Maestría en Matemáticas Aplicadas (tesis)
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Ítem A high-performance hybrid agent-based model for simulating urban vector-borne disease transmission(Universidad EAFIT, 2024) Londoño Montoya, Luisa Fernanda; Escudero Marín, Paula Alejandra; Escudero Marín, Paula AlejandraÍtem On adequate robustness measures for the resource-constrained project scheduling problem(Universidad EAFIT, 2024) Franco Ardila, Julio César; Escudero Marín, Paula Alejandra; Rivera Agudelo, Juan Carlos; Escudero Marín, Paula Alejandra; Rivera Agudelo, Juan CarlosÍtem Colombian Monthly Energy Inflows Predictability(Revista Dyna, 2024) Hurtado Montoya, Andrés Felipe; Moreno Reyes, Nicolás Alberto; Moreno Reyes, Nicolás AlbertoÍtem Estimador Stahel-donoho con direcciones de proyección aleatoria específicas basadas en la asimetría(Universidad EAFIT, 2024) Becerra Sierra, Omar Alexis; Ortiz Arias, SantiagoÍtem The EE-Classifier : A classification method for functional data based on extremality indexes(Universidad EAFIT, 2024) Lesmes Ramírez, Catalina; Zuluaga Díaz, Francisco Iván; Laniado Rodas, HenryÍtem Completion of input images of the elastic registration process for IMRT applied to breast cancer using spline-based interpolation(Universidad EAFIT, 2024) Ríos Querubín, Mateo; Rivera, Juan Carlos; Laniado, Henry; Puerta, María EugeniaCancer is one of the leading causes of death worldwide. Radiotherapy plays a fundamental role in its treatment, but the collateral damage of the process can affect patients' quality of life. Intensity-modulated radiation therapy (IMRT) is an advanced technique that offers promising benefits, but input imaging for IMRT incurs high costs. To mitigate collateral damage and increase treatment efficacy, we propose a methodology to expand the input set for IMRT. In this study, we focused on reducing the uncertainty of the data by preprocessing the input images. By employing bootstrapping, a non-parametric statistical sampling technique, we reduce the input images to regions of interest. Interpolating this information using polynomial splines and B-splines generates intermediate images. Our findings show that both interpolation methods, specifically the degree 1 polynomial spline, effectively reduce the uncertainty of the data. The methods are tested using Pearson correlation tests and bootstrap hypothesis tests, finding them accurate. By expanding the input data set and minimizing uncertainty, our approach promises to improve treatment planning and enhance patient outcomes in radiotherapy.Ítem Genetic algorithm with a Bayesian approach for multiple change-point detection in time series of counting exceedances for specific thresholds(Universidad EAFIT, 2023) Taimal Yepes, Carlos Alberto; Suárez Sierra, Biviana MarcelaAlthough the applications of Non-Homogeneous Poisson Processes (NHPP) to model and study the threshold overshoots of interest in different time series of measurements have proven to provide good results, they needed to be complemented with an eficient and automatic diagnostic technique to establish the location of the change-points, which, when taken into account, make the estimated model it poorly in regards of the information contained in the real one. Because of this, a new method is proposed to solve the segmentation uncertainty of the time series of measurements, where the generating distribution of exceedances of a specific threshold is the focus of investigation. One of the great contributions of the present algorithm is that all the days that trespassed are candidates to be a change-point, so all the possible configurations of overflow days under the heuristics of a genetic algorithm are the possible chromosomes, which will unite to produce new solutions. Also, such methods will be guarantee to non-local and the best possible one solution, reducing wasted machine time evaluating the least likely chromosomes to be a feasible solution. The analytical evaluation technique will be by means of the Minimum Description Length (MDL) as the objective function, which is the joint posterior distribution function of the parameters of the NHPP of each regime and the change-points that determines them and which account as well for the influence of the presence of said times. Thus, one of the practical implications of the present work comes in terms of overcoming the need of modeling the time series of measurements, where the distributions of exceedances of certain thresholds, or where the counting of certain events involving abrupt changes, is the main focus with applications in phenomena such as climate change, information security and epidemiology, to name a few.Ítem Clusterización de variables continuas basada en correlación : una aproximación robusta(Universidad EAFIT, 2023) Valencia Arango, Juan Pablo; Moreno Reyes, Nicolás Alberto; Puerta Yepes, María EugeniaÍtem Nonparametric Generation of Synthetic Data Using Copulas(Universidad EAFIT, 2023) Restrepo Lopera, Juan Pablo; Laniado Rodas, Henry; Rivera Agudelo, Juan CarlosThis article presents a novel nonparametric approach to generate synthetic data using copulas, which are functions that explain the dependency structure of the real data. The proposed method addresses several challenges faced by existing synthetic data generation techniques, such as the preservation of complex multivariate structures presented in real data. By using all the information from real data and verifying that the generated synthetic data follows the same behavior as the real data under homogeneity tests, our method is a significant improvement over existing techniques. Our method is easy to implement and interpret, making it a valuable tool for solving class imbalance problems in machine learning models, improving the generalization capabilities of deep learning models, and anonymizing information in finance and healthcare domains, among other applications.Ítem Robust optimization model based on interval analysis for IMRT treatment plans(Universidad EAFIT, 2022) Gómez López, María Camila; Sevilla Moreno, Andrés Camilo; Cabal Arango, Gonzalo Alfonso; Rivera Agudelo, Juan Carlos; Puerta Yepes, María EugeniaÍtem A case study on scheduling university timetables using a three-phase matheuristic(Universidad EAFIT, 2022) Rodríguez Garzón, Camilo Andrés; Rivera, Juan CarlosÍtem Meshless Method for the Numerical Solution of Coupled Burgers Equation(Universidad EAFIT, 2022) Vallejo-Sánchez, Johny Alexander; Villegas Gutiérrez, Jairo Alberto; Villegas Gutiérrez, Jairo AlbertoThe development and interest in numerical techniques for obtaining approximate solutions to partial differential equations have increased very much in the last decades. Among these are meshless methods. Recently radial base functions have been used in meshless methods applied to numerical solutions of partial differential equations, pioneers' works being those of Kansa, Fasshauer, Wendland and Bohamid among others. In this paper, we employ the method, using two RBFs, TPS and MQ, to obtain a numerical solution to coupled Burgers equation. The development and interest in numerical techniques for obtaining approximate solutions to partial differential equations have increased very much in the last decades. Among these are meshless methods. Recently radial base functions have been used in meshless methods applied to numerical solutions of partial differential equations, pioneers' works being those of Kansa, Fasshauer, Wendland and Bohamid among others. In this paper, we employ the method, using two RBFs, TPS and MQ, to obtain a numerical solution to coupled Burgers equation.Ítem Assessing the effects of Multivariate Functional outlier identification and sample robustification on identifying critical PM2.5 air pollution episodes in Medellín, Colombia(Universidad EAFIT, 2022) Roldán Alzate, Luis Miguel; Zuluaga Díaz, Francisco IvánIdentification of critical episodes of environmental pollution, both as a outlier identification problem and as a classification problem, is a usual application of multivariate functional data analysis. This article addresses the effects of robustifying multivariate functional samples on the identification of critical pollution episodes in Medellín, Colombia. To do so, it compares 18 depth-based outlier identification methods and highlights the best options in terms of precision through simulation. It then applies the two methods with the best performance to robustify a real dataset of air pollution (PM2.5 concentration) in the Metropolitan Area of Medellín, Colombia and compares the effects of robustifying the samples on the accuracy of supervised classification through the multivariate functional DD-classifier. Our results show that 10 out of 20 methods revised perform better in at least one kind outliers. Nevertheless, no clear positive effects of robustification were identified with the real dataset.Ítem Using quantum computing to solve the maximal covering location problem(Universidad EAFIT, 2022) Giraldo Quintero, Alejandro; Lalinde Pulido, Juan Guillermo; Sierra Sosa, Daniel; Duque Cardona, Juan CarlosÍtem Option pricing from Ornstein Uhlenbeck process : explicit valuation formula and numerical approximation(Universidad EAFIT, 2021) Pérez Monsalve, Juan Pablo; Marín Sánchez, Fredy HernanÍtem Diseño de líneas de transporte público con consideraciones ambientales(Universidad EAFIT, 2021) Bolaños Nuñez, Sara Alejandra; Rivera Agudelo, Juan CarlosÍtem Towards a holistic framework to model epidemics in presence of uncertainty : formulation of mathematical models and estimation of confidence intervals(Universidad EAFIT, 2021) Rojas Díaz, Daniel; Vélez Sánchez, Carlos Mario; Puerta Yepes, María Eugenia; Cadavid Moreno, Carlos AlbertoÍtem Estimación de la distribución espacial del ingreso intra-urbano de Medellín y su área Metropolitana, usando imágenes satelitales diurnas(Universidad EAFIT, 2021) Salazar Vásquez, Jessica Patricia; Patiño Quinchía, Jorge Eduardo; Duque Cardona, Juan Carlos; Gómez Escobar, Jairo AlejandroÍtem Homogeneity test for functional data based on depth-depth plots(Universidad EAFIT, 2021) Calle Saldarriaga, Alejandro; Zuluaga, Francisco Iván; Laniado Rodas, HenryÍtem Pronósticos no paramétricos basado en funciones tipo kernel con estimación robusta del ancho de banda(Universidad EAFIT, 2020) Castaño Cárdenas, Andrés Eugenio; Laniado Rodas, Henry