I am a PhD student of R.Keriven (IMAGINE) and O.Faugeras (NeuroMathComp) located at INRIA Sophia Antipolis.

My current research is axed on a spatially-continuous description of cortical neural networks, and its applications to computational neurosciences [optical flow estimation, neuronal illusions, dynamics of population]. This description is done within the Neural Field Equations (NFE) formalism. More specifically, I am interested in the following fields :

• Dynamical properties of the NFE [Functional Analysis, Bifurcation theory].
• Modelling of corticals aeras related to motion analysis [V1, MT, MST...].
• Biologically inspired motion analysis.
• Neural illusions computation [cf. paper 3. below].
• Delay induced effects and more precisely the interplay between effective delays and propagation delays [traveling waves, oscillations...].

My idea is to develop sophisticated tools (numerical/theoritical) that allow an efficient study of these spatially-continuous networks and to draw predictions about the possible behaviors of real populations of neurons.

Sample pictures

Published papers

1. M. Clerc, R. Veltz, D. Guiraud, JL. Divoux The 3D Potential Induced by Functional Electrical Stimulation with Multi-Contact Cuff Electrodes: Simulation and Validation
   13th Annual International FES Society Conference (2008)
2. O. Faugeras, R. Veltz, F. Grimbert Persistent neural states: stationary localized activity patterns in nonlinear continuous n-population, q-dimensional neural networks
   Neural Computation, 21: 1, pp 147–187 (2009)
3. R. Veltz, O. Faugeras Local/global analysis of the stationary solutions of some neural field equations SIAM Journal on Applied Dynamical Systems, vol. 9, pp 954-998 (2010) [link][preprint] A homotopy method to compute neural illusions in nonlinear networks.
4. R. Veltz, O. Faugeras Stability of the stationary solutions of neural field equations with propagation delays. The Journal of Mathematical Neuroscience, 1:1 (2011) [link]
5. R. Veltz An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays. Comptes Rendus de l'Academie des Sciences, (2011) [link]
6. R. Veltz, O. Faugeras A center manifold result for delayed neural fields equations Submitted to SIAM Journal on Mathematical Analysis (2011)

In preparation

1. R. Veltz, O. Faugeras Interplay between effective delays and propagation delays in delayed neural field equations
2. R. Veltz, O. Faugeras Illusory persistent states in the Ring Model of visual orientation selectivity

Biography

Programs

1. (Incoming) A Matlab program for computing the first Hopf bifurcation curves in neural fields equations with space dependent delays.
2. (Incoming) Parallel continuation of periodic orbits in large scale systems using the Trilinos library.

Contact

Address in Sophia: NeuroMathComp Laboratory INRIA Sophia Antipolis 2004, Route des Lucioles 06902 Sophia Antipolis France

Email: romain.veltz@sophia.inria.fr Phone: (Sophia) +33 4 92 38 76 90 Fax: (Sophia) +33 4 92 38 78 45 Office: (Sophia) Y510