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Stochastic chains with unbounded memory applied in neuroscience

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Ricardo Felipe Ferreira
Total Authors: 1
Document type: Doctoral Thesis
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
Defense date:
Examining board members:
Alexsandro Giacomo Grimbert Gallo; Christophe Frederic Gallesco; Nancy Lopes Garcia; Ludmila Brochini Rodrigues; Daniel Yasumasa Takahashi
Advisor: Alexsandro Giacomo Grimbert Gallo

Stochastic chains with unbounded memory are a natural generalization of Markov chains, in the sense that the transition probabilities may depend on the whole past. These process, introduced independently by Onicescu and Mihoc in 1935 and Doeblin and Fortet in 1937, have been receiving increasing attention in the probabilistic literature, because they form a class richer than the Markov chains and have practical capabilities modelling of scientific data in several areas, from biology to linguistics. In this work, we use them to model interactions between spike trains. Our main goal is to develop new mathematical results about stochastic chains with unbounded memory. First, we study conditions that guarantee the existence and uniqueness of stationary chains compatible with a discontinuous family of transition probabilities. Then, we address the understanding of the phenomenology of spike trains and we propose to use directed information to quantify the information flow from one neuron to another. In this occasion, we fix concentration bounds for directed information estimation. (AU)

FAPESP's process: 16/12918-0 - Stochastic chains with unbounded memory and application in neuroscience
Grantee:Ricardo Felipe Ferreira
Support Opportunities: Scholarships in Brazil - Doctorate