@TechReport{Supelec830,

author = {Frédéric Alexandre and Jérémy Fix and Nicolas Rougier and Thierry Vieville},

title = {Algorithmic adjustment of neural field parameters},

year = {2009},

abstract = {Revisiting neural-field calculation maps in the discrete case, we
propose algorithmic mechanisms allowing to choose a right set of
parameters in order to both (i) guaranty the stability of the
calculation and (ii) tune the shape of the output map. These
results do not ``prove'' the existence of stable bump solutions,
this being already known and extensively verified numerically,
but allow to calculate algorithmically the related parameters.
The results apply to scalar and vectorial neural-fields thus
allowing to bypass the inherent limitations brought by mean
frequency models and also take the laminar structure of the
cortex or high-level representation of cortical computations into
account. We obtain an easy to implement procedure that guaranty
the convergence of the map onto a fixed point, even with large
sampling steps. Furthermore, we report how rectification is the
minimal required non-linearity to obtain usual neural-field
behaviors. We also propose a way to control and tune these
behaviors (filtering, selection, tracking, remanence) and
optimize the convergence rate. This applies to both non
parametric profiles, i.e. adjusting the weight values directly,
or to parametric profiles and thus adjusting their parameters
(e.g. Mexican-hat profiles). Beyond these algorithmic results,
the idea of studying neural computations as discrete dynamical
systems and not only the discretization of a continuous system is
emphasized here. The outcome is shared as an open-source plug-in
module, called EnaS (http://enas.gforge.inria.fr), to be used in
existing simulation software}

}