Department of Electrical Engineering
I am focusing on the application of mathematics to the modeling and analysis of neuronal dynamics. My theoretical investigation is accompanied by a tight interaction with electrophysiologists, leading to a fruitful co-existence of rigorous mathematics and physiological soundness, in a continuous ping-pong between experimental observations and theoretical predictions.
In practice, I use tools from bifurcation theory, differential geometry, geometrical singular perturbations, and nonlinear control to help understanding (via modeling and analysis) experimental observations obtained by research partners in Liege University and Brandeis University. Beside the pure scientific interest, we also explore therapeutic applications in different neurodegenerative diseases, such as Parkinson's disease.
Beside neuronal dynamics, I am charmed by the application of mathematics to description of our physical world in general. During my graduate studies in theoretical physics I had the pleasure of being scattered and curved by quantum field theory and general relativity, but the biological universe eventually attracted me more than any black hole or missing particle :-)
af529 (at) cam . ac . uk
T. O'Leary, A. H. Williams, A. Franci, and and E. Marder (2014) Cell types, network homeostasis and pathological compensation from a biologically plausible ion channel expression model Accepted for publication in Neuron.
G. Drion, A. Franci, V. Seutin, and R. Sepulchre (2013) Modulation and Robustness of Endogenous Neuronal Spiking Submitted. Preprint available on arXiv
A. Franci, G. Drion, and R. Sepulchre (2013) Modeling neuronal bursting: singularity theory meets neurophysiology Accepted for publication in SIAM J Appl Dyn Syst. Preprint available on arXiv
A. Franci*, G. Drion*, V. Seutin, and R. Sepulchre (2013) A balance equation determines a switch in neuronal excitability, PLoS Comput Biol, 9(5):e1003040. *Double first author. Preprint available on arXiv
A. Franci*, G. Drion*, and R. Sepulchre (2012) An organizing center in a planar model of neuronal excitability, SIAM J Appl Dyn Syst, 11(4):1698-1722. *Double first author. Preprint available on arXiv
G. Drion*, A. Franci*, V. Seutin, and R. Sepulchre (2012) A novel phase portrait for neuronal excitability, PLoS ONE, p. e41806. *Double first author. Preprint available on arXiv
A. Franci, A. Chaillet, E. Panteley, and F. Lamnabhi-Lagarrigue (2012) Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback, Math. Control Signals Syst. - Special Issue on Large-Scale Nonlinear Systems 24(1):169-217 - Regular paper
A. Franci, A. Chaillet, and W. Pasillas-Lépine (2011) Existence and robustness of phase-locking in Kuramoto oscillators under mean-field feedback, Automatica - Special Issue on Systems Biology 47(6):1193-1202 - Regular paper
A. Franci and A. Chaillet (2010) Quantized control of nonlinear systems: a robust approach, International Journal of Control, 83(12):2453-2462
*Nov. 2008-Apr. 2012: 3 years Ph.D. in Control Theory "Pathological synchronization in neuronal
populations: a control theoretic persepctive", at L2S - Univ. Paris Sud 11 - Supélec (My Ph.D. thesis)
*2006-2008: Master 2 "Theoretical Physics" within University of Pisa, concluded in October 2008 with honors
*2002-2006: Bachelor "Physics" within University of Pisa (Italy), concluded in January 2006 with honors