Seminarios

Abstract: In this presentation we will consider the following scenario: A subject may experience two events, Terminal or Non-terminal, where the Terminal event can still occur after the Non-terminal event, but not vice versa. For example, a situation in which a subject may experience recurrence of a disease, or die from this disease. This situation is known as semicompeting risks. For a better understanding of analysis of data with a semicompeting structure, we will start this presentation by talking about some basic concepts in survival analysis, and we will explain in more detail a situation of semicompeting risks based on competing risks. For modeling, we propose the illness-death model with shared frailty.

Keywords: Semicompeting risks; illness-death process; frailty variable.

Abstract: The purpose of this presentation is to introduce the inhomogeneous @-equation in several complex variables. We will expose some phenomena associated to the existence of solutions to this equation, and some others which appear in the study of functions of several complex variables and show a high contrast with the study of functions of one complex variable.

Keywords: Cauchy-Riemann operator; several complex variables.

Abstract: Mathematical morphology is a theory for processing and analysis of images that uses operators and functions based on topological and geometric concepts. It was originally developed for binary images and then extended for gray-scale images. In this work, we will present a brief introduction to the fuzzy mathematical morphology as part of the extension of binary mathematical morphology for gray-scale mathematical morphology.

Keywords: Mathematical morphology, binary images, gray-scale images, morphological operators, fuzzy set theory.

Abstract: This presentation aims to show in an introductory way, the importance of functional data analysis (fda) and its scope in the treatment of large data sets, through the exposition of its general concepts and the description of some techniques used in research scientic.

Keywords: Functional data, B-Splines, Breakpoints.

Abstract: In many practical situations of human knowledge, there is a need for model variables such as proportions, rates or fractions that are in the continuous interval (0, 1), and these associated with covariates. In this presentation we will mention the beta model, which is the best known model for modeling this type of data, and we will also mention others that are an alternative to this model.

Keywords: Proportions, Beta regression model.

Abstract: This presentation seeks to introduce the Gamma function and show some of its applications in areas such as Statistics and Physics.

Keywords: Gamma function, Complex Analysis, Statistics, Physics.

Abstract: Actual outbreak generated by SARS-CoV-2, presented a challenge to the governments because Public Health, Economy and Society are diferent in every country so actions must fit considering these previous conditions. South America is a region with countries on development-process with limitations, problems and the pandemic highlighted them. Peru is a country with good initial policies to contain the pandemic, a lockdown started on March 15 and lasted more than 100 days. By consequence, people was forced to change daily activities and of course, social and mental problems started to grow. The actual study wants to identify the covid-19 impact on the Social Network, Twitter ltering posts related to the topic. The initial ndings present the high interest on the topic during firsts week and a decreasing pattern in last weeks.

Keywords: Natural Language Processing, Text Mining, Social Network, People behaviour, Covid-19, Pandemic.

Resumen: En esta presentación se estudiara el Teorema del paso de la Montaña que fue publicado en 1973 por Ambrosetti y Rabinowitz, forma parte de la teoría de puntos críticos de funcionales definidos en espacios de Sovolev. Desarrollaremos este teorema sobre funciones reales, funciones en R^n y en funcionales. Finalmente veremos su aplicación.

Palabras clave: Conjuntos compactos, análisis en R^n, análisis funcional, condición de Palais Smale, geometría del paso de la montaña.

Abstract. Regression models play a very important role in many of the data analyzes, providing prediction and classication rules and among the most widely used, simple and multiple linear models but these models often fail or are limited in their ability predictive and classicatory, because in real life, the effects or predictor variables of the regression they are more complex (they are not linear). There are fexible statistical methods that can be used and To characterize the effects of non-linear regression, one of these methods is called "Generalized Additive Models (GAM)" proposed by Hastie and Tibshirani (1990). These methods relax the linear assumption in relation to the effects of the standard models and allow to discover structures in the data that analysts often do not perceive or do not take into account, therefore, the use of GAM allows incorporating this exibility in the behavior of the effects on regression (smooth function). In this work, generalized additive models, the adjustment method, model selection criteria, advantages, disadvantages and some applications will be described.

Keywords: regression, generalized additive models, smooth function.

Abstract. Let be a deformed tube in $R^3$ and $-\delta_D^{\omega}$ the Dirichlet Laplacian operator in $\omega$. In this lecture, we will discuss the spectrum $\sigma(-\delta_D^{\omega})$ of the operator $-\delta_D^{\omega}$. More precisely, we are going to analize how the geometrical characteristics of $\omega$ can influence in the set $\sigma(-\delta_D^{\omega})$. On the other hand, we will coment on some others problems and aplications about the spectrum of Laplacian operator in deformed tubes.

Keywords: Laplacian Operator, Quadratic Forms, Spectrum, Deformed Tubes.

Abstract. In the extant literature, hierarchical models typically assume a flexible distribution for the random-effects. The random-effects approach has been used in the inferential procedure of the generalized linear mixed models . In this paper, we propose a random intercept gamma mixed model to fit correlated asymmetric positive continuous outcomes. The generalized log-gamma (GLG) distribution is assumed as an alternative to the normality assumption for the random intercept. Numerical results demonstrate the impact on the maximum likelihood (ML) estimator when the random-effect distribution is incorrectly misspecied. The extended inverted Dirichlet (EID) distribution is derived from the random intercept gamma-GLG model that leads to the EID regression model by supposing a particular parameter setting of the hierarchical model. Monte Carlo simulation studies are performed to evaluate the asymptotic behavior of the ML estimators from the proposed models. Analysis of diagnostic methods based on quantile residual and COVARATIO statistic are used to assess departures from the EID regression model and identify atypical subjects. Two applications with real data are presented to illustrate the proposed methodology.

Keywords: Generalized mixed model, generalized log-gamma distribution, misspecication of the random-effects, extended inverted Dirichlet model, diagnostic analysis.

Resumen. Consideramos un modelo no convexo a través del cual se busca clasificar datos binarios en presencia de outliers. Este modelo esta basado en el problema de optimización no convexo LOVO y es una modificación de las maquinas de soporte vectorial de margenes suaves. En este trabajo se demuestra que es posible generar una solución optima del problema no convexo considerado a partir de resolver un numero nito de problemas convexos.

Palabras clave: MSV. Dualidad. Optimización DC. Errores. Clasicación.