# Jonathan Touboul

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

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.