Method to assess the mismatch between the measured and nominal parameters of transcranial magnetic stimulation devices

Zacharias L. R., Peres A. S. C., Souza V. H., Conforto A. B. and Baffa O.
Background
Small variations in TMS parameters, such as pulse frequency and amplitude may elicit distinct neurophysiological responses. Assessing the mismatch between nominal and experimental parameters of TMS stimulators is essential for safe application and comparisons of results across studies.

Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Pierre Hodara and Ioannis Papageorgiou

We aim to prove Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Löcherbach to describe the behavior of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e., which lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system. The process studied by Galves and Löcherbach is a point process counting the spike events of the system and is therefore non-Markovian. In this work, we consider a process describing the membrane potential of each neuron that contains the relevant information of the past. This allows us to work in a Markovian framework.

A mathematical object for retrieving the structure of stimuli in EEG data

A recent NeuroMat paper has addressed the conjecture that the brain identifies structures from sequences of stimuli. It means that in order to make predictions the brain analyzes structured  sequences of stimuli and retrieves from them statistical regularities. This classical conjecture is often called "Statistician Brain Conjecture" and is associated to studies on how one learns. The NeuroMat research team has introduced a new class of stochastic processes --sequences of random objects driven by chains with memory of variable length-- to address this conjecture.

Retrieving a Context Tree from EEG Data

Aline Duarte, Ricardo Fraiman, Antonio Galves, Guilherme Ost and Claudia D. Vargas

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli. Here, we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes, namely, sequences of random objects driven by chains with memory of variable length.

The whole paper is available here.

Discrete One-Dimensional Coverage Process on a Renewal Process

Sandro Gallo and Nancy L. Garcia

Consider the following coverage model on \mathbb {N}, for each site i \in \mathbb {N}associate a pair (\xi _i, R_i) where (\xi _i)_{i \ge 0} is a 1-dimensional undelayed discrete renewal point process and (R_i)_{i \ge 0} is an i.i.d. sequence of \mathbb {N}-valued random variables. At each site where \xi _i=1 start an interval of length R_i. Coverage occurs if every site of \mathbb {N} is covered by some interval. We obtain sharp conditions for both, positive and null probability of coverage. As corollaries, we extend results of the literature of rumor processes and discrete one-dimensional Boolean percolation.

The whole paper is available here.

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