Ciclo de Palestras – Segundo Semestre de 2024

Coordenação: Professora Maria Eulalia Vares e Widemberg da Silva Nobre

As palestras ocorrem de forma presencial às quartas-feiras às 15h30 na sala I-044-B, a menos de algumas exceções devidamente indicadas.

Lista completa (palestras previstas para datas futuras podem sofrer alterações)

We consider the classical 2-opinion dynamics known as the voter model on regular random graphs and study the evolution for the discordant edges (i.e. with different opinions at their end vertices) which clarify what happens before the consensus time scale both in the static and in the dynamic graph setting. Further, in the dynamic geometrical setting we can see how consensus is affected as a function of the graph dynamics. Based on recent and ongoing joint works with Luca Avena, Rajat Hazra, Frank den Hollander and Matteo Quattropani.

In this talk, we introduce the Bernoulli percolation model and consider inhomogeneous percolation on random environments on the graph GxZ, where G is an infinite quasi-transitive graph and Z is the set of integers. In 1994, Madras, Schinazi and Schonman showed that there is no percolation in Z^d if the edges are open with a probability of q<1 if they lie on a fixed deterministic axis and with a probability of p<p_c(Z^d) otherwise. Here, we consider a random region given by boxes with iid radii centered along the axis 0xZ of GxZ. We allow each edge to be open with a probability of q<1 if it is inside this region and with a probability of p<p_c(GxZ) otherwise. The goal of the talk is to show that occurrence or not of percolation in this inhomogeneous model depends on how sparse and how large are the boxes placed along the axis. We aim to give sufficient conditions on the moments of the radii as a function of the growth of the graph G for percolation not to occur.
This is a joint work with Rémy Sanchis and Daniel Ungaretti.

An initial screening of which covariates are relevant is a common practice in high-dimensional regression models. The classic feature screening selects only a subset of covariates correlated with the response variable. However, many important features might have a relevant albeit highly nonlinear relation with the response. One screening approach that handles nonlinearity is to compute the correlation between the response and nonparametric functions of each covariate. Wavelets are powerful tools for nonparametric and functional data analysis but are still seldom used in the feature screening literature. In this talk, we introduce a wavelet feature screening method that can be easily implemented. Theoretical and simulation results show that the proposed method can capture true covariates with high probability, even in highly nonlinear models. We also present an example with real data in a high-dimensional setting. This is a joint work with Pedro Morettin and Aluísio Pinheiro.

A detecção da origem de uma epidemia é o problema de identificar o nó da rede que deu origem a uma epidemia a partir de uma observação parcial do processo epidêmico. O problema encontra aplicações em diferentes contextos, como detectar a origem de rumores em redes sociais. Neste trabalho consideramos um processo epidêmico em uma rede finita que começa em um nó aleatório (origem epidêmica) e termina quando todos os nós são infectados, produzindo uma árvore epidêmica enraizada e direcionada que codifica as infecções. Assumindo o conhecimento da rede subjacente e da árvore não direcionada (ou seja, as arestas da infecção, mas não suas direções), é possível inferir a origem da epidemia? Este trabalho aborda esse problema introduzindo o epicentro, um estimador para a origem da epidemia.