Dr. Rodolphe Sepulchre

Biography

Professor Sepulchre’s research aims at developing novel mathematical tools for modelling, analysis, and synthesis of nonlinear signals and systems. His work addresses data that inherently lie in constrained nonlinear spaces, focusing on manifold optimization and providing a novel algorithmic framework for generic optimization tools in processing data specific to these nonlinear contexts. His applications extend to nonlinear statistical processing, including Independent Component Analysis and sparse Principal Component Analysis, as well as low-rank optimization and matrix completion. Additionally, he explores synchronization, coordination, and consensus problems which are central to collective dynamics within distributed multi-scale dynamical systems. A significant aspect of his research addresses challenges posed by the nonlinear nature of system theory in neural behaviors, developing new sensitivity analysis tools based on local analysis of singular points to organize global behavior, which can be applied to enhance robustness and homeostasis in neural functions. His strategic themes include manufacturing, the design of materials, and distributed architectures for multi-scale control problems, with a main focus on bioengineering, particularly advancing the understanding of the role of oscillations in the brain across both time and spatial scales.

Research Interests