Jonathan Touboul

Professor of Mathematics

Departments/Programs

Mathematics
Neuroscience
Summer School Program
Volen National Center for Complex Systems

Degrees

École Polytechnique, Ph.D.
University of Paris VI, M.S.

Expertise

Applied Mathematics, Models in Neuroscience, Ecology, Embryonic Development, Dynamical Systems, Probability and Stochastic Processes.

Profile

Please visit my new faculty profile page.

My research lies at the boundary between mathematics and biology. I chiefly using tools from dynamical systems and stochastic theory to model neuronal activity, competition between ecological species and embryonic development. Dynamical Systems and Stochastic processes allow describing properties of systems evolving in time, possibly partly randomly. I have used these tools to describe the role of disorder, fluctuations and unpredictability in neural computations, with a particular interest in understanding the interplay of structure and function in the brain, from models of single cells activity up to macroscopic limits of large stochastic neuronal areas. I have also worked on the functional organization of the visual cortex in search for their organizing principles, but also on the mechanisms leading, during embryonic development, to the emergence of appropriate brain phenotypes.
My approach often involves data analysis, simplified mathematical models, computer simulations and theoretical and mathematical analysis, using dynamical systems and probability. And in this program, I enthusiastically collaborate with experimentalists, mathematicians and physicists!

Courses Taught

MATH	36a	Probability
MATH	121a	Mathematics for Natural Sciences
MATH	123a	Principles of Mathematical Modeling and Applications to Biology
MATH	126a	Introduction to Stochastic Processes and Models
MATH	161a	Advanced Bifurcation Analysis in Dynamical Systems
NEUR	91g	Introduction to Research Practice

Awards and Honors

NSF DMS Grant Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions (2020 - 2023)

Scholarship

Destexhe, Alain and Touboul, Jonathan. "Is there sufficient evidence for criticality in cortical systems?." eNeuro (2021). (forthcoming)

Rubin, Jonathan, Signerska-Rinkowska, Justyna and Touboul, Jonathan. "Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models." SIAM Journal on Applied Dynamical Systems (2021). (forthcoming)

Samuel Dahan, Jason Lam, Dan Sfedj and Jonathan Touboul. "Predicting Employment Notice Period with Machine Learning: Promises and Limitations." McGill Law Journal (2021). (forthcoming)

Alberto Romagnoni, Matthew Colonnese, Jonathan Touboul, Boris Gutkin. "Development of inhibitory synaptic delay drives maturation of thalamocortical network dynamics." Journal of Neurophysiology (2020).

Alex Mendes, Gaëtan Vignoud, Sylvie Perez, Elodie Perrin, Jonathan Touboul and Laurent Venance. "Concurrent thalamostriatal and corticostriatal spike-timing-dependent plasticity and heterosynaptic interactions shape striatal plasticity map." Cerebral Cortex (2020).

Alexandre Mendes, Gaetan Vignoud, Sylvie Perez, Elodie Perrin, Jonathan Touboul, Laurent Venance. "Concurrent Thalamostriatal and Corticostriatal Spike-Timing-Dependent Plasticity and Heterosynaptic Interactions Shape Striatal Plasticity Map." Cerebral Cortex 30. 8 (2020): 4381-4401.

Charlotte Piette, Jonathan Touboul, Laurent Venance. "Engrams of Fast Learning." Frontiers in Cellular Neuroscience 14. (2020): 342.

Denis D. Patterson, Simon A. Levin, A. Carla Staver & Jonathan D. Touboul. "Probabilistic foundations of spatial mean-field models in ecology and applications." SIAM Journal on Applied Dynamical Systems 19. 4 (2020): 2682–2719.

J. Touboul, C. Piette, L. Venance, G. Bard Ermentrout. "Noise-induced synchronization and anti-resonance in interacting excitable systems; Applications to Deep Brain Stimulation in Parkinson’s Disease." Physical Review X 10. (2020): 011073.

Margarete Diaz-Cuadros, Daniel E. Wagner, Christoph Budjan, Alexis Hubaud, Oscar A. Tarazona, Sophia Donelly, Arthur Michaut, Ziad Al Tanoury, Kumiko Yoshioka-Kobayashi, Yusuke Niino, Ryoichiro Kageyama, Atsushi Miyawaki, Jonathan Touboul & Olivier Pourq. "In vitro characterization of the human segmentation clock." Nature (2020).

Quiñinao, Cristobal and Touboul, Jonathan. "Clamping and Synchronization in the strongly coupled FitzHugh-Nagumo model." SIAM Journal on Applied Dynamical Systems 19. 2 (2020): 788–827.

Richard Bailleul, Marie Manceau, Jonathan Touboul. "A “Numerical Evo-Devo” Synthesis for the Identification of Pattern-Forming Factors." Cells 9. 8 (2020): 1840.

Touboul, Jonathan. "The Hipster Effet: when anticonformists all look the same." DCDS-B 24. 8 (2019): 4379-4415.

Gaetan Vignoud, Laurent Venance, Jonathan Touboul. "Interplay of multiple pathways and activity-dependent rules in STDP." Plos Computational Biology 14. 8 (2018): e1006184.

Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul and Alexandre Vidal,. "Wild oscillations in a nonlinear neuron model with resets: (Ⅰ) Bursting, spike-adding and chaos." DCDS-B 22. 10 (2018): 3967-4002.

Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul and Alexandre Vidal,. "Wild oscillations in a nonlinear neuron model with resets: (Ⅱ) Mixed-mode oscillations." DCDS-B 20. 10 (2018): 4003-4039.

Touboul, Jonathan and Ann Carla Staver and Simon Asher Levin. "On the complex dynamics of savanna landscapes." Proceedings of the National Academy of Sciences USA 115. 7 (2018): E1336-E1345.

Touboul, Jonathan and Cabana, Tanguy. "Large deviations for randomly connected neural networks: I. Spatially extended systems." Advances in Applied Probability 50. 3 (2018): 944-982.

Touboul, Jonathan and Cabana, Tanguy. "Large deviations for randomly connected neural networks: II. State-Dependent interactions." Advances in Applied Probability 50. 3 (2018): 983-1004.