Geometry of the superior colliculus mapping and efficient oculomotor computation

Nicolas Tabareau 1 Daniel Bennequin 2 Alain Berthoz 1 Jean-Jacques Slotine 3 Benoît Girard 1
1 LPPA - Laboratoire de physiologie de la perception et de l'action
2 IMJ - Institut de Mathématiques de Jussieu
3 NSL - Nonlinear System Laboratory
Abstract : Numerous brain regions encode variables using spatial distribution of activity in neuronal maps. Their specific geometry is usually explained by sensory considerations only. We provide here, for the first time, a theory involving the motor function of the superior colliculus to explain the geometry of its maps. We use six hypotheses in accordance with neurobiology to show that linear and logarithmic mappings are the only ones compatible with the generation of saccadic motor command. This mathematical proof gives a global coherence to the neurobiological studies on which it is based. Moreover, a new solution to the problem of saccades involving both colliculi is proposed. Comparative simulations show that it is more precise than the classical one.
keyword : Saccades Superior Colliculus Spatio-Temporal Transformation Computational Model
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Journal articles
Biological Cybernetics (Modeling), Springer Verlag, 2007, 97 (4), pp.279-292. 〈10.1007/s00422-007-0172-2〉
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Nicolas Tabareau, Daniel Bennequin, Alain Berthoz, Jean-Jacques Slotine, Benoît Girard. Geometry of the superior colliculus mapping and efficient oculomotor computation. Biological Cybernetics (Modeling), Springer Verlag, 2007, 97 (4), pp.279-292. 〈10.1007/s00422-007-0172-2〉. 〈hal-00178144〉

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