O instituto promove pesquisa fundamental e interdisciplinar, integrando matemática, estatística, probabilidade, ciência de dados, processamento de sinais, otimização e inteligência artificial, com aplicações em neurociência e ciências da saúde, desenvolvidas em colaboração com o CEPID/CEPIX NeuroMat.

Recent Papers (arXiv)

• Optimal recovery by maximum and integrated conditional likelihood in the general Stochastic Block Model
  Andressa Cerqueira, Florencia Leonardi
  [Submitted on 16 Nov 2023 (v1), last revised 27 Feb 2024 (this version, v2)]

  In this paper, we obtain new results on the weak and strong consistency of the maximum and integrated conditional likelihood estimators for the community detection problem in the Stochastic Block Model with k communities. In particular, we show that maximum conditional likelihood achieves the optimal known threshold for exact recovery in the logarithmic degree regime. For the integrated conditional likelihood, we obtain a sub-optimal constant in the same regime. Both methods are shown to be weakly consistent in the divergent degree regime. These results confirm the optimality of maximum likelihood on the task of community detection, something that has remained as an open problem until now.

• Growth Models Under Uniform Catastrophes
  Joan Amaya, Valdivino V. Junior, Fábio P. Machado, Alejandro Roldán-Correa
  [Submitted on 6 Feb 2026]

  We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events. For these models, we derive explicit expressions for the survival probability and the mean time to extinction, both with and without spatial constraints. In addition, we complement this analysis by comparing uniform catastrophes with binomial and geometric catastrophes in models with dispersion and no spatial restrictions. Here, the terms uniform, binomial and geometric refer to the probability distributions governing the number of individuals that survive immediately after a catastrophe. This comparison allows us to quantify the impact of different types of catastrophic events on population persistence.

• Scaling limits of the Bouchaud and Dean trap model on Parisi's tree in ergodic and aging time scales
  Luiz Renato Fontes, Andrea Hernández
  [Submitted on 26 May 2025 (v1), last revised 14 Oct 2025 (this version, v2)]

  We take scaling limits of the Bouchaud and Dean trap model on Parisi's tree in time scales where the dynamics is either ergodic (close to equilibrium) or aging (far from equilibrium). These results follow from a continuity theorem formulated for a certain kind of process on trees, which we call a cascading jump evolution, defined in terms of a collection of jump functions, with a cascading structure given by the tree.

• The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks
  Nancy Lopes Garcia, Denis Araujo Luiz, Daniel Miranda Machado
  [Submitted on 24 Nov 2025]

  We investigate rumor spreading in a generalized Maki-Thompson model with spontaneous stifling, evolving on quasi-transitive networks. Individuals are either ignorants, spreaders, or stiflers; spreaders stop by contact with other spreaders or stiflers or after an independent random waiting time sampled from a given distribution, modeling a spontaneous loss of interest. The topology of the underlying population network is incorporated by modeling it as a broad class of symmetric networks, whose vertices are partitioned into finitely many orbit types. This yields a unified framework for homogeneous and heterogeneous networks. For sequences of finite quasi-transitive graphs, and for infinite quasi-transitive graphs with subexponential growth, we establish a Functional Law of Large Numbers and a Functional Central Limit Theorem for the densities of each vertex type for the three states. The mean-field limit is described by a system of nonlinear integral equations, while fluctuations are asymptotically Gaussian and governed by a system of stochastic integral equations with explicit covariance. Our results show how the topology and the law of spontaneous stifling jointly shape the speed and variability of rumor outbreaks. As a special case, our model reduces to the classical Maki-Thompson model when spontaneous stifling is absent.

• Finite-sample properties of the trimmed mean
  Roberto I. Oliveira, Paulo Orenstein, Zoraida F. Rico
  [Submitted on 7 Jan 2025]

  The trimmed mean of n scalar random variables from a distribution P is the variant of the standard sample mean where the k smallest and k largest values in the sample are discarded for some parameter k. In this paper, we look at the finite-sample properties of the trimmed mean as an estimator for the mean of P. Assuming finite variance, we prove that the trimmed mean is ``sub-Gaussian'' in the sense of achieving Gaussian-type concentration around the mean. Under slightly stronger assumptions, we show the left and right tails of the trimmed mean satisfy a strong ratio-type approximation by the corresponding Gaussian tail, even for very small probabilities of the order e^{-n^c} for some c>0. In the more challenging setting of weaker moment assumptions and adversarial sample contamination, we prove that the trimmed mean is minimax-optimal up to constants.