Publications

Selected publications:

  • On a kinetic Fizhugh-Nagumo model of neuronal network (with Stéphane Mischler and Cristóbal Quiñinao), Communications in Mathematical Physics 342 (3) pp 1001–1042 (2016) [HAL].
  • The propagation of chaos in neural fields. Annals of Applied Probability 24 (3), 1298-1328 (2014) – Updated! (May 2016) [arXiv]
  • Parsimony, exhaustivity and balanced detection in neocortex (A. Romagnoni*, J. Ribot*, D. Bennequin+, J. Touboul+) – PLoS Comp. Biol. 11(11):e1004623 (2015). [arXiv preprint]
  • Canard explosion in delayed equations with multiple timescales (with Maciej Krupa), Journal of Dynamics and Differential Equations 28 (2), pp 471-491 (2016) [arXiv preprint]
  •  Complex oscillations in the delayed van der Pol equation (with Maciej Krupa) Journal of Nonlinear Science 26 (1), pp 43-81 (2016) [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].
  • Topological and Dynamical Complexity of Random Neural Networks (with G. Wainrib) Physical Review Letters 110 (118101) (Editors’ Selection, 2013) [arXiv preprint]

Full Publication list

Modeling and Biology

  • The hemodynamic signal as a first-order low-pass temporal filter: Evidence and implications for neuroimaging studies (A. Sauvage, G. Hubert, J. Touboul *, J. Ribot*), in review [biorXiv preprint]
  • Enhanced abventricular proliferation compensates cell death in the embryonic cerebral cortex (B Freret-Hodara, Y Cui, A Griveau, L Vigier, Y Arai, J Touboul and A Pierani), Cerebral Cortex (2016, online).
  • 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)

  • Power-law statistics and universal scaling in the absence of criticality (J. Touboul, A. Destexhe) – Physical Review E (in press).
  • 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 Comp. Biol. 11(11):e1004623 (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]
  • C. Quiñinao, A. Prochiantz, J. Touboul, Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues,  Development 142 (10), 1860-1868
  • 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, Fabrice Wendling, Patrick Chauvel, Olivier Faugeras Neural Mass Activity, Bifurcations, and Epilepsy Neural Computation vol.23, number 12, pp. 3232-3286 (2011) [preprint].

Mean-field limits and analysis of solutions

  • A large deviations result for randomly interacting particle systems; Application to the Kuramoto model (with Tanguy Cabana) [arXiv preprint]
  • Large deviations for spatially extended random neural networks (with Tanguy Cabana), submitted [arXiv preprint]
  • On the dynamics of random neuronal networks (with Ph. Robert), Journal of Statistical Physics (in press) – [arXiv preprint]
  • On a kinectic Fizhugh-Nagumo model of neuronal network (with Stéphane Mischler and Cristóbal Quiñinao), Communications in Mathematical Physics 342 (3) pp 1001–1042 (2016) [HAL].
  • The hipster effect: when anticonformists all look the same – [arXiv preprint] 
  • Limits and dynamics of randomly connected neuronal networks (with Cristobal Quininao) Acta Applicandae Mathematicae 136 (1), pp 167-192 (2015) [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. Ann. Appl. Probab. 24 (3), 1298-1328 (2014) – Updated! (May 2016) [arXiv Updated]
  • 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].
  • Limits and dynamics of stochastic neuronal networks with random delays Journal of Statistical Physics vol. 149, issue 4, pp. 569-597 (2012) [Udpated arXiv]
  • 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].
  • 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].
  • 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].

Dynamical Systems and Applications

  • Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos (with Jonathan Rubin, Justyna Signerska and Alexandre Vidal) [arXiv preprint] 
  • A geometric mechanism for mixed-mode bursting oscillations in a hybrid neuron model (with Justyna Signerska and Alexandre Vidal) [arXiv preprint]
  • Canard explosion in delayed equations with multiple timescales (with Maciej Krupa), Journal of Dynamics and Differential Equations 28 (2), pp 471-491 (2016) [arXiv preprint]
  •  Complex oscillations in the delayed van der Pol equation (with Maciej Krupa) Journal of Nonlinear Science 26 (1), pp 43-81 (2016) [arXiv preprint]
  • Jonathan Touboul, Martin Krupa, Mathieu Desroches Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales SIAM Journal on Applied Mathematics 75 (5), pp. 2024–2049 (2016) [arXiv preprint].
  • Absorption properties of stochastic equations with Hölder diffusion coefficients (with Gilles Wainrib) Physica D 307, 2015 pp 42–60 (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].
  • 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].
  • 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, 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]
  • 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
  • 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].

Random matrices, Networks and gases

  • Real eigenvalues of non-symmetric random matrices: Transitions and Universality (with L.C. Garcia del Molino and K. Pakdaman) [arXiv preprint]
  • The real Ginibre ensemble with k=O(n) real eigenvalues (with L.C. García del Molino, K.Pakdaman and G. Wainrib). Journal of Statistical Physics 163 (2) pp 303-323 (2016) [arXiv preprint]
  • 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]
  • 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].
  • Topological and Dynamical Complexity of Random Neural Networks (with G. Wainrib) Physical Review Letters 110 (118101) (Editors’ Selection, 2013) [arXiv preprint]
  •  Heterogeneous connections induce oscillations in large scale networks (with G. Hermann) Physical Review Letters 109 (1), 018702 (2012) [arXiv preprint]

Integrate-and-fire Neurons and first hitting times

  • 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).
  • 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, 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]
  • 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].

Misc. Math.

Popularization Papers

  • Simplexité et activité corticale: explorations mathématiques, Complexité-Simplexité, edt: A. Berthoz & JL Petit.
  • Nombres premiers et cryptologie: l’algorithme RSA, Dec. 2007 )i(nterstice

Invited & Contributed Talks

  1. Summer school PDEs and Probability for Life science – invited organized for the workshop on mathematical modeling in neuroscience (CIRM, Marseille)
  2. Invited to give a lecture at the CIMPA Summer School (I had to cancel my participation)
  3. Optimal Topology in the brain, Institut Math. Toulouse, May ’16
  4. The brain, between order and disorder, French National Academy, May ’16
  5. Pinwheel and Dipoles in the visual cortex, LMI, Harvard Medical School, March 1st, 2016
  6. Noise and Collective patterns of activity in neuronal networks, Workshop Interplay of Stochastic and Deterministic dynamics in networks, MBI- Columbus, Feb. 25th, 2016.
  7. The complex interplay of noise and dynamics in neuroscience, Department of Mathematics and Applications, ENS Paris, 2016.
  8. Neurodevelopment and boundary formations, Complex Systems Digital Campus, Oct. 1st 2015.
  9. Power law statistics and universal scalings in the absence of criticality, CNS 2015, Prague.
  10. Competitive reaction diffusion systems with spatial cues: homeoprotein and the stability of compartments in developing nervous system, ICMSN, Antibes, June 2015 (presented by C. Quiñinao)
  11. Pinwheel-Dipoles topologies in cat visual cortex, ICMNS, Antibes, June 2015 (presented by A. Romagnoni)
  12. The role of disordered connections in the dynamics of large networks of the brain, Workshop Beyond Mean-Field Theory, Goettingen, June 2015.
  13. Strucutre and function in brain: from models to experiments and back, plenary speaker at the Mathematics in Action conference organized by the Polish Mathematics Academy of Science, Bedlewo, May 28th, 2015
  14. Around the complex interplay between organization, heterogeneity and collective dynamics of neuronal networks, Courant Institute, NYU, May 2015
  15. On Pinwheel-Dipole Topologies in Cat Visual Cortex: Exhaustivity, Parsimony and Balanced Detection, Center for Neural Science, NYU, May 2015
  16. Complexity and synchronization of randomly connected networks and the eigenvalues of real random matrices, Columbia University, New York, May 2015
  17. The role of disorder in the synchronization of randomly connected neural networks, City College, CUNY, New-York, May 2015
  18. Power laws and universal scalings in the absence of criticality, European Institute for Theoretical Neuroscience workshop, Paris, March 12th, 2015
  19. Exhaustivity, Parsimony and Balanced Detection in Cat Visual Cortex, Princeton Biophysics Seminar, Dec. 4th, 2014

  20. Noise-induced dynamics in mean-field stochastic neural fields, Bernstein Conference, Göttingen, Sept. 2 2014.
  21. Tutorial: Mean-field methods for the reduction of large stochastic neural networks, Bernstein Conference, Göttingen, Sept. 2 2014.
  22. The stochastic Brain, workshop @ SPA Conference, Buenos Aires, Aug. 2014.
  23. The retarded Canard, International Workshop on Neurodynamics, Castro-Urdiales, 2014.
  24. Spatially Extended Stochastic Neural Networks, Nonlocally
    Coupled Dynamical Systems: Analysis and Applications workshop, AIMS Conference 2014, Madrid.
  25. Emergence of synchrony in randomly coupled networks, Random dynamical systems in the life sciences workshop, AIMS Conference 2014, Madrid
  26. Pinwheel, Dipoles and the Organizing principles of visual cortex, Nottingham Center for Mathematical Medicine and Biology, University of Nottingham, UK
  27. Limits and Dynamics of Spatially extended networks, KI-Net conference on Collective behaviour: Macroscopic vs Kinetic Descriptions, May 19th-23rd (Imperial College, London, UK)
  28. 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)
  29. 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
  30. Spectral Properties of random matrices and the dynamics of randomly connected networks, Rockefeller University seminar on Mathematical Physics, Nov. 2013.
  31. The dynamics of randomly connected networks, Insights from Random Matrix Theory GdT Math-Bio-Santé, U. Jussieu, Paris (Nov. 2013)
  32. 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.
  33. Macroscopic states of large neuronal networks , IConet 2013 PhD Conference, Bernstein Center, Freiburg (Sep. 2013).
  34. Out of equilibrium phenomena in the noisy brain , IMA, Minneapolis, Minnesota. Conference Stochastic Modeling of Biological Processes (May 2013)
  35. 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.
  36. Topological and Dynamical Complexity at the Edge of ChaosPhysics Department, Princeton University, October 2012.
  37. Bifurcations of stochastic differential equations with singular diffusion coefficients Random Models in Neuroscience, July 2012, Paris, Thursday, July 2012
  38. Simplexity and cortical activity: a mathematician’s viewSeminaire Simplexite/Complexite, Fondation Hugo du College de France, May 2012
  39. 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).
  40. Limites de champ-moyen pour les champs neuronaux: extension spatiale, délais et dynamiques périodiques GT Limites de champ moyen, IHP, Paris, February 2012
  41. How levels of noise and heterogeneity govern large-scale neuronal networks dynamics? Neurodynamics 2012, Edinburgh, March 2012.
  42. Mean-field limits in neural fields: spatial extensions, delays and periodic activity Workshop on mean-field limits,, IHP, Feb. 16th 2012
  43. Stochastic neural fields: mean-field limits and dynamics.Institute for Stochastics, Johannes Kepler University, Linz, Jan. 9th 2012
  44. Mathematical and Numerical Analysis of Hybrid Nonlinear Integrate-and-Fire Neuron Models, Equadiff Conference, August 2011, Loughborough, UK.
  45. Mathematical and Numerical Analysis of Hybrid Nonlinear Integrate-and-Fire Neuron Models,Equadiff Conference, Loughborough (UK), August 2011.
  46. Probabilistic methods for neuronal mean-field dynamics,SIAM Dynamical Systems Conference, May 2011, Snowbird, Utah.
  47. Kinetic Theory for Neural NetworksWorkshop: Probabilistic Methods in Kinetic Theory, Luminy, France (2011).
  48. 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.
  49. Mathematical neuroscience: a few result, a lot of novel mathematical challengesBCAM, March 2011, Bilbao
  50. Correlation effects in large networks and mean-field limitsSIAM Life Science 2010, Pittsburgh, July 2010.
  51. First hitting times of stochastic processes ans Mean-Field Methods in NeurosciencesInstitut Henri Poincaré, Paris, January 2010
  52. Stochastic and nonlinear approaches for epilepsyHarvard Medical School, Kreiman Lab, October 2009.
  53. Planar Nonlinear integrate-and-fire Neuron ModelsDepartment of Mathematics, University of Pittsburgh, Ermentrout’s lab.
  54. A constructive approach for multipopulation Mean-Field equations4th workshop on computational neuroscience, Gif sur Yvette, april 2008
  55. The spikes trains probability distributions: a stochastic calculus approachSeminar: Biology, Probability and Statistics, University Paris VI, Chevaleret – November 2007
  56. Nonlinear neuron models and their bifurcationsLaboratory of Computational Neurosciences,EPFL, Lausanne
  57. Stochastic and Nonlinear approaches of neuronal activity, East Coast summer tour, July 2007! (NYU, Courant Institute, Columbia, NJIT, Princeton seminars)
  58. Nonlinear neuron models and their bifurcationsWorkshop on Biomathematics and Dynamical Systems (CIRM 2007) and Nonlinear Physics school (Peyresq 2007)
  59. Statistics of spike train: the point of view of the continuous stochastic calculus (invited) 1st workshop on computational neurosciences, Gif-Sur-Yvette (2006).
  60. 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).

Posters

  1. Noise and heterogeneities induce oscillations in neural networks, Variance and Invariants in Brain and Behavior , May 2012, Haifa (Israel).
  2. 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.
  3. 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
  4. Dynamics and chaos in bidimensional nonlinear integrate-and-fire neurons (with R. Brette)Workshop CHAOS and DYNAMICS in BIOLOGICAL NETWORKS, Cargese, 2008.
  5. Event-driven mathematical framework for noisy integrate-and-fire neuron networks (with O.Faugeras and O. Rochel) Computational Neuroscience Meeting (CNS, Toronto 2007)
  6. 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)

PhD Thesis


  • 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.

Research reports


  • 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.

Patents


  • “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)