Pace and motor control optimization for a runner.

We present a model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem, that allows to define an approximate optimal velocity. We provide numerical simulations quite consistent with this approximation which leads to a simplified problem.

Correction to 'How to build a new athletic track to break records'.

[This corrects the article DOI: 10.1098/rsos.200007.

How to build a new athletic track to break records.

We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular, in the bend.

Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations.

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer, and they generalize the usual Lotka-Volterra ordinary differential equations.

Minimal time spiking in various ChR2-controlled neuron models.

We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls.