Antonio Galves, Charlotte Galves, Jesús E. García, Nancy L. Garcia, Florencia Leonardi
The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.
Artem Logachov, A. Mogulskii and Anatoly Yambartsev
Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.
Andressa Cerqueira, Aurélien Garivier and Florencia Leonardi
In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.
We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced by Galves and Löcherbach. As a result, we obtain concentration properties for empirical approximations of the process.
Fernando Borges, Paulo Protachevicz, Rodrigo Pena, Ewandson Lameu, Guilherme Higa, Fernanda Matias, Alexandre Kihara, Chris Antonopoulos, Roberto de Pasquale, Antonio Roque, Kelly Iarosz, Peng Ji and Antonio Batista
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means of studying intracellular recordings from CA1 neurons in rats and results from numerical simulations, we demonstrate that self-sustained activity presents high variability of patterns, such as low neural firing rates and activity in the form of small-bursts in distinct neurons. In our numerical simulations, we consider random networks composed of coupled, adaptive exponential integrate-and-fire neurons. The neural dynamics in the random networks simulates regular spiking (excitatory) and fast spiking (inhibitory) neurons. We show that both the connection probability and network size are fundamental properties that give rise to self-sustained activity in qualitative agreement with our experimental results. Finally, we provide a more detailed description of self-sustained activity in terms of lifetime distributions, synaptic conductances, and synaptic currents.
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