arXiv subjects

Fernando A. Morales

Publications and source records attributed to Fernando A. Morales.

4 recordsLinked to original sources

arXiv2022

A Mathematical Assessment of the Isolation Tree Method for Outliers Detection in Big Data

In this paper, the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection is presented. We show that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved using the Law of Large Numbers. A couple of counterexamples are presented to show that the original method is inconclusive and no quality certificate can be given, when using it as a means to detect anomalies. Hence, an alternative version of IRF is proposed, whose mathematical foundation, as well as its limitations, are fully justified. Finally, numerical experiments are presented to compare the performance of the classic IRF with the proposed one.

stat.ME↗

arXiv2020

The RaPID-OMEGA system: Room and Proctor Intelligent Decider for large scale tests programming

We present the mathematical modeling for the problem of choosing rooms and proctoring crews for massive tests, together with its implementation as the open-box system RaPID-Omega. The mathematical model is a binary integer programming problem: a combination of the 0-1 Knapsack problem and the job-assignment problem. The model makes decisions according the following criteria in order of priority: minimization of labor-hours, maximization of equity in the distribution of duties and maximization of the proctoring quality. The software is a digital solution for the aforementioned problem, which is a common need in educational institutions offering large, coordinated, lower-division courses. The system can be downloaded from \url{https://sites.google.com/a/unal.edu.co/fernando-a-morales-j/home/research/software}

cs.MS↗

arXiv2016

Diffusion Processes Homogenization for Scale-Free Metric Networks

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal singularities in the global system which, together with the high complexity of large networks constitute significant difficulties in the direct analysis of the problem. At the same time, these facts also suggest homogenization as a viable approach for modeling the global behavior of the problem. To that end, we study the asymptotic behavior of a sequence of boundary problems defined on a nested collection of metric graphs. This paper presents the weak variational formulation of the problems, the convergence analysis of the solutions and some numerical experiments.

math.AP↗

arXiv2013

On the Homogenization of Geological Fissured Systems With Curved non-periodic Cracks

We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(ε)$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and setting coefficients of low resistance $\mathcal{O}(ε)$ on the network. The singularities are removed performing asymptotic analysis as $ε\rightarrow 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.

math.AP↗