Systems with infinitely many point processes with interactions of variable length in space and time

• Grant number: 23/01264-3
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2023
• End date: November 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Jefferson Antonio Galves
• Grantee: Eduardo Janotti Cavalcante
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID

Abstract

We consider the class of models introduced by A. Galves and Löcherbach 2013 in discrete timeand by De Masi et al. 2014 in countinuous time. These processes are systems of interactingpoint processes with memory of variable length. They provide a realistic description of nets ofspiking neurons. This Ph.D. project continues the study of this class of processes by addressingthe following question. What does the time evolution of a subset of components reveal aboutthe main features of the system's interaction graph? (AU)