Normal Forms and Sparse Reconstruction for Networks

• Grant number: 23/04294-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2023
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Sajjad Bakrani Balani
• 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

Abstract

In the theory of dynamical systems, normal forms are considered as simple sparse forms of systems. On the other hand, in the reconstructing of a system using data, assuming the desired system is sparse, a natural question is the possible connection between the normal form of this system and the system that the sparse recovery recovers. A recent work of Nijholt, et al, 2022, shows that having data of a network of systems, each defined near a Hopf bifurcation, in hand, the sparse recovery indeed recovers the normal form it. This has an important impact on the field of network science, since if the desired system describes the dynamics of a sparse network but, the sparse reconstruction recovers the normal form of it, then it suggests that the network topology might be better described by a hyper-network. In this project, our aim is to establish connections between normal form theory and data-driven sparse recovery. We will study the conditions for which the sparse recovery recovers the normal form of a system, and whether or not this reconstruction is unique. Establishment of connections between the normal form theory and the sparse recovery methods can also lead to an important progress in the later field since, started from the late 19th century, the literature on the normal form theory is very rich and well-studied.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BAKRANI, SAJJAD; KIRAN, NARCICEGI; EROGLU, DENIZ; PEREIRA, TIAGO. Cycle-Star Motifs: Network Response to Link Modifications. JOURNAL OF NONLINEAR SCIENCE, v. 34, n. 4, p. 34-pg., 2024-08-01. (23/04294-0, 13/07375-0)