J. M. Calabuig

• Polytechnic University of Valencia

After reviewing various notions of symmetry in graph theory, which are typically defined by the connections between vertices, we demonstrate that traditional concepts of symmetry, such as vertex transitivity, can be too restrictive for certain applications. For instance, in some areas of graph analysis, symmetry based on metric properties (such as...

In this paper we develop a mathematical model combined with machine learning techniques to predict shade-seeking behavior in cows exposed to heat stress. The approach integrates advanced mathematical features, such as time-averaged thermal indices and accumulated heat stress metrics, obtained by mathematical analysis of data from a farm in Titaguas...

Performance analysis, utilizing video technology and recent technological advancements in soccer stadiums, provides a wealth of data, including player trajectories and real-time game statistics, which are crucial for tactical evaluation and decision-making by coaches and players. These data allow for the definition of metrics that not only enrich t...

Performance analysis, utilizing video technology and recent technological advancements in soccer stadiums, provides a wealth of data, including player trajectories and real-time game statistics, which are crucial for tactical evaluation and decision-making by coaches and players. This data allows for the definition of metrics that not only enriches...

Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lattices. Motivated by certain procedures in Reinforce...

Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in...

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the s...

We analyse and characterise the notion of lattice Lipschitz operator (a class of superposition operators, diagonal Lipschitz maps) when defined between Banach function spaces. After showing some general results, we restrict our attention to the case of those Lipschitz operators which are representable by pointwise composition with a strongly measur...

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample...

Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the n-dimensional case, such a map can be represented as a vector of size n of real-valued functions of one variable. In this paper we develop a method to approximate almost diagonal ma...

The objective of this study is to build a mathematical model that predicts the success of a goal kick in soccer. The model is based on an ensemble of neural networks whose inputs are five features extracted directly from the goal kick and one more that depends on the opposing team. This new variable is calculated using a hierarchical cluster analys...

Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the $n-$dimensional case, such a map can be represented as a vector of size $n$ of real-valued functions of one variable. In this paper we develop a method to approximate almost diagona...

This work is inspired by some recent developments on the extension of Lipschitz real functions based on the minimization of the maximum value of the slopes of a reference set for this function. We propose a new method in which an integral p–average is optimized instead of its maximum value. We show that this is a particular case of a more general t...

We present a new class of Lipschitz operators on Euclidean lattices that we call lattice Lipschitz maps, and we prove that the associated McShane and Whitney formulas provide the same extension result that holds for the real valued case. Essentially, these maps satisfy a (vector-valued) Lipschitz inequality involving the order of the lattice, with...

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means,...

Here, we prove some general results that allow us to ensure that specific representations (as well as extensions) of certain Lipschitz operators exist, provided we have some additional information about the underlying space, in the context of what we call enriched metric spaces. In this conceptual framework, we introduce some new classes of Lipschi...

A new model for the control of financial processes based on metric graphs is presented. Our motivation has its roots in the current interest in finding effective algorithms to detect and classify relations among elements of a social network. For example, the analysis of a set of companies working for a given public administration or other figures i...

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 no...

One of the main challenges posed by the healthcare crisis generated by COVID-19 is to avoid hospital collapse. The occupation of hospital beds by patients diagnosed by COVID-19 implies the diversion or suspension of their use for other specialities. Therefore, it is useful to have information that allows efficient management of future hospital occu...

We provide a new separation-based proof of the domination theorem for (q, 1)-summing operators. This result gives the celebrated factorization theorem of Pisier for (q, 1)-summing operators acting in C(K)-spaces. As far as we know, none of the known versions of the proof uses the separation argument presented here, which is essentially the same tha...

p class="p1">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 matemá...

Gobierno abierto y acceso a la información: un estudio de caso sobre el impacto en la economía local.

We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curve P of the virus. Together with the function of the newly infected individuals I, this model allows us to predict the evolution of the resulting epidemic process in terms of the number E of the death patients plus individuals who have overc...

One of the problems when working with data is the lack of uniformity in the criteria for their collection, which makes their reuse difficult if not impossible. Data collection and standardization protocols must be clear. This problem has been seen in the global pandemic caused by Covid-19, in which uniform data have been urgently needed to make rap...

Countries are recording health information on the global spread of COVID-19 using different methods, sometimes changing the rules after a few days. They are all publishing the number of new individuals infected, cured and dead, along with some supplementary data. These figures are often recorded in a non-uniform manner and do not match the standard...

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...

Let (Ω,Σ,μ) be a finite measure space and consider a Banach function space Y(μ). We say that a Banach space E is representable by Y(μ) if there is a continuous bijection I:Y(μ)→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 re...

Let [Formula: see text] be a finite measure space and consider a Banach function space [Formula: see text]. Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Köthe–Bochner (vector-valued) function spaces. We analyze operator-valued kernels [For...

Using some representation results for Köthe–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 ex...

Given \(\sigma \)-finite measure spaces \((\Omega _1,\Sigma _1, \mu _1)\) and \((\Omega _2,\Sigma _2,\mu _2)\), we consider Banach spaces \(X_1(\mu _1)\) and \(X_2(\mu _2)\), consisting of \(L^0 (\mu _1)\) and \(L^0 (\mu _2)\) measurable functions respectively, and study when the completion of the simple tensors in the projective tensor product \(X...

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 hel...

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...

Given a set $\Omega$ and a proximity function $\phi: \Omega \times \Omega \to \mathbb R^+$, we define a new metric for $\Omega$ by considering a path distance in $\Omega$, that is considered as a complete graph. We analyze the properties of such a distance, and several procedures for defining the initial proximity matrix $( \phi(a,b) )_{(a,b) \in \...

We extend the notions of p-convexity and p-concavity for Banach ideals of measurable functions following an asymptotic procedure. We prove a representation theorem for the spaces satisfying both properties as the one that works for the classical case: each almost p-convex and almost p-concave space is order isomorphic to an almost-L p -space. The c...

Given a finite measure space $(\Omega,\Sigma,\mu)$, we show that any Banach space $X(\mu)$ consisting of (equivalence classes of) real measurable functions defined on $\Omega$ such that $f \chi_A \in X(\mu) $ and $ \|f \chi_A \| \leq \|f\|, \, f \in X(\mu), \ A \in \Sigma$, and having the subsequence property, is in fact an ideal of measurable func...

Se presentan nociones básicas sobre indicadores que muestran un cambio de modelo económico productivo desarrollado durante los cuatro años que dura un gobierno. Seguidamente se presentan las características (fuentes, tecnología utilizada) del prototipo de portal indicaME (acrónimo de “indicadores de modelo económico”), creado para la visualización...

We study bilinear operators acting on a product of Hilbert spaces of integrable functions—zero-valued for couples of functions whose convolution equals zero—that we call convolution-continuous bilinear maps. We prove a factorization theorem for them, showing that they factor through ℓ1. We also present some applications for the case when the range...

Let $(\Omega,\Sigma,\mu)$ be a complete probability space, $X$ a Banach space and $1\leq p<\infty$. In this paper we discuss several aspects of $p$-Dunford integrable functions $f:\Omega \to X$. Special attention is paid to the compactness of the Dunford operator of $f$. We also study the $p$-Bochner integrability of the composition $u\circ f:\Omeg...

Let $(\Omega,\Sigma,\mu)$ be a complete probability space, $X$ a Banach space and $1\leq p<\infty$. In this paper we discuss several aspects of $p$-Dunford integrable functions $f:\Omega \to X$. Special attention is paid to the compactness of the Dunford operator of $f$. We also study the $p$-Bochner integrability of the composition $u\circ f:\Omeg...

We analyze domination properties and factorization of operators in Banach spaces through subspaces of $L^{1}$ -spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of $L^{1}$ -spaces of finite measures. Some special cases inv...

We study the properties of Gâteaux, Fréchet, uniformly Fréchet and uniformly Gâteaux smoothness of the space \(L^p(m)\) of scalar p-integrable functions with respect to a positive vector measure m with values in a Banach lattice. Applications in the setting of the Bishop–Phelps–Bollobás property (both for operators and bilinear forms) are also give...

A mathematical structure for defining multi-valued bibliometric indices is provided with the aim of measuring the impact of general sources of information others than articles and journals—for example, repositories of datasets. The aim of the model is to use several scalar indices at the same time for giving a measure of the impact of a given sourc...

We show a picture of the relations among different types of summability of series in the space of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so-called m-1-summing operators. We give several applications regarding the existence of copies of c0 in , as well...

Compactness type properties for operators acting in Banach function spaces are not always preserved when the operator is extended to a bigger space. Moreover, it is known that there exists a maximal (weakly) compact linear extension of a (weakly) compact operator if and only if its maximal continuous linear extension to its optimal domain is (weakl...

El objetivo de este trabajo es mostrar cómo la modelización se puede integrar a todos los niveles del sistema educativo, desde primaria hasta la educación superior. A partir de las experiencias descritas, se puede deducir que la modelización puede entenderse de forma dual como herramienta para el aprendizaje de contenidos matemáticos o como un obje...

En este trabajo presentamos una propuesta entorno a cómo se puede utilizar la Descomposición en valores singulares de una matriz para desarrollar un temario de una asignatura de Álgebra lineal en un grado de ingeniería. Para ello introducimos algunas técnicas especiales, resultados y ejemplos.

We provide a tensor product representation of Köthe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Köthe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of th...

In this paper we provide two representation theorems for two relevant classes of operators from any p-convex order continuous Banach lattice with weak unit into a Banach space: the class of continuous operators and the class of cone absolutely summing operators. We prove that they can be characterized as spaces of vector measures with finite p-semi...

We consider the problem of extending or factorizing a bounded bilinear map defined on a couple of order continuous Banach function spaces to its optimal domain, i.e. the biggest couple of Banach function spaces to which the bilinear map can be extended. As in the case of linear operators, we use vector measure techniques to find this space, and we...

We study some Banach lattice properties of the space [TEX equation: L_w^1(\nu )] of weakly integrable functions with respect to a vector measure [TEX equation: \nu ] defined on a [TEX equation: \delta ] -ring. Namely, we analyze order continuity, order density and Fatou type properties. We will see that the behavior of [TEX equation: L_w^1(\nu )] d...

We investigate natural sufficient conditions for a space \(L^p(m)\) of \(p\) -integrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth...

We study compactness and related topological properties in the space L1(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norm...

Let $X(\mu )$ be a p-convex ( $1\le p<\infty $ ) order continuous Banach function space over a positive finite measure $\mu $ . We characterize the subspaces of $X(\mu )$ which can be found simultaneously in $X(\mu )$ and a suitable $L^1(\eta )$ space, where $\eta $ is a positive finite measure related to the representation of $X(\mu...

In this paper we present three examples that can be used to motivate and introduce classical notions of a course of Linear Algebra (and its connection with other subjects such as Probability and Computing) in an Engineering degree. More specifically in this article we shown how the use of Linear algebra allows us to study odds and winning strategie...

Let ν be a countably additive vector measure defined on the Borel subsets of a compact Hausdorff abelian group G. In this paper we define and study a vector valued Fourier transform and a vector valued convolution for functions which are (weakly) integrable with respect to ν. A form of the Riemann Lebesgue Lemma and a Uniqueness Theorem are estab...

We study the lattice properties of the Banach lattices L p (ν) and L w p (ν) of p-integrable real-valued functions and weakly p-integrable real-valued functions with respect to a vector measure ν defined on a δ-ring. The relation between these two spaces, the study of the continuity and some kind of compactness properties of certain multiplication...

Let m be a vector measure taking values in a Banach space X. We prove that if the integration operator Im : L1(m) → X, Im(f) = R f dm, is completely continuous and X is Asplund, then m has finite variation and L1(m) = L1(|m|).

Let X(μ) be a Banach function space. In this paper we introduce two new geometric notions, q-convexity and weak q-convexity associated to a subset S of the unit ball of the dual of X(μ), 1 ≤ q < ∞. We prove that in the general case both notions are not equivalent and we study the relation between them, showing that they can be used for describing t...

Let m be a Banach space valued measure. We study some domina-tion properties of the integration operator that are equivalent to the existence of Banach ideals of L 1 (m) that are interpolation spaces. These domination properties are closely connected with some interpolated versions of summing operators, like (p, θ)-absolutely continuous operators.

Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe–Bochner space E(X) is a multiplication operator (by a function in L∞(μ)) if and only if the equality T(g〈f,x∗〉x)=g〈T(f),x∗〉x holds for every g∈L∞(μ), f∈E(X), x∈X and x∗∈X∗.

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spa...

In general, Banach space-valued Riemann integrable functions defined on [0, 1] (equipped with the Lebesgue measure) need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this...

Geometric and summability properties of the integration operator associated to a vector measure m can be translated in terms of structure properties of the space L 1(m). In this paper we study the cases of the integration operator being: (i) p-concave on L p (m), or (ii) positive p-summing on L 1(m) (where \(1 \leq p < \infty\)). We prove that (i)...

Several results about convolution and about Fourier coefficients for X-valued functions defined on the torus satisfying the condition sup‖y‖=1 ∫−π π ‖ B(f(eiϑ ), y)‖dϑ/2π < ∞ for a bounded bilinear map B: X × Y → Z are presented and some applications are given.

The Silences of the Archives, the Reknown of the Story. The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, befor...

Let m, n be a couple of vector measures with values on a Banach space. We develop a sepa-ration argument which provides a characterization of when the Radon–Nikodým derivative of n with respect to m—in the sense of the Bartle–Dunford–Schwartz integral—exists and belongs to a particular sublattice Z (μ) of the space of integrable functions L 1 (m)....

We introduce the spaces Vp(X) (respectively p(X)) of the vector measures :Σ→X of bounded (p,)-variation (respectively of bounded (p,)-semivariation) with respect to a bounded bilinear map :X×Y →Z and show that the spaces Lp(X) consisting of functions which are p-integrable with respect to , defined in by Blasco and Calabuig [‘Vector-valued function...

Let (Ω, Σ, μ) be a σ-finite measure space, 1 ≤ p < ∞, X be a Banach space X and B: X × Y → Z be a bounded bilinear map. We say t∫at an X-valued function f is p-integrable with respect to B whenever sup{∫Ω ∥B(f(w), y)∥pdμ: ∥y∥ = 1} is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from Hölder's and Y...

Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY...

Let ( , ,µ) be a finite measure space, 1 p < 1, X be a Banach space X and u : X ◊Y ! Z be a bounded bilinear map. We say that an X-valued function f is p-integrable with respect to u whenever supkyk=1 ku(f(w),y)kpdµ < 1. We get an analogue to Holder's inequality in this setting.

In this paper, we characterize the space of multiplication operators from an L p -space into a space L 1(m) of integrable functions with respect to a vector measure m, as the subspace L1p,m(m)L^1_{{\rm p},\mu}({\bf m}) defined by the functions that have finite p-semivariation. We prove several results concerning the Banach lattice structure of suc...

It is shown that $Z$ does not contain a copy of $c_0$ if and only if for every bilinear map $B:X\times Y\to Z$, every function $f:[0,1]\to X$ of bounded $({\cal B})$-variation is $({\cal B})$-regulated.