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IM Stochastic Adding Machines Noticia1Title: Stochastic Adding Machines
Speaker: Ali Messaoudi (Unesp, São José do Rio Preto)
Date: 25/09/2023
Horário: 3:30 p.m. to 4:30 p.m.
Local: C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.

Abstract: A stochastic adding machine (defined in [PR Killeen and T. J. S. Taylor, Nonlinearity 13 (2000), no. 6, 1889–1903]) is a Markov chain whose states are natural integers, which models the process of adding the number $1$ but where there is a probability of failure in which a carry is not performed when necessary.
In this lecture, we will talk about probabilistic properties of extensions for the stochastic adding machine and their connections with other areas of mathematics such as Complex Dynamics and Linear Dynamics.
This is a joint work with Danilo Caprio and Glauco Valle.

More complete information about the seminars can be found clicking HERE..


Organizers: Giulio Iacobelli e Maria Eulalia Vares

11 09 IM ProbabilitySeminar noticiaTítulo: Central Limit Theorem for the limit process of the discrete time RAP seen from the origin
Palestrante: Mariela Pentón Machado (IME-USP)
Data: 18/09/2023
Horário: 3:30 p.m. to 4:30 p.m.
Sala: C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.

Resumo: Pablo Ferrari and Luiz Renato Fontes introduced The Random Average Process (RAP) in 98. We are interested in the discrete-time version of the RAP. This process is a random surface whose heights evolve taking a convex combination of the previous heights. In this dynamic, a random matrix of probabilities with independent and identically distributed rows determines the weights of the convex combinations. The process seen from the height in the origin is the random surface result of subtracting the height in the origin to all the heights in the initial surface. Under certain conditions, Ferrari and Fontes proved in 98 the existence of a limit process for the process seen from the height of the origin. In this talk I will discuss a Central Limit Theorem in the spacial variable for the limit process seen from  the height in the origin.  This is a joint work with Luiz Renato Fontes and Leonel Zuaznabar.

More complete information about the seminars can be found clicking HERE.

Organizers: Giulio Iacobelli e Maria Eulalia Vares


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08 09 IM COLMEA noticiaTitulo:  Modeling the Spatio-temporal Spread of COVID-19 via a Reaction-diffusion System. 
Palestrante: Malú Grave (UFF)
Data: 13/09/2023
Horário: 14:30h
Local: Auditório RAV 62, 6o andar, Bloco F UERJ — Campus Maracanã Rua São Francisco Xavier, 524 Maracanã, Rio de Janeiro - RJ
Resumo: The COVID-19 outbreak in 2020 sparked significant interest in mathematical models of infectious diseases. These models categorize the population into compartments based on characteristics. While often expressed as ordinary differential equation (ODE) models, which depend solely on time, recent research has explored partial differential equation (PDE) models, particularly reaction-diffusion models that incorporate spatial variation in epidemics. These PDE models, within the Susceptible, Infected, Exposed, Recovered, and Deceased (SEIRD) framework, have shown promise in describing COVID-19’s progression. However, the rapid movement of people over long distances can result in nonlocal disease transmission, a phenomenon not well represented by diffusion alone. In contrast, ODE models can account for this by treating different regions as network nodes, connected by edges to represent nonlocal transmission. To address these complexities, a reaction-diffusion PDE model is developed with an integrated network structure. This approach aims to enhance our understanding and prediction of COVID-19 contagion dynamics in a more realistic and comprehensive way.

Titulo 2: Generation of Uniform Point Distributions on Hyper-Surfaces: Methods and Application
Palestrante: Lisandro Lovisolo (UERJ)
Data: 13/09/2023
Horário: 16:10h 
Local: Auditório RAV 62, 6o andar, Bloco F UERJ — Campus Maracanã Rua São Francisco Xavier, 524 Maracanã, Rio de Janeiro - RJ
Resumo: In many applications, it is necessary to obtain point arrangements on a hypersphere (or Nsphere) that are approximately uniform from a geometric perspective, i.e., with approximately constant angles between each point and its nearest neighbors. We discuss the use of these distributions in various applications. This problem is trivial in a two-dimensional space (N=2), and there are known solutions for certain quantities of points (K) in specific-dimensional spaces (N). On the other hand, the problem of selecting points uniformly distributed in a probabilistic sense is solved using Gaussian random variables. We describe how to generate geometric arrangements of approximately K uniformly distributed points on an N-sphere from uniform point distributions on the N-sphere.

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IM Palestra Seminário NOTICIATitulo:  Asymptotic description for the localized solution of the Cauchy problem for the  wave equation with fast-oscillating coefficient.
Palestrante: Sergey Sergeev (PUC-Rio)
Data: 23/08/2023
Horário: 12h
Sala: C-119
Resumo: We consider the Cauchy problem with localized initial conditions for the multidimensional wave equation. The coefficient of this wave equation is assumed to be fast-oscillating. We are interested in the asymptotic (while localization parameter of initial condition is small) description of the given Cauchy problem. Such formulation leads to the appearance of two small parameters: the localization parameter and the parameter of oscillating in the wave equation coefficient. The ratio between the given parameters is crucial and affects the form of the main part of the asymptotic solution. We use  the homogenization procedure which takes into account this ratio and as result we obtain the equation with smooth coefficients. This equation is of the form of the wave equation with dispersion correction, which appears due to the homogenization procedure. The main part of the asymptotic solution for the initial Cauchy problem thus can be described with the help of the asymptotic solution of the homogenized equation with the smooth coefficients  and can be presented in the analytical form with the help of the Airy functions and related to them.