Icms Complexity Science Winter School

Lecture 1: Feedback, sensitivity, and complexity A central paradigm of control theory is that feedback shapes sensitivity. This lecture will review the basics of this theory and its relevance to analyse complex systems, when understood as large networks of interconnected systems. Lecture 2: Sensitivity analysis of neuronal behaviors The heritage of Hodgkin and Huxley confers a unique place to neurophysiology in the general challenge of assisting biological experimentation with mathematical modeling. Detailed quantitative knowledge of the ion channels controlling the excitability of a specific neuron type can be incorporated in conductance based models, leading to mathematical models governed by high-dimensional nonlinear differential equations that can simulate experimental predictions with great accuracy. Ever increasing computational power and improving knowledge about the connectome of neural circuits thus suggest the possibility of reliable simulation of large scale neural simulations. In this second lecture, we will review the modeling principles of those behaviors and illustrate that some of the simplest sensitivity analysis questions of an experimentalist are intractable or extremely fragile in this nonlinear state-space framework. We will contrast the complexity of large-scale conductance-based models with the simplicity of neuronal behaviors that they aim at reproducing. This calls for alternative modeling principles with a narrower gap between experimental questions and model-based answers. We will argue that excitability is at the core of neuronal behaviors and that the specifics of excitability pave the way to local analysis methods. Lecture 3: Switchlets: analysis and design of multiresolution sensitivity Balancing positive and negative feedback provides a versatile mechanism to localize the sensitivity of a behavior in a given window. And the mixed feedback amplifier is the essence of excitable behaviors. This third lecture will illustrate how localized behaviors can be interconnected to create behaviors that can be analyzed and designed at different resolutions. Biography Rodolphe Sepulchre is Professor of Engineering at Cambridge University and a fellow of Sidney Sussex College. His research interests are in nonlinear dynamics, control and optimization. He is currently Editor-in-Chief of Systems and Control Letters and has been an Associate Editor for SIAM Journal of Control and Optimization, the Journal of Nonlinear Science, and Mathematics for Control, Signals, and Systems. In 2008, he was awarded the IEEE Control Systems Society Antonio Ruberti Young Researcher Prize. He is an IEEE fellow and an IEEE CSS distinguished lecturer since 2010. His current research interests are in nonlinear control and optimization, distributed control and synchronization, and the analysis of neuronal behaviors.