Differential Equations and Fuzzy Analysis (EDAD)

Session 290: Fuzzy Differential Equations: Some Approaches to Analysis and Solution | March 2, 2026

Abstract: Differential equations are a fundamental mathematical tool for modeling real-world phenomena. However, these phenomena are often associated with varying levels of uncertainty and subjectivity, arising from both a lack of information and the poor quality of available data. In order to incorporate this uncertainty into mathematical models, fuzzy differential equations (FDEs) have been developed.

This talk aims to introduce some approaches to dealing with FDEs, including the use of fuzzy derivatives (the Hukuhara derivative, the generalized Hukuhara derivative, among others) and a differentiability approach based on “granular” arithmetic. Some illustrative examples will also be presented, together with their main advantages and limitations in the solution and analysis of an FDE.

Speaker: Leidy Espitia, Universidad de Tarapacá, Chile.

Session 289: An Introduction to Stochastic Differential Equations | February 23, 2026

Abstract: Stochastic Differential Equations (SDEs) are a widely used tool for modeling situations that are currently the subject of study, whether as theoretical formulations for describing physical phenomena or as financial forecasting models for economic decision-making.

The main purpose of this talk is to introduce participants to the fundamental concepts and basic properties of SDEs, providing a theoretical understanding through both qualitative and quantitative analysis. Some relevant examples will also be discussed, including Itô processes and geometric Brownian motion, which have been widely studied due to their applications in probabilistic forecasting. Finally, some open problems and possible approaches to their solutions will be presented.

Speaker: Jesús Fernando Carreño Díaz, Universidad Nacional Autónoma de México.

Session 288: Finite Element Approximation for the Fractional Bessel -Laplacian | February 16, 2026

Abstract: We will study the Dirichlet problem for a class of fractional -Laplacian operators defined through the Riesz fractional gradient. This formulation differs fundamentally from the standard fractional -Laplacian. Our analysis combines the framework of Lions–Calderón spaces, Besov embeddings, and an adaptation to the Riesz fractional setting of Nirenberg’s difference quotient method, originally developed by Savaré. As our main result, we obtain global Besov-type regularity estimates for weak solutions. In particular:

Speaker: José Camilo Rueda, Universidad de la República, Uruguay.

Session 287: SIRS Model of the Hepatitis B Virus in the Human Population | November 10, 2025

Abstract: The hepatitis B virus (HBV) is one of the world’s major public health problems, as it is considered the most common chronic viral infection and one of the most contagious among humans. Since its discovery in the 1960s and the identification of the surface antigen in 1965, vaccines and treatments have been developed that, although they have not achieved its complete eradication, have contributed significantly to reducing associated morbidity and mortality.

This study examines mathematical models of HBV and subsequently proposes a SIRS-type mathematical model based on Ordinary Differential Equations (ODEs) to describe HBV dynamics in the human population, incorporating vertical and horizontal transmission, loss of immunity, and the chronic infection stage. The basic reproduction number (R₀), equilibrium points, stability, and local sensitivity analysis of the parameters are determined. Finally, numerical simulations were performed using the fourth-order Runge–Kutta method (RK4), making it possible to confirm the theoretical results and visualize the dynamic behavior of the system as the parameters affecting the infected population vary.

Speaker: Jesús David Hernández Galindo, Undergraduate Student in Mathematics Education, Universidad de los Llanos.

Session 286: Theoretical and Numerical Study of a Differential System in Magnetohydrodynamics | October 27, 2025

Abstract: Magnetohydrodynamics (MHD) is the branch of physics concerned with studying the behavior and interaction of fluids through, or in the presence of, a magnetic field. The MHD equations consist of a coupling between Maxwell’s equations and the Navier–Stokes equations, an interesting feature considering that the two models originate from fields of physics that are, in principle, unrelated: electromagnetism and fluid mechanics. Due to their numerous scientific applications, the study of these equations has attracted considerable research interest in recent years. Applications include the study of the Earth’s magnetic field, involving the outer core and the motion caused by the Earth’s rotation, as well as the aurora borealis, which is generated by the interaction between the magnetosphere and the solar wind.

This talk focuses on the theoretical and numerical study of MHD equations in both their evolutionary and stationary forms. The first part, concerning theoretical analysis, will address the existence of weak solutions to these models and analyze the stability of weak solutions to the stationary problem. The second part, concerning numerical analysis, will present two numerical schemes—one for approximating each model—based on the finite element method. The well-posedness of these approximation schemes will be demonstrated, and the stability of the discrete stationary solutions will be studied, determining the conditions under which the discrete solution of the evolutionary scheme converges to the solution of the stationary scheme as the number of time steps tends to infinity. Finally, results from simulations performed using FreeFem++ software will be presented. This talk is part of Luis David Salazar’s undergraduate thesis in Mathematics.

Speaker: Luis David Salazar Anaya, Mathematics Student, School of Mathematics, UIS.

Session 285: Some Fundamental Ideas in Control Theory | October 20, 2025

Abstract: In general terms, a controllability problem can be formulated as follows. Consider an evolutionary system described in terms of Partial or Ordinary Differential Equations (PDEs/ODEs). We can act on the trajectories of the system by means of an appropriate control. Thus, given a time interval t ∈ (0, T), as well as initial and final states, we must find a control such that the solution matches both the initial state at t = 0 and the final state at t = T. This talk aims to provide a brief introduction to controllability theory with state equations given by finite-dimensional systems, demonstrating the equivalence between controllability and the Kalman rank condition. Where possible, parallels with optimal control theory will also be established.

Speaker: Élder Jesús Villamizar Roa, Professor, School of Mathematics, UIS.

Session 284: Numerical Study of a Differential System Describing Prostate Cancer Growth | September 29, 2025

Abstract: Prostate cancer (PCa) is one of the most common types of cancer; specifically, according to the WHO, it is the second most common type of cancer among men worldwide. In most cases, PCa is an adenocarcinoma, a form of cancer that begins in the epithelial tissue of the prostate. Its growth and progression depend on several factors, including genetic alterations that initiate the disease and conditions within the tumor microenvironment.

From a mathematical perspective, cancer modeling and computational simulation have shown promise in improving our understanding of these diseases and in predicting tumor growth and the outcomes of certain treatments. Specifically, with regard to prostate cancer, [1] proposes and theoretically studies a mathematical model consisting of a system of Partial Differential Equations (PDEs) to model prostate cancer dynamics in the presence of chemotherapy and antiangiogenic therapy.

This talk focuses on the numerical study of the PDE system proposed in [1]. A numerical scheme based on the Finite Element Method is proposed, and several qualitative properties are studied, including its well-posedness, pointwise estimates for the discrete variables—which are relevant from both biological and mathematical perspectives—and convergence of the discrete solutions toward a stationary state as the number of time steps tends to infinity. Finally, results from numerical simulations demonstrating the good performance of the proposed scheme are presented. This talk is based on the results obtained in [2] and is part of Mathematics student Juan Diego Ríos’s undergraduate thesis.

Speaker: Diego Armando Rueda Gómez, Professor, School of Mathematics, UIS.

Session 283: Analysis of the Basic Reproduction Number in Epidemiological Models with a Stochastic Component | September 22, 2025

Abstract: This research develops stochastic SIR and SEIR epidemiological models with random perturbations to analyze the dynamics of COVID-19 and Acute Respiratory Infections (ARIs) in Bogotá. Using a data updating method and maximum likelihood estimation, populations for which data were unavailable and the basic reproduction number (R₀) were estimated. The key results show that variability in particulate matter and temperature significantly increases volatility in the infection rate. The study concludes that incorporating these environmental factors and stochastic noise is crucial for improving outbreak prediction and designing more effective public health policies to address the endemic transmission of these diseases.

Speaker: Andrés Sebastián Ríos Gutiérrez, Professor, School of Mathematics, UIS.

Session 282: A Level Set Based Mesh Evolution Method for Shape and Topology Optimization | August 11, 2025

Speaker: Charles Dapogny, Professor, Université Grenoble Alpes, CNRS, Grenoble, France.

Session 281. May 26, 2025.

Title: A family of systems including models for viscoplastic fluids.

Abstract: In this talk, we first present some explanations of viscoplastic fluids and aim to provide some motivation to the study of mathematical models for this type of fluid. Then we will discuss a family of systems of equations which includes the Bingham model for viscoplastic fluids (more generally, the Herschel-Bulkley model). In this family, the “viscous stress tensor” is the subgradient of a convex potential, which can depend on the space-time variables. We also intend to show an initial boundary value problem for those systems in a bounded region in R3, with a nonlinear boundary condition containing the Navier friction/slip boundary condition. This is a joint work with Nikolai V. Chemetov (University of São Paulo (USP) in Ribeirão Preto, SP, Brazil).

Speaker: Marcelo Martins Dos Santos, Professor, Universidade Estadual de Campinas, Brazil.

Session 280. May 12, 2025.

Title: Theoretical Analysis of an Optimal Control Problem Associated with a Schnakenberg-Type Reaction-Diffusion System.

Abstract: This talk will present some results related to the study of a system of reaction-diffusion partial differential equations that models the interaction between two chemical substances. The system is a generalization of the Schnakenberg model, which has applications in morphogenesis and chemical reaction dynamics and gives rise to the formation of Turing patterns. Three main aspects are addressed: first, a linear and decoupled numerical scheme based on finite elements with mass lumping is proposed, for which well-posedness and positivity of the discrete solutions are demonstrated; second, the existence and uniqueness of global solutions to the system in appropriate function spaces are analyzed; and third, an optimal control problem associated with the model is formulated, the existence of optimal solutions is demonstrated, and optimality conditions are established.

Speaker: Andrés Felipe Ortiz Flórez, Master’s Student in Applied Mathematics, School of Mathematics, UIS.

Session 279. April 28, 2025.

Title: Existence of Global Weak Solutions for a p-Navier-Stokes System.

Abstract: The Navier-Stokes equations consist of a system of partial differential equations that describe the dynamics of incompressible viscous fluids. In the non-Newtonian context, there are several models that are variants of the classical Navier-Stokes model. One of these is the so-called p-Navier-Stokes equations, proposed in: Lei Li and Jian-Guo Liu, p-Euler equations and p-Navier–Stokes equations, Journal of Differential Equations, Volume 264, Issue 7, (2018), 4707-4748.

This seminar will present the existence of global weak solutions to the system for p>2. The existence of weak solutions to the system is proved using the Galerkin method by constructing an appropriate Schauder basis for the solution space, which is a subspace of W^{1,p}_0. This basis is constructed using the Leray projector. Once the system of Galerkin approximations has been constructed, uniform estimates are obtained and compactness arguments are used to extract a convergent subsequence whose limit corresponds to a weak solution of the system.

The content of this seminar is based on a description of the results of the article: Existence of weak solutions to $p$-Navier-Stokes equations, Discrete and Continuous Dynamical Systems – Series B Vol. 29, No. 4, April 2024, pp. 1868-1890, by Feng, Yuanyuan, Li, Lei, Liu, Jian-Guo, and Xu Xiaoqian.

Speaker: Juan Nicolás Peña, Mathematics Student, School of Mathematics, UIS.

Session 278. April 21, 2025.

Title: Design, Creation, and Management of Relational Databases: A Practical Approach Using SQL and Python.

Abstract: The authors of this presentation have designed a manual covering the basic use of SQL, particularly MySQL. This talk provides an explanation of relational databases, including fundamental concepts, classification, and management through database management systems. It then introduces some basic SQL commands and their main uses. The importance of the Python language for managing relational databases is explained, along with an outline of its integration with MySQL for data analysis. Finally, four examples of Python code implementation are presented, with the data previously managed using SQL. This presentation is part of the authors’ Undergraduate Project II, conducted in the seminar modality.

Speakers: María Catalina Ballesteros, Adriana Lucía Guerrero, Émerzon Steven Mendoza, Angélica Liliana Porras, Mathematics Students, School of Mathematics, UIS.

Session 277. March 31, 2025.

Title: On Controllability and Inverse Problems in Partial Differential Equations.

Abstract: In this talk, we will discuss some general aspects of the necessary and sufficient conditions for controlling the solutions of a Partial Differential Equation. We will also examine what can be said about some related inverse problems. We will then explore how a well-known technique for addressing this type of problem, known as Carleman inequalities, comes into play and examine its relationship with classical energy estimates for a PDE.

Speaker: Juan Carlos López Ríos, Professor, School of Mathematics, UIS.

Session 272. December 2, 2024.

Title: Models Based on Ordinary Differential Equations and Parameter Estimation (Part 2).

Abstract: This talk presents approaches to parameter estimation in models based on ordinary differential equations, particularly epidemiological models. An example using simulated data is presented, and parameter estimation is implemented in R using ordinary least squares. Participants are encouraged to bring a personal computer with a Posit Cloud account already created: Posit Cloud

Speaker: Andrés Sebastián Ríos Gutiérrez, Professor, School of Mathematics, UIS.

Session 271. November 18, 2024.

Title: Models Based on Ordinary Differential Equations and Parameter Estimation

Abstract: This talk presents several models based on ordinary differential equations and their applications in epidemiology. It provides an introduction to the different methods used to estimate these models and discusses the advantages and disadvantages of each method.

Speaker: Andrés Sebastián Ríos Gutiérrez, Professor, School of Mathematics, UIS.

Session 270. October 28, 2024.

Title: Comparative Analysis of Fuzzy Modeling Approaches for the Analysis of Chemical Substance Degradation.

Abstract: This talk will present a comparative analysis of two fuzzy modeling approaches for analyzing the degradation of chemical substances. We will focus on a particular case involving the analysis of chemical residues in agriculture. It is well known that chemical pest control in agriculture involves the use of chemical agents that affect final crop products. Therefore, the analysis of chemical residues in harvested products is an important issue when assessing product quality and suitability for human consumption.

The mathematical modeling of pesticide residues in potato tubers is presented to predict the evolution of pesticide concentration following the final spraying of the potato crop, using two fuzzy modeling approaches. First, a fuzzy initial value problem (FIVP) associated with a system of fuzzy differential equations that models pesticide concentration in potato tubers is proposed and solved. In particular, thiamethoxam residues in potatoes are studied using a small set of field data, from which the parameters involved in the FIVP are estimated. In the second approach, a Takagi-Sugeno-Kang model is designed to approximate the degradation of thiamethoxam concentration by defining a set of fuzzy inference rules. These two approaches show similar behavior, even with limited fuzzy data. This analysis can be applied to a broad class of dynamic systems.

Speaker: Leidy Espitia, Master’s Student in Mathematics, School of Mathematics, UIS.

Session 269. October 21, 2024.

Title: A Comparative Analysis of the Finite Difference Method and the Mimetic Method for the One-Dimensional Convection-Diffusion Equation.

Abstract: This work presents a comparative analysis of the finite difference method and the mimetic method applied to the one-dimensional convection-diffusion equation under steady-state conditions. Since numerical methods are fundamental for solving partial differential equations in numerous scientific and engineering applications, several finite difference schemes are implemented and compared, including the second-order central difference scheme, the second-order upwind scheme, the QUICK scheme, and the second-order theta scheme. These are compared with the mimetic method, which uses discrete versions of conservative differential operators.

Speaker: Sergio Andrés Rivera Antolinez, Mathematics Student, School of Mathematics, UIS.

Session 268. October 7, 2024.

Title: Inverse Source Problems for Coupled Heat Systems Using Measurements of a Scalar State.

Abstract: This talk addresses the study of inverse source problems for coupled systems of heat equations with constant or space-dependent coupling terms, whose internal measurements involve a reduced number of observed states. The analysis considers two types of systems. The first consists of parabolic equations with zero-order coupling terms (also known as a non-self-adjoint matrix potential), with coefficients that may depend on space. The second consists of parabolic equations with coupling in the diffusion matrix. In all configurations, the source is decomposed into separated variables, where the temporal component is known and scalar, while the spatial dependence is an unknown vector field. Numerical algorithms are implemented using the finite element method in 1D and 2D. Several examples show that the algorithms are capable of recovering space-dependent sources.

Speaker: Cristhian David Montoya Zambrano, Professor, School of Applied Sciences and Engineering, Universidad EAFIT.

Session 252. December 18, 2023

Title: Geometric Integration with Julia.

Abstract: In this talk, we aim to present some Geometric Integration (Differential Geometry) techniques applied to numerical optimization. Practical examples will be presented using Julia.

Speaker: Cedric Martínez Campos, Professor, Universidad Rey Juan Carlos, Madrid, Spain.

Session 251. December 11, 2023

Title: A Property in the Category of Quasi-Normed Spaces.

Abstract: A property P in the category of quasi-normed spaces is said to be a 3-space property if a quasi-normed space X has this property whenever a closed subspace Y of X and X/Y have property P. Over the past decades, many examples and counterexamples concerning these properties have been developed. However, one of the most important questions was posed by the mathematician Palais: If Y and X/Y are Hilbert spaces, must X be isomorphic to a Hilbert space? This question will serve as the starting point for the talk. We will study the theory of twisted sums in locally bounded spaces, their relationship with 3-space properties, and the construction of a counterexample to Palais’ problem known as the “Kalton-Peck space.”

Speaker: Jeison Moreno Carrillo, Mathematics Student, School of Mathematics, UIS.

Session 250. November 20, 2023

Title: Optimization of Fluid Gathering and Treatment Processes for Colombian Crude Oils.

Abstract: One of the main unit operations in the Oil & Gas (O&G) industry is the separation of fluids produced during oil extraction from reservoirs. One of the main challenges in transporting and refining extracted crude oil is that it contains various constituents, such as water, gas, chlorides, sulfates, and other minerals, which negatively affect these operations. To optimize the crude oil and water separation process, the oil undergoes a dehydration process to remove these impurities and meet industry regulatory requirements for commercialization. This process is monitored daily to support decision-making and identify optimal dilution points according to the viscosity of the crude oil being treated.

In developing a model to predict crude oil viscosity, the different correlations compiled by Sánchez et al. [2] are initially considered for crude oil viscosity at the different temperatures and API gravities evaluated in laboratory studies. Finally, as is well known, crude oil can easily form stable emulsions with water due to the presence of certain surface-active components, such as asphaltenes and resins. These emulsions exhibit a significant increase in apparent viscosity and non-Newtonian shear-thinning behavior, which occur in almost every stage of oil extraction, gathering, and transportation. In particular, due to differences in their internal microstructure, accurately predicting the viscosity and rheological properties of these emulsions is difficult. Based on the work of Shi S., Wang Y., and collaborators in [3], this study presents a model fitted to laboratory data for calculating emulsion viscosity as a function of temperature (°F), brine water cut (%), and properties that depend on the composition of the mixture, specifically density in °API@60°F.

References:

[1] Arenas-Rueda, E.A., Cardona-Romero, C.A., López-Agredo, J.L. & Torres-Ardila, L. (2023). Revisión de ECODIDESH en la estación CHICHIMENE. Parte I, Medellín-Colombia, ICP, 1-50.

[2] Sánchez-Minero, F., Sánchez-Reyna, G., Ancheyta, J., & Marroquin, G. (2014). Comparison of correlations based on API gravity predicting viscosity. Fuel, 138, 193-199.

[3] Shi, S., Wang, Y., Liu, Y., & Wang, L. (2018). A new method for calculating the viscosity. Journal of Petroleum Science and Engineering, 171, 928-937.

[4] Wang, W., Wang, P., Li, K., Duan, J., Wu, K., & Gong, J. (2013). Prediction of the apparent viscosity of non-Newtonian. Petroleum Exploration and Development, 40(1), 130-133.

Speaker: Jorge Leonardo López Agredo, Professor, School of Mathematics, UIS.

Session 249. October 23, 2023

Title: Training a Neural Network Using the Structured BFGS Method.

Abstract: Nonlinear least squares (NLS) problems are common in various areas of science and engineering, where mathematical models are fitted to experimental data in order to minimize the difference between observed values and those predicted by the model. These problems are often nonlinear due to the presence of unknown parameters in the model. Several optimization methods have been developed to address these challenging problems. Three of the most prominent approaches are structured methods: the Gauss-Newton method, the Levenberg-Marquardt method, and the structured BFGS secant method. These optimization methods play a fundamental role in solving nonlinear least squares problems across a wide range of applications. The choice of the most appropriate method depends on the specific nature of the problem and the characteristics of the data, and each approach offers advantages and disadvantages that must be carefully considered when selecting the optimal algorithm. In the context of neural networks, the structured BFGS secant method is used to adjust weights, biases, and errors at each iteration of the learning process.

Speaker: Jhovanny Alexander Gutiérrez Caballero, Mathematics Student, School of Mathematics, UIS.

Session 248. October 9, 2023

Title: Intrinsic Growth Rate and Population Dynamics of Premnotrypes vorax Using Fuzzy Information.

Abstract: The Andean potato weevil (Premnotrypes vorax) is one of the pests responsible for significant damage to potato crops and economic losses for farmers. Therefore, understanding its life cycle and estimating its intrinsic growth rate are crucial for selecting an appropriate chemical control method, reducing environmental impact, and ensuring profitable production suitable for consumption. This talk presents a fuzzy Malthusian model describing the evolution of the Andean potato weevil population in crops, considering both the fuzzy nature of the intrinsic growth rate and the data reported for the problem.

The main contribution and novelty of this work is the estimation of the intrinsic growth rate of the Andean potato weevil as a function of temperature using a Takagi-Sugeno-Kang fuzzy logic rule-based control system. Furthermore, since the initial population of the Andean potato weevil in a crop is, in practice, non-deterministic, once the intrinsic growth rate is known, an initial value problem associated with a fuzzy ODE is proposed and solved to determine the evolution of the population dynamics of the Andean potato weevil. Thus, given an average weekly temperature, it is possible to estimate the Andean potato weevil population per unit area within an interval whose length depends on the degree of uncertainty in the initial population and the intrinsic growth rate.

Speaker: Leidy Vanesa Espitia Cruz, Master’s Student in Mathematics, School of Mathematics, UIS.

. 

Session 234. December 12, 2022

Title: Numerical Analysis of a Mathematical Model Describing the Evolution of Hypoxic Glioma Cells.

Abstract: Glioblastoma belongs to a broad class of brain and spinal cord tumors arising from glial cells, the main brain cells that can develop into neoplasms. These are among the most common types of primary brain tumors and originate from mutations in glial cells of the central nervous system. In this work, a fully discrete, semi-implicit, linear, and decoupled numerical scheme is proposed, using finite differences in time and finite elements (FE) in space to approximate the solutions of the system presented in [1]. Several properties of the scheme are proved, including well-posedness, non-negativity, a maximum principle, uniform estimates, convergence to weak solutions, optimal error estimates, and the asymptotic behavior of the discrete solutions. Additionally, two numerical experiments are presented that reproduce the theoretical results, with simulations performed using the open-source software FreeFem++. Finally, some additional comments are presented on the case of the variable diffusion coefficient D(x,σ) for tumor cells, studying a fully discrete, semi-implicit, linear, and decoupled numerical scheme using finite differences in time and FE in space to approximate the solutions presented in [2]. This scheme has several properties, including well-posedness, positivity, a maximum principle, and asymptotic behavior of the discrete solutions. These results, analogous to those of the continuous case, are similar to those obtained with the numerical scheme proposed for the constant diffusion case D(x,σ) = D_1 > 0. However, this approach is more restrictive, as it assumes a stronger condition on the triangulation of the domain Ω.

References:

[1] M. Conti, S. Gatti and A. Miranville, Mathematical analysis of a model for proliferativeto-invasive transition of hypoxic glioma cells. Nonlinear Anal 189 (2019), 111572.

[2] S. Gatti, An oxygen driven proliferative-to-invasive transition of glioma cells: An analytical study. Discrete and Continuous Dynamical Systems-S (2022), 2233-2248.

[3] J.L. López-Agredo, D.A. Rueda-Gómez, É.J. Villamizar-Roa, Numerical analysis of a mathematical model describing the evolution of hypoxic glioma cells. Submitted (2022).

Speaker: Jorge Leonardo López, Master’s Student in Applied Mathematics, UIS.

Session 233. November 21, 2022

Title: Almost-Fraïssé Banach Spaces.

Abstract: A Banach space is transitive if, given any two points on its unit sphere, there exists an isometry mapping one onto the other. One separable space satisfying this property is l_2, and it is not known whether there is another space distinct from it with this property (the Banach-Mazur problem). One approach to addressing this problem is through its multidimensional version. This is where the objects discussed in this talk arise.

Speaker: Michael Rincón Villamizar, Professor, School of Mathematics, UIS.

Session 232. October 31, 2022

Title: Discussion on Parameter Estimation in Mathematical Epidemiological Models with Random Perturbations.

Abstract: Mathematical epidemiological models are widely used tools for predicting the behavior of infected populations during an epidemic. However, certain difficulties arise when estimating parameters, and these will be addressed in this presentation. Based on these issues, a data updating methodology is proposed to estimate certain parameters in these models, initially applied to two simple models: SIR and SEIR. A model for COVID-19 is then proposed, and the methodology is applied to it. Around mid-2005, models with random perturbations were introduced in [Tornatore]. These models consider climatic fluctuations and any other external factors that may modify the infection rate of an epidemic [Sturrock]. This talk will address several models with random perturbations, an introduction to the concept of the basic reproduction variable, and the possible construction of the Akaike Criterion [Ríos] for model validation.

References:

[Ríos] Ríos, A. Modelos epidemiológicos estocásticos y su inferencia: casos SIS y SEIR. Tesis de Maestría, Universidad Nacional de Colombia, Bogotá D.C., 2019.

[Sturrock] Sturrock, R. N., Frankel, S. J., Brown, A. V., Hennon, P. E., Kliejunas, J. T., Lewis, K. J., … & Woods, A. J. (2011). Climate change and forest diseases. Plant pathology, 60(1), 133-149.

[Tornatore] Tornatore, E., Buccellato, S & Vetro, P. (2005) Stability of a Stochastic SIS System, Physica A. 354, p·g. 1.

Speaker: Andrés Ríos Gutiérrez, Professor, School of Mathematics, UIS.

Session 231. October 24, 2022

Title: Uncomplemented Subspaces in Operator Ideals.

Abstract: The problem of establishing sufficient conditions to determine when the space of compact operators K(E, F) is complemented in the space of bounded linear operators L(E, F) has been extensively studied by many researchers in the field of Functional Analysis.

In this talk, we will examine the following question: Given Banach spaces E and F, is it always the case that K(E, F) = L(E, F), or that K(E, F) is not complemented in L(E, F)?

This question remains an open problem. We will attempt to provide partial solutions to the aforementioned problem, not only for the ideal of compact operators K, but more generally for a broader class of Operator Ideals.

Speaker: Sergio Pérez León, Professor, School of Mathematics, UIS.

Session 230. October 10, 2022

Title: An Introduction to Fuzzy Control Systems.

Abstract: When attempting to explain and model real-world phenomena, we encounter subjective or imprecise information involving a certain degree of uncertainty. Although this information can be communicated, it cannot be interpreted by a computer using classical logic. To address this uncertainty, Lotfi A. Zadeh developed a multivalued logic known as fuzzy logic in 1965. Fuzzy logic extends the classical concepts of set operations, logical operators, and fuzzy relations. It also introduces concepts such as linguistic variables to establish the notions of fuzzy propositions and fuzzy implications.

One of the most important applications of fuzzy logic is the development of control systems capable of representing human experience and knowledge. These control systems based on fuzzy logic rules are known as fuzzy control systems. There are essentially two inference systems, giving rise to the Mamdani model and the Takagi-Sugeno-Kang (T.S.K.) model. These models can be used in fields such as agroindustry, for example, to control pesticide concentration for effective spraying in blackberry crops through a Mamdani control system. They can also be used to determine the growth rate of a pest through a Takagi-Sugeno-Kang (T.S.K.) control system in order to study the behavior of a population over time.

Speaker: Leidy Vanesa Espitia, Master’s Student in Mathematics, UIS.