Publicações

A test of hypotheses for random graph distributions built from EEG data

Andressa Cerqueira, Daniel Fraiman, Claudia D. Vargas, Florencia Leonardi

The theory of random graphs is being applied in recent years to model neural interactions in the brain. While the probabilistic properties of random graphs has been extensively studied in the literature, the development of statistical inference methods for this class of objects has received less attention. In this work we propose a non-parametric test of hypotheses to test if two samples of random graphs were originated from the same probability distribution.

Minimum number of edges in a hypergraph guaranteeing a perfect fractional matching and the MMS conjecture

Vladimir Blinovsky

In this paper we prove the Ahlswede-Khachatrian conjecture [1] up to a finite number of cases, which can be checked using modern computers. This conjecture implies the conjecture from [2] and the Manickam-Miklós-Singhi conjecture.

The whole paper is available here.

Modeling networks of spiking neurons as interacting processes with memory of variable length

Antonio Galves, Eva Löcherbach

We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given time. The system evolves as follows. For each component, the rate (in continuous time) or the probability (in discrete time) of having a spike depends on the entire time evolution of the system since the last spike time of the component.

Identifying interacting pairs of sites in Ising models on a countable set

Antonio Galves, Enza Orlandi and Daniel Yasumasa Takahashi

This paper addresses the problem of identifying pairs of interacting sites from a finite sample of independent realizations of the Ising model. We consider Ising models in a infinite countable set of sites under Dobrushin uniqueness condition. The observed sample contains only the values assigned by the Ising model to a finite set of sites. Our main result is an upper bound for the probability of misidentification of the pairs of interacting sites in this finite set.

Stochastically Perturbed Chains of Variable Memory

Garcia, N. L. and Moreira, L. - In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider a chain of variable memory on a finite alphabet containing zero, at each instant of time an independent coin is flipped and if it turns head a contamination occurs.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

Ribeiro, T. L. ; Ribeiro, S. ; Belchior, H. ; Caixeta, F. and Copelli, M. - The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent τ=3/2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally.

Hydrodynamic limit for interacting neurons

De Masi, A. ; Galves, A. ; Löcherbach, E. and Presutti, E. - This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses.

Independence tests for continuous random variables based on the longest increasing subsequence

García, J. E. and González-López, V. A. - We propose a new class of nonparametric tests for the supposition of independence between two continuous random variables X and Y. Given a size n sample, let π be the permutation which maps the ranks of the X observations on the rank of the Y observations.

Modeling of acoustic signal energies with a generalized Frank copula. A linguistic conjecture is reviewed

García, J. E. and González-López, V. A. - In this paper was selected a generalized Frank copula to model the dependence between the energy on two frequency bands of the speech signal, coming from eight languages. Was developed an algorithm that uses maximum likelihood to choose the best fitting copula's parameters.


Loss of Memory of Hidden Markov Models and Lyapunov Exponents

Collet, P. and Leonardi, F. - In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices.


Páginas

 

NeuroMat

O Centro de Pesquisa, Inovação e Difusão em Neuromatemática está sediado na Universidade de São Paulo e é financiado pela FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo).

 

Login do usuário

 

Contato

Endereço:
Rua do Matão, 1010 - Cidade Universitária - São Paulo - SP - Brasil. 05508-090. Veja o mapa.

Telefone:
55 11 3091-1717

Email:
neuromat@numec.prp.usp.br

Contatos de mídia:
comunicacao@numec.prp.usp.br