BOSCH PÉREZ, PAUL JESÚS

Preferred name
BOSCH PÉREZ, PAUL JESÚS
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Email
pbosch@udd.cl
ORCID
0000-0001-5194-4173
Scopus Author ID
8630247500
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    On a generalization of the Opial inequality
    (2024)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Ana Portilla
    ;
    Jose M. Rodriguez
    ;
    Jose M. Sigarreta
    Inequalities are essential in pure and applied mathematics. In particular, Opial’s inequality and its generalizations have been playing an important role in the study of the existence and uniqueness of initial and boundary value problems. In this work, some new Opial-type inequalities are given and applied to generalized Riemann-Liouville-type integral operators.
    Scopus© Citations 5  3
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    ANALYSIS OF DENGUE FEVER OUTBREAK BY GENERALIZED FRACTIONAL DERIVATIVE
    (2020)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    J. F. GÓMEZ-AGUILAR
    ;
    JOSÉ M. RODRÍGUEZ
    ;
    JOSÉ M. SIGARRETA
    In this paper, we use the generalized fractional derivative in order to study the fractional differential equation associated with a fractional Gaussian model. Moreover, we propose new properties of generalized differential and integral operators. As a practical application, we estimate the order of the derivative of the fractional Gaussian models by solving an inverse problem involving real data on the dengue fever outbreak.
      22Scopus© Citations 18
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      20  1Scopus© Citations 7
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    Some new Milne-type inequalities
    (2024)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    ;
    Eva Tourís
      9
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    Generalized inequalities involving fractional operators of the Riemann-Liouville type
    (2021)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Héctor J. Carmenate
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    In this paper, we present a general formulation of the well-known fractional drifts of Riemann-Liouville type. We state the main properties of these integral operators. Besides, we study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving these general fractional operators.
      1Scopus© Citations 12  2
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    Mining EEG with SVM for Understanding Cognitive Underpinnings of Math Problem Solving Strategies
    (2018)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    HERRERA MARÍN, MAURICIO RENÉ  
    ;
    Julio López
    ;
    Sebastián Maldonado
    <jats:p>We have developed a new methodology for examining and extracting patterns from brain electric activity by using data mining and machine learning techniques. Data was collected from experiments focused on the study of cognitive processes that might evoke different specific strategies in the resolution of math problems. A binary classification problem was constructed using correlations and phase synchronization between different electroencephalographic channels as characteristics and, as labels or classes, the math performances of individuals participating in specially designed experiments. The proposed methodology is based on using well-established procedures of feature selection, which were used to determine a suitable brain functional network size related to math problem solving strategies and also to discover the most relevant links in this network without including noisy connections or excluding significant connections.</jats:p>
      12  1Scopus© Citations 9
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    Total Outer-Independent Domination Number: Bounds and Algorithms
    (MDPI AG, 2025-03-10)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Ernesto Parra Inza
    ;
    Ismael Rios Villamar
    ;
    José Luis Sánchez-Santiesteban
    In graph theory, the study of domination sets has garnered significant interest due to its applications in network design and analysis. Consider a graph G(V,E); a subset of its vertices is a total dominating set (TDS) if, for each x∈V(G), there exists an edge in E(G) connecting x to at least one vertex within this subset. If the subgraph induced by the vertices outside the TDS has no edges, the set is called a total outer-independent dominating set (TOIDS). The total outer-independent domination number, denoted as γtoi(G), represents the smallest cardinality of such a set. Deciding if a given graph has a TOIDS with at most r vertices is an NP-complete problem. This study introduces new lower and upper bounds for γtoi(G) and presents an exact solution approach using integer linear programming (ILP). Additionally, we develop a heuristic and a procedure to efficiently obtain minimal TOIDS.
      3
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    A New Genetic Algorithm Encoding for Coalition Structure Generation Problems
    (2020)
    Juan Pablo Contreras
    ;
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    VARAS VALDÉS, MAURICIO ANDRÉS  
    ;
    Franco Basso
    Genetic algorithms have proved to be a useful improvement heuristic for tackling several combinatorial problems, including the coalition structure generation problem. In this case, the focus lies on selecting the best partition from a discrete set. A relevant issue when designing a Genetic algorithm for coalition structure generation problems is to choose a proper genetic encoding that enables an efficient computational implementation. In this paper, we present a novel hybrid encoding, and we compare its performance against several genetic encoding proposed in the literature. We show that even in difficult instances of the coalition structure generation problem, the proposed approach is a competitive alternative to obtaining good quality solutions in reasonable computing times. Furthermore, we also show that the encoding relevance increases as the number of players increases.
    Scopus© Citations 12  1
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      10Scopus© Citations 5
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    On the Inverse Degree Polynomial
    (2019)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José Manuel Rodríguez
    ;
    Omar Rosario
    ;
    José María Sigarreta
    <jats:p>Using the symmetry property of the inverse degree index, in this paper, we obtain several mathematical relations of the inverse degree polynomial, and we show that some properties of graphs, such as the cardinality of the set of vertices and edges, or the cyclomatic number, can be deduced from their inverse degree polynomials.</jats:p>
      12