- Large deviations for spatially extended random neural networks (with Tanguy Cabana) [arXiv preprint]
- A geometric mechanism for mixed-mode bursting oscillations in a hybrid neuron model (with Justyna Signerska and Alexandre Vidal) [arXiv preprint]
- Power-law statistics and universal scaling in the absence of criticality (J. Touboul, A. Destexhe) – [arXiv preprint]
- The hipster effect: when anticonformists all look the same – [arXiv preprint]
- On the dynamics of random neuronal networks (with Ph. Robert) – [arXiv preprint]
- The real Ginibre ensemble with k=O(n) real eigenvalues (with L.C. García del Molino, K.Pakdaman and G. Wainrib). To Appear in J. Stat. Phys.
- On a kinetic FitzHugh-Nagumo model of neuronal network (with Stéphane Mischler and Cristóbal Quiñinao) to appear in the Communications in Mathematical Physics [HAL].
- Pinwheel-Dipole configuration in cat visual cortex (J. Ribot*, A. Romagnoni*, C. Milleret, D. Bennequin+, J. Touboul+) – NeuroImage 128, 63–73 (2016) [bioRxiv preprint]
- Parsimony, exhaustivity and balanced detection in neocortex (A. Romagnoni*, J. Ribot*, D. Bennequin+, J. Touboul+) – PLoS Comput Biol. 2015 Nov 20;11(11):e1004623.[arXiv preprint]
- Canard explosion in delayed equations with multiple timescales (with Maciej Krupa) Journal of Dynamics and Differential Equations (2015): 1-21. [arXiv preprint]
- Complex oscillations in the delayed van der Pol equation (with Maciej Krupa) Journal of Nonlinear Science 08/2015; DOI:10.1007/s00332-015-9268-3
- Lhx2 regulates the timing of β-catenin-dependent cortical neurogenesis (CL Hsu, S Nam, Y Cui, CP Chang, CF Wang, PS Hou, HC Kuo, J Touboul and SJ Chou) Proceedings of the National Academy of Science 112 (39), pp. 12199–12204 (2015).
- Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales (Jonathan Touboul, Martin Krupa, Mathieu Desroches) SIAM Journal on Applied Mathematics 75 (5), pp. 2024–2049 (2015) [arXiv preprint].
- Competition and boundary formation in heterogeneous media: Application to neuronal differentiation (with Cristobal Quiñinao and Benoît Perthame) Mathematical Models and Methods in Applied Science 25 (13) 2477–2502 (2015) [arXiv preprint]
- Absorption properties of stochastic equations with Hölder diffusion coefficients (with Gilles Wainrib), Physica D 307, 42–60 (2015) [arXiv preprint].
- C. Quiñinao, A. Prochiantz, J. Touboul, Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues, Development 142 (10), 1860-1868 (2015).
- The heterogeneous gas with singular interaction: Generalized circular law and heterogeneous renormalized energy (with Luis-Carlos Garcia del Molino & Khashayar Pakdaman) Journal of Physics A: Mathematical and Theoretical 48 (4) 045208 (2015) [arXiv preprint]
- Limits and dynamics of randomly connected neuronal networks (with Cristobal Quininao) Acta Applicandae Mathematicae 136 (1), 167-192 (2015) [arXiv preprint].
- Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension (with Grégory Faye) SIAM J. on Applied Mathematics 74 (5), pp. 1657-1690 (2014) [arXiv preprint].
- Spatially extended networks with singular multi-scale connectivity patterns Journal of Statistical Physics 56 (3), p. 546-573 (2014) [arXiv preprint].
- The propagation of chaos in neural fields The Annals of Applied Probability, 24 (3), 1298-1328 (2014) [Journal version] .
- Index Distribution of the Ginibre Ensemble (with Romain Allez & Gilles Wainrib) Journal of Physics A: Mathematical and Theoretical; Fast Track Communication, Vol. 27 4, 042001 (2014) [arXiv preprint].
- Synchronization in random balanced networks (with L. Garcia del Molino, K. Pakdaman & G. Wainrib) Phys. Rev. E 88 Issue 4 [Featured in the journal’s Kaleidoscope section] (2013) [arXiv preprint].
- Macroscopic equations governing noisy spiking neuronal populations (with M. Galtier) PLoS ONE 8(11): e78917 [arXiv preprint].
- Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks (with T. Cabana) Journal of Statistical Physics vol 153, issue 2, pages 211-269 (2013) [arXiv preprint].
- Topological and Dynamical Complexity of Random Neural Networks (with G. Wainrib) Physical Review Letters 110 (118101) (Editors’ Selection, 2013) [arXiv preprint]
- Limits and dynamics of stochastic neuronal networks with random delays vol. 149, issue 4, pp. 569-597 (2012) [updated arXiv]
- Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain AIMS Mathematical Control and Related Fields (MCRF), vol. 2 number 4, pp. 429 – 455, (2012) [arXiv preprint]
- Heterogeneous connections induce oscillations in large scale networks (with G. Hermann) Physical Review Letters 109 (1), 018702 (2012) [arXiv preprint]
- Mean-Field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions Physica D, Volume 241, Issue 15, pp 1223–1244 (2012) [arXiv preprint].
- Thibaud Taillefumier, Jonathan Touboul and Marcelo Magnasco Exact Event-Driven Implementation for Recurrent Networks of Stochastic Perfect Integrate-and-Fire Neurons Neural Computation vol. 24, number 12, pp. 3145-3180 (2012).
- On an explicit representation of the solution of general linear differential equations (with M. Galtier). Comptes-Rendus de l’académie des Sciences, Paris, Ser. I, vol. 35:3-4, pp. 167-172 (2012)[arXiv preprint].
- Jonathan Touboul, Geoffroy Hermann and Olivier Faugeras Noise-induced behaviors in neural mean field dynamics. SIAM Journal on Applied Dynamical Systems, vol. 11, number 1, pp. 49-81 (2012) [arXiv preprint].
- Multi-Resolution Schauder Approach To Multidimensional Gauss-Markov Processes (with T. Taillefumier) International Journal of Stochastic Analysis Vol. 2011 (2011), Article ID 247329, 89 pages [arXiv preprint]
- Jonathan Touboul, Fabrice Wendling, Patrick Chauvel, Olivier Faugeras Neural Mass Activity, Bifurcations, and Epilepsy Neural Computation vol.23, number 12, pp. 3232-3286 (2011) [preprint].
- Jonathan Touboul, Olivier Faugeras A Markovian event-based framework for stochastic spiking neural networks Journal of Computational Neuroscience vol.31, number 3, pp. 485-507 (2011) [arXiv preprint].
- Jonathan Touboul, Bard Ermentrout Finite-size and correlation-induced effects in Mean-field Dynamics Journal of Computational Neuroscience vol.31, number 3, pp. 453-484 (2011) [arXiv preprint].
- Jonathan Touboul On the simulation of nonlinear bidimensional spiking neuron models Neural Computation vol. 23, No 7, pages 1704-1742 (2011) [arXiv preprint]
- Jonathan Touboul, Alain Destexhe Can power-law scaling and neuronal avalanches arise from stochastic dynamics? (2010) PLoS ONE 5(2): e8982. doi:10.1371/journal.pone.0008982 [arXiv preprint].
- Jonathan Touboul, Romain Brette Spiking dynamics of bidimensional integrate-and-fire neurons (2009) SIAM Journal on Applied Dynamical Systems, vol. 8, pages 1462-1506 [Preprint].
- Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model (2009), Neural Computation vol. 21, number 2 [Preprint]
- Olivier Faugeras, Jonathan Touboul, Bruno Cessac A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs. (2009) Frontiers in Computational Neurosciences, vol. 3, number 1, doi:10.3389/neuro.10.001.2009. [pdf].
- Jonathan Touboul, Romain Brette Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. (2008) Biological Cybernetics, vol. 99, number 4-5, pp. 319-334. [Preprint], Brian python scripts for the figures here
- Jonathan Touboul, Olivier Faugeras First hitting times of Double Integral Process to curved boundaries. (2008) Advances in Applied Probability vol.40, number 2, pp. 501-528 [Preprint]
- Bifurcation analysis of a general class of non-linear integrate and fire neurons. SIAM Journal on Applied Mathematics, 2008, vol.68, number 4, pp.1045-1079 [Preprint].
- Jonathan Touboul, Olivier Faugeras The spikes trains probability distributions: A stochastic calculus approach (2007) Journal of Physiology, Paris vol. 101 number 1–3, pp. 78-98 [Preprint].
- Simplexity and cortical activity: a mathematician’s view, Complexité-Simplexité, edt: A. Berthoz & JL Petit.
- Nombres premiers et cryptologie: l’algorithme RSA, Dec. 2007 )i(nterstice
- The complex interplay between structure and function in the brain, World e-Conference on complex systems CS-DC 15, September 2015, Temple, AZ.
- Randomly connected networks and their dynamics, Beyond Mean-Field Theory workshop, Goettingen, June 2015.
- The complex interplay between structure and function in the brain, Plenary talk at the Mathematics in action workshop, Polish Academy of Science, Bedlewo, May 2015.
- Propagation of chaos, Power laws and universal scalings in neuronal networks, Computational Neuroscience Conference (CNS), Prague, 2015.
- Power laws and universal scalings in the absence of criticality, European Institute for Theoretical Neuroscience workshop, Paris, March 12th, 2015.
- Noise-induced dynamics in mean-field stochastic neural fields, Bernstein Conference, Göttingen, Sept. 2 2014.
- Tutorial: Mean-field methods for the reduction of large stochastic neural networks, Bernstein Conference, Göttingen, Sept. 2 2014.
- The stochastic Brain, workshop @ SPA Conference, Buenos Aires, Aug. 2014.
- The retarded Canard, International Workshop on Neurodynamics, Castro-Urdiales, 2014.
- Spatially Extended Stochastic Neural Networks, Nonlocally
Coupled Dynamical Systems: Analysis and Applications workshop, AIMS Conference 2014, Madrid.
- Emergence of synchrony in randomly coupled networks, Random dynamical systems in the life sciences workshop, AIMS Conference 2014, Madrid
- Pinwheel, Dipoles and the Organizing principles of visual cortex, Nottingham Center for Mathematical Medicine and Biology, University of Nottingham, UK
- Limits and Dynamics of Spatially extended networks, KI-Net conference on Collective behaviour: Macroscopic vs Kinetic Descriptions, May 19th-23rd (Imperial College, London, UK)
- The pinwheel-dipole organization of orientation and spatial frequency maps, and their common organizing principles. 5th France-Israël binational conference on neurosciences, Feb, 11th-14th, Sde Boker (Israël)
- Collective phenomena in large neural networks: the role of noise, heterogeneity and balance in the emergence of synchronized activity, Symposium Balance of excitation and inhibition in sensory cortex ; Paris, Jan. 8th 2014
- Spectral Properties of random matrices and the dynamics of randomly connected networks, Rockefeller University seminar on Mathematical Physics, Nov. 2013.
- The dynamics of randomly connected networks, Insights from Random Matrix Theory GdT Math-Bio-Santé, U. Jussieu, Paris (Nov. 2013)
- Random phenomena in large neural networks & Spectral properties of Random Matrices Sixth Workshop on Random Dynamical Systems, Bielefeld, (Oct 2013) – I had to cancel my travel.
- Macroscopic states of large neuronal networks , IConet 2013 PhD Conference, Bernstein Center, Freiburg (Sep. 2013).
- Out of equilibrium phenomena in the noisy brain , IMA, Minneapolis, Minnesota. Conference Stochastic Modeling of Biological Processes (May 2013)
- Out of equilibrium statistical physics in Neuronal Systems: How levels of noise and heterogeneity govern large-scale neuronal networks dynamics Virtual Working Group on Neural Dynamics, MBI, Ohio State University, January 2013.
- Topological and Dynamical Complexity at the Edge of ChaosPhysics Department, Princeton University, October 2012.
- Bifurcations of stochastic differential equations with singular diffusion coefficients Random Models in Neuroscience, July 2012, Paris, Thursday, July 2012
- Simplexity and cortical activity: a mathematician’s viewSeminaire Simplexite/Complexite, Fondation Hugo du College de France, May 2012
- A probabilistic view on neural fields: Bridging microscopic stochastic activity and neural fields Progress in Neural Field Theory 2012, Reading, April 2012 (I had to cancel my travel).
- Limites de champ-moyen pour les champs neuronaux: extension spatiale, délais et dynamiques périodiques GT Limites de champ moyen, IHP, Paris, February 2012
- How levels of noise and heterogeneity govern large-scale neuronal networks dynamics? Neurodynamics 2012, Edinburgh, March 2012.
- Mean-field limits in neural fields: spatial extensions, delays and periodic activity Workshop on mean-field limits,, IHP, Feb. 16th 2012
- Stochastic neural fields: mean-field limits and dynamics.Institute for Stochastics, Johannes Kepler University, Linz, Jan. 9th 2012
- Mathematical and Numerical Analysis of Hybrid Nonlinear Integrate-and-Fire Neuron Models, Equadiff Conference, August 2011, Loughborough, UK.
- Mathematical and Numerical Analysis of Hybrid Nonlinear Integrate-and-Fire Neuron Models,Equadiff Conference, Loughborough (UK), August 2011.
- Probabilistic methods for neuronal mean-field dynamics,SIAM Dynamical Systems Conference, May 2011, Snowbird, Utah.
- Kinetic Theory for Neural NetworksWorkshop: Probabilistic Methods in Kinetic Theory, Luminy, France (2011).
- Mean-Field approaches in Neurosciences: Bridging cellular and population levels?Inauguration of the Center for Interdisciplinary Research in Biology, Collège de France, Paris, May 2011.
- Mathematical neuroscience: a few result, a lot of novel mathematical challengesBCAM, March 2011, Bilbao
- Correlation effects in large networks and mean-field limitsSIAM Life Science 2010, Pittsburgh, July 2010.
- First hitting times of stochastic processes ans Mean-Field Methods in NeurosciencesInstitut Henri Poincaré, Paris, January 2010
- Stochastic and nonlinear approaches for epilepsyHarvard Medical School, Kreiman Lab, October 2009.
- Planar Nonlinear integrate-and-fire Neuron ModelsDepartment of Mathematics, University of Pittsburgh, Ermentrout’s lab.
- A constructive approach for multipopulation Mean-Field equations4th workshop on computational neuroscience, Gif sur Yvette, april 2008
- The spikes trains probability distributions: a stochastic calculus approachSeminar: Biology, Probability and Statistics, University Paris VI, Chevaleret – November 2007
- Nonlinear neuron models and their bifurcationsLaboratory of Computational Neurosciences,EPFL, Lausanne
- Stochastic and Nonlinear approaches of neuronal activity, East Coast summer tour, July 2007! (NYU, Courant Institute, Columbia, NJIT, Princeton seminars)
- Nonlinear neuron models and their bifurcationsWorkshop on Biomathematics and Dynamical Systems (CIRM 2007) and Nonlinear Physics school (Peyresq 2007)
- Statistics of spike train: the point of view of the continuous stochastic calculus (invited) 1st workshop on computational neurosciences, Gif-Sur-Yvette (2006).
- The statistics of spike trains for some simple types of neuron models NeuroComp Conference (Pont-à-Mousson, 2006) (with Olivier Faugeras, Theo Papadopoulo, Denis Talay, Etienne Tanre and Mireille Bossy).
- Noise and heterogeneities induce oscillations in neural networks, Variance and Invariants in Brain and Behavior , May 2012, Haifa (Israel).
- Trajectory Analysis of Positive-Negative Emotional Balance in the Treatment of Depression, (with Robert Schwartz), 1st World Congress on Positive psychology IPPA, June 2009, Philadelphia.
- Mean-field analysis of multi population neural networks with random synaptic weights and stochastic inputs ( with O. Faugeras and B. Cessac) COSYNE 2009, Salt Lake City, Utah
- Dynamics and chaos in bidimensional nonlinear integrate-and-fire neurons (with R. Brette)Workshop CHAOS and DYNAMICS in BIOLOGICAL NETWORKS, Cargese, 2008.
- Event-driven mathematical framework for noisy integrate-and-fire neuron networks (with O.Faugeras and O. Rochel) Computational Neuroscience Meeting (CNS, Toronto 2007)
- Dynamics of noisy inhibitory networks of integrate-and-fire neurons: a stochastic network theory approach: (with Romain Brette) Poster presented at the NeuroMath Conference (Andorra 2006)
- Nonlinear and Stochastic Models in Neurosciences. PhD in Mathemtics of the Ecole Polytechnique prepared at INRIA (O. Faugeras).Manuscript Reviewers: Terrence Sejnowski, Jean-Christophe Yoccoz, Marc YorDefense Committee: Alain Destexhe, Yves Fregnac, Wulfram Gerstner, Claude Viterbo. Manuscript and Defense.
- Robert Schwartz, Jonathan Touboul (co-first authors) Positive and Negative Affect Balance Trajectories in the Treatment of Depression . [arXiv preprint].
- The Statistics Of Spikes Trains For Some Simple Types Of Neuron Models (with Olivier Faugeras and Theodore Papadopoulo) (2006) .
- Jonathan Touboul Stochastic Processes and Hitting Times in Mathematical Neurosciences (2006): Master thesis of Université Pierre et Marie Curie.
- Jonathan Touboul, Bard Ermentrout, Olivier Faugeras, Bruno Cessac Stochastic firing rate models arXiv preprint: http://arxiv.org/abs/1001.3872.
- “Dispositif pour detecter des yeux rouges sur une image et dispositif d’impression d’image mettant en oeuvre ce procede” ( Red eyes detection device on an image and printing device using this process) (inventor), owned by Sagem Inc: French patent number FR0550181 (publication number FR2880969)) (published 2006-07-21 (BOPI 2006-29))
- “Procédé pour détecter des yeux rouges basé sur détection d’une zone de peau” (Red eyes detection process based on skin detection) : European patent EP06300026 (publication number EP1684210) (published 2006-07-26 (Bulletin 2006-30)