Dynamics of complex heterogeneous networks: reduction techniques

• Grant number: 18/26107-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2019
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Zheng Bian
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
• Associated scholarship(s): 21/11091-3 - Probabilistic reduction principle in complex network dynamics, BE.EP.DR

Abstract

Recent results have revealed that typical networks have multiple scales characterised by different levels of connectivity. These heterogeneous networks exhibit coherent behaviour at various connectivity scales. Striking examples are found in the brain, where the coherent dynamics between highly connected neurons shapes the network. These important coherent phenomena are high-dimensional and vastly unexplored. The major challenge is to develop dimension reduction principles at different network scales that allow the description of the coherent behaviour. The goal of this proposal is to establish a theory for multiscale coherence in heterogeneous networks. We aim at following objective. A probabilistic theory for complex networks. This theory will provide a low-dimensional description over finite time scales. Thereby, it allows for a description of collective phenomena in terms of the network structure. A theory for emergent phenomena explains how the interactions affect the system and opens the possibility to predict critical transitions by reconstructing the network dynamics from data. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BIAN, Zheng. Rigorous mean-field dimensional reduction in heterogeneous network dynamics. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.