Matemáticas
URI permanente para esta colecciónhttp://hdl.handle.net/11349/30143
Examinar
Envíos recientes
Ítem Construcción y depuración de una base de datos como insumo para el desarrollo de un modelo de segmentación de clientes.Baquero Gómez, Paula Andrea; Masmela Caita, Luis AlejandroThis internship was conducted at DataKnow, an analytics consulting firm specialized in providing data-driven services through various tools. Founded in 2018 in Medellin, Colombia, DataKnow stands out in the technology sector by collaborating with leading companies such as Microsoft and SAS. The main focus of the internship was to develop an interest rate modeling for the banking sector, using data analysis to segment customers and determine optimal rates for various banking products. This involved building a database that encompassed risk, sociodemographic, transactional, and product information for both new and existing customers. Tools such as SAS® Guide, SQL, and Python were used for data analysis and exploration, ensuring data quality throughout the process.Ítem Distribuciones Weibull en el marco de una ley de potencias y su implementación con datos de asesinos seriales.Guerrero Veloza, Sheida Melissa; Torres Rico, Angela Maritza; Masmela Caita, Luis AlejandroThis study aims to analyze the intervals between homicides committed by serial killers by determining their probability functions. The ordinary least squares technique was used to estimate the parameters of a power law, and the Kolmogorov-Smirnov test was applied to validate the hypothesis that the variable of interest follows a Type II Weibull distribution. The results indicate that both the power law and the Type II Weibull distribution are suitable methods for modeling the time gaps between each murder, providing an accurate approximation of serial killers' activity. This study offers a novel perspective on understanding serial killers' behavior patterns through the application of precise and effective mathematical tools.Ítem Modelos de predicción de renuncia de colaboradores en el Banco de BogotáGonzález Osorio, Yhan Carlos; Masmela Caita, Luis AlejandroThis report, titled “Prediction Models for Employee Resignation at Banco de Bogotá,” aims to present the work completed during my internship at the company. The primary objective is to develop and implement models to predict potential employee resignations among active staff members. To achieve this, two models were utilized: Random Forests and Logistic Regression. For the latter, regularization techniques such as Lasso, Ridge, and Elastic Net were employed to create heat maps for detecting potential talent attrition. Additionally, the most influential variables were identified, providing valuable insights that will help the company take concrete actions, such as implementing employee retention projects, ultimately aiding in the preservation and management of human talent.Ítem Un nuevo espacio de sucesiones usando la noción de variación acotadaLópez Gaviria, Wilmer; Ospina Cañón, Laura Angélica; Ramos Fernández, Julio César; Ramos Fernández, Julio César [0000-0002-9997-6550]A study of new spaces of sequences in 2-norm spaces is proposed, which is defined through the Orlicz function and using the notion of bounded variation. More precisely, it will review and give the details of the article “Some New Sequence Spaces Defined by Bounded Variation in 2-Normed Spaces” [8]. Complementing the results with examples.Ítem Automatización en la identificación de pólizas de seguro con siniestros atípicos mediante el método de máxima verosimilitud en RGarcía Pérez, Santiago; Másmela Caita, Luis AlejandroThis degree work in the form of an internship was carried out in the Actuarial Management of La Previsora S.A. Insurance Company. The objective of this work consists of implementing the calculation methodology for the selection of atypical claims, whose applicability is found both in the calculation of severity in pure risk premiums and in the calculation of technical reserves. The methodology used was the maximum likelihood method, which consists of the use of the distributional adjustment. The process was programmed in R software.Ítem Curvas tangentes al conjunto parabólico en un punto cúspide de GaussBello Tellez, Rafael Enrique; Barajas Sichacá, Martín; Barajas Sichacá, Martín [0000-0001-9442-5015]In this monograph we consider the study of curves that in particular are tangent to the parabolic set at special points called Gaussian cusp points. We want to geometrically characterize a particular case of tangent curves through their torsion.Ítem Modelado y preservación de prototipos virtuales, aplicativos, flujos de navegación y datos en Banca EmpresasRodríguez Lidueñas, Stefanny; Villarraga Poveda, Luis FernandoThis document provides a formal, theoretical, and practical perspective from the field of mathematics, grounded and applied to the internship work I completed at Banco de Bogotá. The organization features several departments and areas that not only comprise its structure but also assist employees in implementing better strategies to enhance customer service. Notably, these include departments specializing in data analysis, innovation, digital development, and productivity within Corporate Banking. Supported by mathematical fields such as logic, computing, and statistical foundations, the aim is to ensure the maintenance, preservation, modeling, and creation of applications, as well as precise and accurate data identification. This is intended to facilitate effective and efficient communication between commercial teams and clients in Corporate Banking.Ítem Análisis de algoritmos para la imputación de datos y modelos de predicciónNúñez Sánchez, Nicole Daniela; Villarraga Poveda, Luis FernandoConduct a study on algorithms and mathematical techniques for data imputation, making a comparison that allows recognizing accuracy capabilities, errors or biases that may occur in each of the algorithms studied, in order to improve the quality and quantity of data for analysis and thus develop more accurate prediction models.Ítem Pasantía en la corte constitucional: contribución al análisis de datos y depuración de accionados en pythonLeón García, Nelson Miguel; Villarraga Poveda, Luis FernandoThis report presents the development of an internship at the Corte Constitucional de Colombia (Constitucional Court of Colombia), specifically in the support team to the presidency of the court. The main focus of this internship was the cleansing of the databases related to the defendants in lawsuit cases that come to be reviewed to the court. To carry out this task, the programming language Python was used, taking advantage of the Natural Language Processing capabilities within the field of artificial intelligence.Ítem Estudio de las ecuaciones diferenciales implícitas mediante una motivación físicaCapera Yara, Yazmin; Suárez Ávila, Carlos Alberto; Barajas Sichacá, Martín; Barajas Sichacá, Martín [0000-0001-9442-5015]In this work, a physical problem is posed that consists of the motion of a particle of mass m moving under the action of two forces. The first is a force having a potential U and the second is the frictional force Fr . Taking into account both kinetic and potential energy, we can obtain an implicit differential equation (EDB) that models the phenomenon and to which, we will apply qualitative methods, for its study near an equilibrium point and provide an idea of the behavior of the solutions.Ítem Steve Turing: Minecraft es Turing completoMontoya Rodríguez, Jhon Alexander; Rodríguez Aponte, Omar; Mejía Moreno, Carolina; Mejía Moreno, Carolina [0000-0002-2852-0644]A machine is Turing complete if it has the computing power of a universal Turing machine. This work seeks to prove that Minecraft, the Swedish construction video game, is a complete Turing machine. To test this type of results, a universal machine must be built within the same system, in this case the game. However, this would make the machine very slow, so we chose to delve deeper into the concept of completeness of a Turing machine and we were able to test our result by generating logic gates within Minecraft that allow us to conclude that the system is capable of executing any algorithm.Ítem Aplicaciones de las formas diferenciales en el análisis complejoPedrozo Quiceno, Jorge Camilo; Orduz Chávez, Juan Esteban; Sanjuán, Arturo; Sanjuán, Arturo [0000-0002-0309-8299]In this work we provide a proof of the Cauchy’s Theorem for analytic functions using the theory of 1-forms over R2. For this we are making a study of 1-forms and his properties. Whith this application of the vectorial analysis to complex analysis, we present an unconventional proof for the Cauchy’s Theorem.Ítem Solución de un sistema de ecuaciones integro-diferencial utilizando el método de iteración variacionalGarcía García, Jeison Armando; Ramos Fernández, Julio CésarThe objective of this work is to provide approximate solutions of a system of integro-differential equations using the numerical method of variational iteration, the Legendre pseudo-spectral method will be presented in order to compare some results obtained and an application of a model describing biological species living together will be shared.Ítem Aplicativo en Knime - Cuentas maestras pagadorasVenegas Chaparro, Stefania; Villarraga Poveda, Luis FernandoThis thesis presents a workflow carried out on the Knime data mining platform, which relates to an application that allows consolidating all the report files of the information of the Master Paying Accounts that each banking entity supervised by the Financial Superintendence of Colombia makes before the Ministry of Finance and Public Credit on a monthly basis within the first twenty (20) days of each month. In the application, it is possible to identify the territorial entities that have incurred in alleged risk events within the framework of Decree 028 of 2008 and complementary regulations regarding the reporting and operation conditions of Master Accounts, and consequently, of Master Paying Accounts, in order to ensure the non-suspension of transfers of resources from the General System of Participations, thus ensuring the proper management of public resources and a high coverage of the product.Ítem Transformaciones de Möbius: una mirada al análisis complejoSánchez Castellanos, Jeisson Jarvey; Sanjuán Cuéllar, Álvaro ArturoIn this work we are going to study the basic aspects of Möbius transformations, for this We will expose the notation of fundamental circles, their association with transformations and some elementary properties. The objective of this work is to show in a summary way the conservation of the forms that the Möbius transformations, showing in turn that these transformations are bilinear and projectives observing that they transform in the complex plane and in the Riemann sphere.Ítem La existencia de una correlación negativa entre el índice de riesgo de liquidez (IRL) y el valor en riesgo (VaR) de Corredores DaviviendaFerrucho Vides, María Camila; Villarraga Poveda, Luis FernandoThe present document will present the final work of the internship carried out at Corredores Davivienda in the area of financial risks. Corredores is the Brokerage firm subsidiary of Davivienda, one of the most recognized and important brokerage firms in all of Colombia, which is part of the Bolívar Group. Different financial risk analyses were carried out in both Panama and Colombia using programming tools such as Visual Studio and Python, where a predictive mathematical model was generated for the internal VaR through the internal IRL of Corredores Davivienda.Ítem Aprendizaje automático para la clasificación de consumidores y predicción del IPCAMariño Parra, Alejandra; Villarraga Poveda, Luis FernandoThis document explains the development of the internship project carried out with the market analysis team belonging to Kantar WorldPanel, a multinational leader in data, insights, consulting and understanding the consumer through consumer panels. In the development of the internship, different optimization and machine learning projects are carried out through the Python programming language for the implementation of models that generate results of variation, trends, predictions, and classification, while respecting the confidentiality rules that were given to me.Ítem Series temporales para el pronóstico de tasas de tributación - Grupo BancolombiaMoreno Ruiz, Adriana Lucia; Villarraga Poveda, Luis FernandoThis document presents the development of the internship project carried out at the Tax Department of Bancolombia Group, which is a financial leader with over 146 years of experience promoting sustainable economic development.In the internship, Python is implemented as a programming language to perform different data analysis and, based on statistical measures, determine and implement the most suitable models for predicting tax figures.Ítem Impacto del derecho de inspección en el Fondo Nacional de GarantíasParra Espejo, Iván Javier; Masmela Caita, Luis Alejandro; Masmela Caita, Luis Alejandro [0000-0003-3882-4980]The Fondo Nacional de Garantías (FNG) is a public entity whose objective is to facilitate access to credit for the self-employed and companies of all sizes by providing guarantees. Given that the FNG manages the State budget, it is crucial that rigorous control of its operation is carried out. In this regard, the area of Inspection Rights is of fundamental importance. The main objective of the project is to examine the results obtained to date in the inspection rights process in order to analyze the financial impact it has had on the FNG.Ítem Norma y traza: una mirada matricial y algunas aplicaciones en la diferenciabilidad con el operador lineal trazaDuarte Gómez, Gerson; Correa Malagón, Laura Marcela; Mejía Moreno, Carolina; Mejía Moreno, Carolina [0000-0002-2852-0644]This work focuses on studying different definitions of the concepts of trace and norm, which are initially associated with the concept of a matrix. Then, the relationships, differences, and equivalences between these concepts are explored. Finally, an interesting application of trace to the notion of differentiability is presented. Derivatives of some matrices will be found, both of the first derivative and higher-order derivatives.