Show Reference: "Geometry of the superior colliculus mapping and efficient oculomotor computation"

Geometry of the superior colliculus mapping and efficient oculomotor computation Biological Cybernetics, Vol. 97, No. 4. (1 October 2007), pp. 279-292, doi:10.1007/s00422-007-0172-2 by Nicolas Tabareau, Daniel Bennequin, Alain Berthoz, Jean-Jacques J. Slotine, BenoƮt Girard
@article{tabareau-et-al-2007,
    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.},
    address = {UMR 7152, Laboratoire de Physiologie de la Perception et de l'Action, CNRS-Coll\`{e}ge de France, Paris, France.},
    author = {Tabareau, Nicolas and Bennequin, Daniel and Berthoz, Alain and Slotine, Jean-Jacques J. and Girard, Beno\^{i}t},
    citeulike-article-id = {2462709},
    citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00422-007-0172-2},
    citeulike-linkout-1 = {http://view.ncbi.nlm.nih.gov/pubmed/17690902},
    citeulike-linkout-2 = {http://www.hubmed.org/display.cgi?uids=17690902},
    citeulike-linkout-3 = {http://www.springerlink.com/content/y12758r036q76846},
    day = {1},
    doi = {10.1007/s00422-007-0172-2},
    issn = {0340-1200},
    journal = {Biological Cybernetics},
    keywords = {biology, eye-saccades, motor, saccades, sc},
    month = oct,
    number = {4},
    pages = {279--292},
    pmid = {17690902},
    posted-at = {2014-09-10 13:06:11},
    priority = {2},
    publisher = {Springer-Verlag},
    title = {Geometry of the superior colliculus mapping and efficient oculomotor computation},
    url = {http://dx.doi.org/10.1007/s00422-007-0172-2},
    volume = {97},
    year = {2007}
}

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Activity in the SC drives the saccade burst generators which are oculomotor neurons in the reticular formation.

Tabareau et al. propose a scheme for a transformation from the topographic mapping in the SC to the temporal code of the saccadic burst generators.

According to their analysis, that code needs to be either linear or logarithmic.