Research Lines
Research Lines
Given an algebraic structure, is there a topological space that realizes it? This is the main question of this part of my research. I have been able to answer this question positively for many algebraic structures with some of my collaborators.
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal, Topological realization of groups in Alexandroff spaces. Rev. R. Acad. Cien. Serie A. Mat., 115(25). 2021. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal, On some topological realizations of groups and homomorphisms. Trans. Amer. Math. Soc., 375(12), 8635-8649, 2022. (Link)
Pedro J. Chocano, Realization of finite groups as isometry groups and problems of minimality. Math.Nachr., 298(2):419-426, 2025 (Link)
Pedro J. Chocano, Realizing regular representations of finite groups, J. Algebra, 663: 454-467, 2025. (Link)
In this part of my research we focus on the study of dynamical systems defined on Alexandroff spaces or finite topological spaces. The aim is to develop a ''good'' notion of dynamical system within this framework, enabling us to approximate classical dynamical systems. This approach will facilitate the development of new computational methods for analyzing classical dynamics.
Pedro J. Chocano, Manuel A. Morón, D. Mondéjar & Francisco R. Ruiz del Portal, On the triviality of flows in Alexandroff spaces. Topol. Appl. 339 (Part A) 108580, 2023. (Link)
Pedro J. Chocano, On the dynamics of the combinatorial model of the real line. Dynamical Systems, 38 (3), 395-404, 2023. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal, Coincidence theorems for finite topological spaces. Topol. Method Nonl. An., 65(1): 219-263, 2025 (Link).
Pedro J. Chocano, Semiflows on finite spaces, (Link), 2024.
Pedro J. Chocano, Conley Index for Finite Spaces, (in Preparation), 2025.
This part of my research addresses problems of various natures, all strongly related to topology. Among the questions we analyze are the combinatorial description of shape theory, a generalization of homotopy for finite spaces, the reconstruction of compact metric spaces, and the study of topological properties of Riordan matrices.
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. Computational approximations of compact metric spaces. Phys. D., 433, 133168, 2022. (Link)
Pedro J. Chocano, Ana Luzón, Manuel A. Morón & Luis Felipe Prieto Martínez. Characteristic curves and the exponentiation in the Riordan Lie group: A connection through examples. J . Math. Anal. Appl., 532(1), 127989, 2024. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. A category to classify compact Hausdorff spaces and finite spaces. Homol. Homotopy Appl., 27 (1), 17-28, 2025 (Link).
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. A combinatorial perspective on shape theory. J. Math. Soc. Japan, (Link), 2025.
Pedro J. Chocano. Eigenvalues and signature of quadratic forms associated to finite topological spaces, Linear Algebra Appl., (Link) 2025.
Pedro J. Chocano. A Generalization of homotopy for finite spaces, (Preprint), 2024.
Pedro J. Chocano. Matrix Invariants as Homotopy Invariants in Finite T0-spaces, (Link), 2024.
Pedro J. Chocano. From Samples to Shape: A Finite Approach to Topological Invariants, (Preprint), 2025.
Pedro J. Chocano, Ana Luzón, Manuel A. Morón & Luis Felipe Prieto-Martínez. Riordan pattern's quest within simplicial complexes, (Link), 2025.
The classical parametric approach for statistical inference is usually based on Maximum Likelihood estimation. Although it is known to lead to optimum results under true assumption of the model, is also known to be non-robust in presence of outliers. With the use of divergence measures we can define alternative estimators and procedures in diverse statistical models.
E. Castilla. & Pedro J. Chocano.. On the choice of the optimal tuning parameter in robust one-shot device testing analysis. Balakrishnan, Gil, Martín, Morales and Pardo (eds.). Trends in Mathematical, Information and Data Sciences. Studies in Systems, Decision and Control. vol 445. Springer, Cham, pp. 169-180, 2023. (Link)
E. Castilla. & Pedro J. Chocano. A new robust approach for multinomial logistic regression with complex design model. IEEE trans. Inf. Theory, 86(11), pp. 7379-7395, 2022. (Link)
E. Castilla & Pedro J. Chocano. Robust copula estimation for one-shot devices with correlated failure modes. (Link)