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Blob Formation

Blob formation on a layer of neurons can easily be achieved by local cooperation and global inhibition [1]. Local cooperation generates clusters of activity, and global inhibition lets the clusters compete against each other. The strongest one will finally suppress all others and grow to an equilibrium size determined by the strengths of cooperation and inhibition. The corresponding equations are (cf. Equations 1, 3, and 4):

 

The internal state of the neurons is denoted by , where is a two-dimensional Cartesian coordinate for the location of the neuron. The neurons are arranged on a regular square lattice with spacing 1, i.e., . The neural activity (which can be interpreted as a mean firing rate) is determined by the squashing function of the neuron's internal state . The neurons are connected excitatorily through the Gaussian interaction kernel g. The strength of global inhibition is controlled by . It is obvious that a blob can only arise if (imagine only one neuron is active), and that the blob is larger for smaller . Infinite growth of is prevented by the decay term , because it is linear, while the blob formation terms saturate due to the squashing function . The special shape of is motivated by three factors. Firstly, vanishes for negative values to suppress oscillations in the simulations by preventing undershooting. Secondly, the high slope for small arguments stabilizes small blobs and makes blob formation from low noise easier, because for small values of the interaction terms dominate over the decay term. Thirdly, the finite slope region between low and high argument values allows the system to distinguish between the inner and outer parts of the blobs by making neurons in the center of a blob more active than at its periphery. Additional multiplicative parameters of the decay or cooperation terms would only change time and activity scale, respectively, and do not generate qualitatively new behavior. In this sense the parameter set is complete and minimal.


next up previous
Next: Blob Mobilization Up: The System Previous: Architecture and Dynamics