Cuadernos de Ingeniería Matemática, Vol. 01 Núm. 01 (2021)
URI permanente para esta colección
Editor Jefe: Paula Escudero Marín - pescuder@eafit.edu.co
Editores operativos: Pablo Alberto Osorio Marulanda - paosoriom@eafit.edu.co, Ana Sofía Gutierrez Tejada - asgutierrt@eafit.edu.co
Contacto: Cuadernos de Ingeniería Matemática - cuadernos.ing.mat@eafit.edu.co
Examinar
Envíos recientes
Ítem El modelo depredador-presa de Lotka-Volterra en las especies de lince canadiense y liebres raqueta de nieve(Universidad EAFIT, 2021-02-13) Rengifo Castro, Juan David; Arango Restrepo, Isabella; Gómez Piedrahita, Mariana; Universidad EAFIT, Escuela de Ciencias, Departamento de Ciencias MatemáticasEn este trabajo se abordará el estudio de sistemas dinámicos que describen la interacción de dos especies que coexisten en un espacio común. En particular, se considerará la relación depredador-presa en un caso de la vida real, la evolución poblacional de los linces canadienses y liebres raqueta de nieve en Canadá entre 1900 y 1935. Se hará uso del modelo depredador-presa de Lotka-Volterra clásico y con saturación de presas para modelar el sistema del cual provienen los datos suministrados por Hudson Bay Company. Cabe resaltar que toda la implementación y análisis desde la óptica de los sistemas dinámicos se realizará en MATLAB y Simulink. No hay que olvidar que lo anterior, se hace con el objetivo de entender las interacciones entre ambas especies y determinar si estos modelos están en la capacidad de representar el sistema de manera adecuada.Ítem Supervised Statistical Methods to Identify Credit Acceptance Rate(Universidad Eafit, 2021-04-10) Yusty, Valentina; Laniado, Henry; Universidad Eafit, School of Sciences, Department of Mathematical SciencesSince incorrect decisions can have detrimental effects on financial institutions, the possibility for these to forecast business failures becomes indispensable. In the financial domain, the focus of research problems rarely revolves around the identification of the clients who desist their credit offering, but rather on bankruptcy prediction and credit scoring. The general objective of this paper revolves around the implementation of supervised machine learning algorithms that will allow CrediOrbe, a credit company, to target customers whose profile assimilates those who desist their credit offering. Machine learning algorithms have been greatly studied as tools to aid decisions makers in the realm of finance. Performance measurements are calculated and analyzed through the use of statistical classification measurements. Suggestions for further research are providedÍtem Mathematical modelling and simulation of a rocket’s take-off trajectory(Universidad Eafit, 2021-04-08) Vidal Correa, Juan Pablo; Murillo Gonzalez, Alejandro; Botero Botero, Maria Alejandra; Universidad Eafit, School of Sciences, Department of Mathematical SciencesA rocket is a vehicle that launches into space or describes a suborbital flight. It’s subjected to the forces of weight, thrust, and the aerodynamic forces, lift and drag. The relative magnitude and direction of the forces determines the flight trajectory of the rocket. The objectives of this paper are to model the rocket’s take-off trajectory and understand the tradeoff when using the main engine in conjunction with the lateral thrusters. Also, to obtain a linear model that represents the altitude obtained by the rocket in the ascending phase and to examine system behavior through stability and sensitivity analysis. Rocket’s trajectory is obtained in four situations depends on the engine or thrusters that are in operation. Linearization methods were used to replace the model by a simpler function due to the possibility of use tools for studying linear systems to analyze the behavior of a nonlinear function near a given point and because a linear model is required for certain types of analysis such as stability analysis. Finally, sensitivity analysis of the parameters of the model is used to study how the uncertainty in the output of a mathematical model can be apportioned to different sources of uncertainty in its inputsÍtem Entendiendo la contaminación: un enfoque basado en sistemas dinámicos(Universidad EAFIT, 2021-04-30) Alvarez Zuluaga, Susana; Bonnett García, Mateo; Yusty Mosquera, Valentina; Universidad EAFIT, Escuela de Ciencias, Departamento de Ciencias MatemáticasLas concentraciones de material particulado en el aire han aumentado durante los últimos años, tal como muestra la evidencia científica. Sin embargo, tal como muestran los datos acá recolectados y (Bonnett, et al. 2019), estas concentraciones han disminuido en los últimos meses en el Valle de Aburrá, esto debido a las medidas sociales y políticas tomadas por el gobierno local. Pero, a pesar de que la calidad del aire muestre una mejora, los estudios para entender este fenómeno, no deberían parar. Es por esto que se presenta acá un modelo basado en la teoría de sistemas dinámicos para entender mejor cómo las condiciones climáticas, tales como viento, humedad y temperatura, afectan las concentraciones de PM10 y la calidad del aire. Por último, la sección de análisis de sensibilidad muestra como cambios en estos parámetros afectan las concentraciones de PM10.Ítem Modeling, simulation, and control of the spacecraft attitude dynamics(Universidad EAFIT, 2021-03-26) Ocampo, Carlos; Universidad EAFIT, School of Sciences, Department of Mathematical SciencesBased on the three-dimensional dynamics of a rigid body and Newton’s laws, the simplified dynamics of a spacecraft is studied and described through the systematical representation, mathematical modeling and also by a block diagram representation, to finally simulates the spacecraft dynamics in the Matlab programming environment called Simulink. It is paramount to be able to identify and recognize the attitude (often represented with the Euler angles) and position variables like the degrees of freedom (DOF) of the system and also the linear behavior. All this to conclude up about the non-linear behavior presented by the accelerations, velocities, positions and Euler angles (attitude) when those mentioned are plotted against time. In addition to this, the linearized system is found in order to facilitate the control analysis and stability analysis, at using linear analysis tools of Simulink and concepts like controllability and observability, reaching the point of determining under the previous concepts to proceed with the control design phase. Lastly, an uncertainty and sensitivity analysis is realized, by means the Monte-Carlo and the Linear regression method (in Simulink too), to find the torque like critical model input, since it has the greatest effect on the response variables in the system; and thus finally, to implement the Linear Quadratic Regulator (LQR) controller, at using the lqr Matlab functionÍtem Improving customer waiting time for medicine-retrieval center(Universidad Eafit, 2021-04-12) Plazas Escudero, David; Cárdenas-Rodríguez, Juan Sebastian; Restrepo Sierra, Mateo; Universidad Eafit, School of Sciences, Department of Mathematical SciencesNeuromedica is a Colombian pharmacy which provides treatment for people with neurological diseases. Recently, Neuromedica started attending patients from other pharmacy which led to a significant increase in the waiting time. In this pharmacy, people are classified and attended due to certain priorities. The data, given by Neuromedica, is analyzed using boxplots, Kruskal-Wallis and Kolmogorov-Smirnov tests with Python’s library Scipy. The objective of this work is to determine the number of assistants and queue logistic such that the waiting time has a significant reduction, with the purpose to provide a satisfactory level of service. A discrete-event simulation model was created and implemented in Python. A heuristic approach to minimize the waiting time is used. Additionally, a sensitivity analysis is made on the assumed distributions.Ítem Evaluation of Robust Covariance Estimation for Object Detection(Universidad EAFIT, 2021-04-07) Tamayo-Arango, Andres Felipe; Plazas Escudero, David; Vidal-Correa, Juan Pablo; Universidad EAFIT, School of Sciences, Department of Mathematical SciencesThis work presents an initial approach to the evaluation of robust covariance estimation for object detection (localization) using the “region covariance” technique from the literature. The covariance estimation is performed using the Comedian, Kendall, Spearman and Ledoit and Wolf robust approaches for covariance, and the procedure was also compared using two different matrix norms for estimating dissimilarity. The performance was measured quantitatively using linear regression and Pareto boundaries, yielding the Ledoit and Wolf estimation with best overall performance in object detection in normal and noisy images.Ítem Agent-Based Model for Studying Diabetes under the Influence of Relationships(Universidad Eafit, 2021-04-12) Plazas Escudero, David; Cárdenas-Rodríguez, Juan Sebastian; Restrepo Sierra, Mateo; Universidad Eafit, School of Sciences, Department of Mathematical SciencesDiabetes is a disease which affects levels of blood insulin and recently has turned into a public health threat. This disease presents a huge risk for the individual, as it can reduce life expectancy. Furthermore, many models of diabetes just focus on biological or eating habits, without taking into account social or cultural factors. In this work, an agent-based model is proposed for the diabetic population taking into account interpersonal relationships and body mass index. The model is implemented in NetLogo and validated by results under extreme conditions. Then, it is simulated to test the influence that marriage has on the diabetic population. Finally, a sensitivity analysis is madeÍtem Estimación de parámetros, análisis de sensibilidad y validación del modelo SIR aplicado a datos históricos del virus A(H1N1) en México.(Universidad EAFIT, 2021-04-13) Gómez Osorio, Hamilton; Isaza Cadavid, Santiago; Osorio Marulanda, Pablo A.; Universidad EAFIT, Escuela de Ciencias, Departamento de Ciencias MatemáticasEste trabajo busca analizar el comportamiento epidemiológico de una enfermedad transmisible como la influenza A(H1N1), a partir de un modelo SIR, aplicado a un grupo de personas diagnósticadas con la enfermedad en México en el año 2009. En este se realiza una respectiva estimación de parámetros poblacionales, como lo es la tasa de contagio y la tasa de recuperación, y un análisis de sensibilidad utilizando la herramienta Simulink de MATLAB.Ítem Verificacion del Modelo de Silenciamiento Genetico(Cuadernos de Ingeniería Matemática, 2021-05-27) Garcia Jimenez, Manuel Eduardo; Becerra Sierra, Omar Alexis; Romero Millan, David Andres; Universidad Eafit, Escuela de Ciencias, Departamento de Ciencias MatemáticasEn el presente trabajo se analiza un sistema dinamico planteado por Barbosa [1] que describe el comportamiento de ciertas moleculas dentro de un macrofago infectado con Leishmaniasis al administrar una dosis de tetraciclina (antibiotico). La investigación indica que la Leishmaniasis ataca a los macrófagos del paciente y que el proceso infeccioso se da cuando ciertas prote´ınas del parésito interact´uan con ciertas otras del macrófago [1]. La hipótesis sugiere que es posible modificar la genética del macrófago, a ótravés del uso de antibióticos, para controlar o hasta posiblemente eliminar la infección [1]. La contribución principal de este documento es la verificación de los resultados del modelo planteado para determinar su validez. Para cumplir con este objetivo, se realiza una revisión teórica y una simulación del modelo con el paquete de software Simulink. Los resultados indican que el modelo es consistente con los hallazgos reportados por Barbosa. Estos mismos son congruentes con los principios de silenciamiento genético, por tanto se concluye que el modelo es apto para su utilización en la investigación de Leishmaniasis