Aiming at new possibilities for the diagnosis of Parkinson's Disease

A NeuroMat-led initiative has aimed at developing a new tool for early diagnosis of Parkinson's Disease. This initiative relies on a game to identify behaviorial patterns associated to this disease in a cost efficient way. Parkinson's Disease is a degenerative disorder of the nervous system and affects 1% of the world population of over 65 years, according to the Association Brazil Parkinson. This work is part of the NeuroMat-led network AMPARO.

An almost virtual museum

The NeuroMat dissemination team has led the release of images from museums at the University of São Paulo to an open media repository, and this initiative has now been started with the Paulista Museum. Eduardo Nunomura, Carta Capital, 9/13/2017.

Multi-class oscillating systems of interacting neurons

Susanne Ditlevsen and Eva Löcherbach

We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each class can be described by a nonlinear limit differential equation driven by a Poisson random measure, and state associated central limit theorems. We study situations in which the limit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markov processes and their diffusion approximations.

The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton-Milner family

Jie Han and Yoshiharu Kohayakawa

The celebrated Erdos–Ko–Rado theorem determines the maximum size of a k-uniform intersecting family. The Hilton–Milner theorem determines the maximum size of a k-uniform intersecting family that is not a subfamily of the so-called Erdos–Ko–Rado family. In turn, it is natural to ask what the maximum size of an intersecting k-uniform family that is neither a subfamily of the Erdos–Ko–Rado family nor of the Hilton–Milner family is. For k ≥ 4, this was solved (implicitly) in the same paper by Hilton–Milner in 1967. We give a different and simpler proof, based on the
shifting method, which allows us to solve all cases k ≥ 3 and characterize all extremal families achieving the extremal value.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

Ariadne A. Costa, Ludmila Brochini and Osame Kinouchi

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

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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).

 

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