DS for Neuro

Publications

  1. Selected publications
  2. Articles
  3. Thesis

My Google Scholar

Selected publications

  • A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics. See article 30 below. It was selected by the Society for Neuroscience to appear in their highlights 2023

  • Exponential stability of the stationary distribution of a mean-field of spiking neural network. See article 25 below. Important landmark in mathematical neurosciences because we lack a general bifurcation theory for the law of stochastic processes solutions of McKean-Vlasov equations. This paper is one important step toward such a theory.

  • On a toy network of neurons interacting through their dendrites. See article 20 below. Arguably my best mathematical production since my PhD. Neurons produce waves in their dendrites which annihilate when they collide. The nice trick of this paper is to use a partial order to mathematically describe these annihilations in one neuron described by a stochastic process.

Articles

37. (in prep.) Bifurcation theory can predict behaviors of large assemblies of neurons
O. Faugeras, R. Veltz,
preprint, 2026,

36. (in prep.) The tractography equation
S. Deslauriers-Gauthier, R. Veltz,
preprint, 2026,

35. Paradoxical pinching effect in probabilistic tractography
S. Deslauriers-Gauthier, R. Veltz,
preprint, 2026, [link]

34. Mean-field analysis of a neural network with stochastic STDP
P. Helson, E. Tanré, R. Veltz,
Physical Review E, 2026, [link]

33. Analysis of a mean-field limit of interacting two-dimensional nonlinear integrate-and-fire neurons
R. Veltz,
preprint, 2025, [preprint]

32. Excitable response of a noisy adaptive network of spiking lasers
S. Barland, O. D’Huys, R. Veltz,
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2025, [link] [preprint]

31. Theoretical / numerical study of modulated traveling waves in inhibition stabilized networks
S. Habib, R. Veltz,
preprint, 2024, [preprint]

30. A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics
Y. E. Rodrigues, C. M. Tigaret, H. Marie, C. O'Donnell, R. Veltz,
eLife, 2023, [link] [PDF]

29. Dual contribution of ASIC1a channels in the spinal processing of pain information by deep projection neurons revealed by computational modeling
M. Chafaï, A. Delrocq, P. Inquimbert, L. Pidoux, K. Delanoe, M. Toft, F. Brau, E. Lingueglia, R. Veltz, E. Deval,
PLOS Computational Biology, 2023, [link]

28. Spatial and color hallucinations in a mathematical model of primary visual cortex
O. D. Faugeras, A. Song, R. Veltz,
Comptes Rendus. Mathématique, 2022, [link]

27. Hopf bifurcation in a Mean-Field model of spiking neurons
Q. Cormier, E. Tanré, R. Veltz,
Electronic Journal of Probability, 2021, [link] [preprint]

26. Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems
O. D’Huys, R. Veltz, A. Dolcemascolo, F. Marino, S. Barland,
Journal of Physics: Photonics, 2021, [link]

25. Exponential stability of the stationary distribution of a mean field of spiking neural network
A. Drogoul, R. Veltz,
Journal of Differential Equations, 2021, [link] [preprint] [PDF]

24. BifurcationKit.jl
R. Veltz,
preprint, 2020, [link]

23. Effective low-dimensional dynamics of a mean-field coupled network of slow-fast spiking lasers
A. Dolcemascolo, A. Miazek, R. Veltz, F. Marino, S. Barland,
Physical Review E, 2020, [link]

22. Local Theory for Spatio-Temporal Canards and Delayed Bifurcations
D. Avitabile, M. Desroches, R. Veltz, M. Wechselberger,
SIAM Journal on Mathematical Analysis, 2020, [link]

21. Long time behavior of a mean-field model of interacting neurons
Q. Cormier, E. Tanré, R. Veltz,
Stochastic Processes and their Applications, 2020, [link] [preprint]

20. On a toy network of neurons interacting through their dendrites
N. Fournier, E. Tanré, R. Veltz,
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2020, [link] [preprint] [PDF]

19. A neural field model for color perception unifying assimilation and contrast
A. Song, O. Faugeras, R. Veltz,
PLOS Computational Biology, 2019, [link] [preprint]

18. Mean-field limit of interacting 2D nonlinear stochastic spiking neurons
B. Aymard, F. Campillo, R. Veltz,
preprint, 2019, [preprint]

17. Resonator neuron and triggering multipulse excitability in laser with injected signal
A. Dolcemascolo, B. Garbin, B. Peyce, R. Veltz, S. Barland,
Physical Review E, 2018, [link]

16. Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity
T. Górski, R. Veltz, M. Galtier, H. Fragnaud, J. S. Goldman, B. Teleńczuk, A. Destexhe,
Journal of Computational Neuroscience, 2018, [link]

15. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
A. Drogoul, R. Veltz,
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017, [link]

14. A new twist for the simulation of hybrid systems using the true jump method
R. Veltz,
preprint, 2015, [preprint]

13. On the Effects on Cortical Spontaneous Activity of the Symmetries of the Network of Pinwheels in Visual Area V1
R. Veltz, P. Chossat, O. Faugeras,
The Journal of Mathematical Neuroscience (JMN), 2015, [link]

12. ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations
R. Veltz, O. Faugeras,
SIAM Journal on Mathematical Analysis, 2015, [link]

11. Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling
R. Veltz, T. J. Sejnowski,
Neural Computation, 2015, [link]

10. Short-term synaptic plasticity in the deterministic Tsodyks–Markram model leads to unpredictable network dynamics
J. M. Cortes, M. Desroches, S. Rodrigues, R. Veltz, M. A. Muñoz, T. J. Sejnowski,
Proceedings of the National Academy of Sciences, 2013, [link]

9. Bifurcation analysis applied to a model of motion integration with a multistable stimulus
J. Rankin, É. Tlapale, R. Veltz, O. Faugeras, P. Kornprobst,
Journal of Computational Neuroscience, 2013, [link]

8. Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations
R. Veltz,
SIAM Journal on Applied Dynamical Systems, 2013, [link]

7. A Center Manifold Result for Delayed Neural Fields Equations
R. Veltz, O. Faugeras,
SIAM Journal on Mathematical Analysis, 2013, [link]

6. An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays
R. Veltz,
Comptes Rendus Mathematique, 2011, [link]

5. Stability of the stationary solutions of neural field equations with propagation delays
R. Veltz, O. Faugeras,
The Journal of Mathematical Neuroscience, 2011, [link]

4. Illusions in the Ring Model of visual orientation selectivity
R. Veltz, O. Faugeras,
preprint, 2010, [preprint]

3. Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations
R. Veltz, O. Faugeras,
SIAM Journal on Applied Dynamical Systems, 2010, [link]

2. Persistent Neural States: Stationary Localized Activity Patterns in Nonlinear Continuous n-Population, q-Dimensional Neural Networks
O. Faugeras, R. Veltz, F. Grimbert,
Neural Computation, 2009, [link]

1. The 3d potential induced by functional electrical stimulation with multi-contact cuff electrodes: simulation and validation
M. Clerc, R. Veltz, D. Guiraud, J. L. Divoux,
"International Functional Electrical Stimulation Society Conference", 2008,

Thesis

  • Veltz, Romain. Applications of Jump Processes to Neuroscience. Habilitation Thesis, Université Côte d’Azur, Inria, France, 2024. url

  • Veltz, Romain. Nonlinear Analysis Methods in Neural Field Models. Phd thesis, Université Paris-Est, 2011. url

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