arXiv subjects

E. A. Sánchez-Pérez

Publications and source records attributed to E. A. Sánchez-Pérez.

7 recordsLinked to original sources

arXiv2023

On vector measures with values in $\ell_\infty$

We study some aspects of countably additive vector measures with values in $\ell_\infty$ and the Banach lattices of real-valued functions that are integrable with respect to such a vector measure. On the one hand, we prove that if $W \subseteq \ell_\infty^*$ is a total set not containing sets equivalent to the canonical basis of $\ell_1(\mathfrak{c})$, then there is a non-countably additive $\ell_\infty$-valued map $ν$ defined on a $σ$-algebra such that the composition $x^* \circ ν$ is countably additive for every $x^*\in W$. On the other hand, we show that a Banach lattice $E$ is separable whenever it admits a countable positively norming set and both $E$ and $E^*$ are order continuous. As a consequence, if $ν$ is a countably additive vector measure defined on a $σ$-algebra and taking values in a separable Banach space, then the space $L_1(ν)$ is separable whenever $L_1(ν)^*$ is order continuous.

math.FA↗

arXiv2020

Kaplan-Meier type survival curves for COVID-19: a health data based decision-making tool

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 definitions of these variables. However, in this paper we show that the Kaplan-Meier curves calculated with them could provide useful information about the dynamics of the disease in different countries. Our aim is to present a robust and simple model to show certain characteristics of the evolution of the dynamic process, showing that the differences of evolution among the countries is reflected in the corresponding Kaplan-Meier-type curves. We compare the curves obtained for the most affected countries so far, proposing possible interpretations of the properties that distinguish them.

q-bio.PE↗

arXiv2020

Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial markets

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.

q-fin.ST↗

arXiv2020

A class of summing operators acting in spaces of operators

Let $X$, $Y$ and $Z$ be Banach spaces and let $U$ be a subspace of $\mathcal{L}(X^*,Y)$, the Banach space of all operators from $X^*$ to $Y$. An operator $S: U \to Z$ is said to be $(\ell^s_p,\ell_p)$-summing (where $1\leq p <\infty$) if there is a constant $K\geq 0$ such that $$ \Big( \sum_{i=1}^n \|S(T_i)\|_Z^p \Big)^{1/p} \le K \sup_{x^* \in B_{X^*}} \Big(\sum_{i=1}^n \|T_i(x^*)\|_Y^p\Big)^{1/p} $$ for every $n\in \mathbb{N}$ and every $T_1,\dots,T_n \in U$. In this paper we study this class of operators, introduced by Blasco and Signes as a natural generalization of the $(p,Y)$-summing operators of Kislyakov. On one hand, we discuss Pietsch-type domination results for $(\ell^s_p,\ell_p)$-summing operators. In this direction, we provide a negative answer to a question raised by Blasco and Signes, and we also give new insight on a result by Botelho and Santos. On the other hand, we extend to this setting the classical theorem of Kwapień characterizing those operators which factor as $S_1\circ S_2$, where $S_2$ is absolutely $p$-summing and $S_1^*$ is absolutely $q$-summing ($1<p,q<\infty$ and $1/p+1/q \leq 1$).

math.FA↗

arXiv2019

Extension of Lipschitz-type operators on Banach function spaces

We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced.%more appropriate. Thus, we adapt the classical definition of Lipschitz map to the context of spaces of integrable functions by introducing such elements. We analyze Lipschitz type inequalities in two fundamental cases. The first concerns a.e. pointwise inequalities, while the second considers dominations involving integrals. These Lipschitz type inequalities provide the suitable frame to work with operators that take values on Banach function spaces. In the last part of the paper we use some interpolation procedures to extend our study to interpolated Banach function spaces.

math.FA↗

arXiv2019

Graph distances for determining entities relationships: a topological approach to fraud detection

Given a set $Ω$ and a proximity function $ϕ: Ω\times Ω\to \mathbb R^+$, we define a new metric for $Ω$ by considering a path distance in $Ω$, that is considered as a complete graph. We analyze the properties of such a distance, and several procedures for defining the initial proximity matrix $( ϕ(a,b) )_{(a,b) \in Ω\times Ω}.$ Our motivation has its roots in the current interest in finding effective algorithms for detecting and classifying 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 in which automatic fraud detection systems are needed. Using this formalism, we state our main idea regarding fraud detection, that is founded in the fact that fraud can be detected because it produces a meaningful local change of density in the metric space defined in this way.

cs.SI↗

arXiv2016

On $p$-Dunford integrable functions with values in Banach spaces

Let $(Ω,Σ,μ)$ 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 $f:Ω\to X$. Special attention is paid to the compactness of the Dunford operator of $f$. We also study the $p$-Bochner integrability of the composition $u\circ f:Ω\to Y$, where $u$ is a $p$-summing operator from $X$ to another Banach space $Y$. Finally, we also provide some tests of $p$-Dunford integrability by using $w^*$-thick subsets of $X^*$.

math.FA↗