EA Sánchez-Pérez. 2019. "Survival Analysis of Author Keywords: An Application to the Library and Information Sciences Area." Journal of the Association for Information Science and Technology 71 (4). Wiley: 462-73. doi:10.1002/asi.24248, which has been published in final form at https://doi.org/10.1002/asi.24248. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.", [EN] Our purpose is to adapt a statistical method for the analysis of discrete numerical series to the keywords appearing in scientific articles of a given area. As an example, we apply our methodological approach to the study of the keywords in the Library and Information Sciences (LIS) area. Our objective is to detect the new author keywords that appear in a fixed knowledge area in the period of 1 year in order to quantify the probabilities of survival for 10 years as a function of the impact of the journals where they appeared. Many of the new keywords appearing in the LIS field are ephemeral. Actually, more than half are never used again. In general, the terms most commonly used in the LIS area come from other areas. The average survival time of these keywords is approximately 3 years, being slightly higher in the case of words that were published in journals classified in the second quartile of the area. We believe that measuring the appearance and disappearance of terms will allow understanding some relevant aspects of the evolution of a discipline, providing in this way a new bibliometric approach.

[EN] Two new classes of summing multilinear operators, factorable (q,p)-summing operators and (r;p,q)-summing operators are studied. These classes are described in terms of factorization. It is shown that operators in the first (resp., the second) class admit the factorization through the injective tensor product of Banach spaces (resp., through some Banach lattices). Applications in different contexts related to Grothendieck Theorem and Fourier integral bilinear operators are shown. Motivated by Pisier¿s Theorem on factorization of (q,1)-summing operators from C(K)-spaces through Lorentz spaces Lq,1 on some probability Borel measure spaces, we prove two variants of Pisier¿s Theorem for bilinear operators on the product of C(K)-spaces. We also prove bilinear versions of Mityagin¿Pe¿czy¿ski and Kislyakov Theorems.

[EN] Let (X, Sigma, mu) be a finite measure space and consider a Banach function space Y(mu). Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Kothe Bochner (vectorvalued) function spaces. We analyze operator-valued kernels Gamma that define integration maps L-Gamma between Kothe-Bochner spaces of Hilbert-valued functions Y(mu; kappa). We show a reduction procedure which allows to find a factorization of the corresponding kernel operator through weighted Bochner spaces L-P(gd mu; kappa) and L-P (hd mu; kappa) - where 1/p + 1/p' = 1 - under the assumption of p-concavity of Y(mu). Equivalently, a new kernel obtained by multiplying Gamma by scalar functions can be given in such a way that the kernel operator is defined from L-P (mu; kappa) to L-P (mu; kappa) in a natural way. As an application, we prove a new version of Mercer Theorem for matrix-valued weighted kernels.

[EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of ¿kDk is fulfilled by f. In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a p-power domination, we say that the elements of Dk are p-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz p-concave real valued maps.

[EN] We present a constructive technique to represent classes of bilinear operators that allow a factorization through a bilinear product, providing a general version of the well-known characterization of integral bilinear forms as elements of the dual of an injective tensor product. We show that this general method fits with several known situations coming from different contexts-harmonic analysis, C*-algebras, C(K)-spaces, operator theory, polynomials-, providing a unified approach to the integral representation of a broad class of bilinear operators. Some examples and applications are also shown, regarding for example operator spaces and summability properties of bilinear maps. (C) 2019 Elsevier Inc. All rights reserved.

[EN] We explore the connection between p-regular operators on Banach function spaces and weighted p-estimates. In particular, our results focus on the following problem. Given finite measure spaces mu and nu, let T be an operator defined from a Banach function space X(nu) and taking values on L-p(vd mu) for v in certain family of weights V subset of L-1(mu)+ we analyze the existence of a bounded family of weights W subset of L-1(nu)+ such that for every v is an element of V there is w is an element of W in such a way that T : L-p(wd nu) -> L-p (vd mu) is continuous uniformly on V. A condition for the existence of such a family is given in terms of p-regularity of the integration map associated to a certain vector measure induced by the operator T.

[EN] Choosing a journal to publish a work is a task that involves many variables. Usually, the authors' experience allows them to classify journals into categories, according to their suitability and the characteristics of the article. However, there are certain aspects in the choice that are probabilistic in nature, whose modelling may provide some help. Suppose an author has to choose a journal from a preference list to publish an article. The researcher is interested in publishing the paper in a journal with a rank number less than or equal to k. For this purpose, a simple classification model is presented in order to choose the best journal from the list, from which some fundamental consequences can be deduced and simple rules derived. For example, if the list contains 100 journals and is ordered using 2-year impact factor, the rule "send to the journal at the k - 10 position" is adequate.

[EN] We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curvePof the virus. Together with the function of the newly infected individualsI, this model allows us to predict the evolution of the resulting epidemic process in terms of the numberEof the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation ofEas the convolution ofIandP. It allows introducing information about latent patients-patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation ofPusing real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model.