It makes use of my function matrix notation, and I consider it a simplified model of a single neuron (in the physics tradition of if something is too hard, simplify it until you have something you can actually work with, at least as a starting point).

[ y1 ] [ s1[x1,t1] ] [ sum[x1,t] ] [ a1 a2 a3 a4 a5 ] [ x1 ] [ y2 ] [ s2[x1,t2] ] [ x2 ] [ y3 ] [ s3[x1,t3] ] [ x3 ] [ y4 ] = [ s4[x1,t4] ] [ x4 ] [ y5 ] [ s5[x1,t5] ] [ x5 ] [ y6 ] [ s6[x1,t6] ] [ y7 ] [ s7[x1,t7] ] [ y8 ] [ s8[x1,t8] ]where:

{a1,a2,a3,a4,a5} are reals/floats and can be positive or negative. sum[x,t] sums the input x for a time-slice of length t (with output 0 during this time slice), then spits out the result at the end of that time slice. If we don't include the sum[] term, assume t = 0. Indeed, we only need t > 0 if we want time-dependence. s_k[x,t_k] are sigmoids, with passed in parameter t_k.Note that there are a lot of free parameters here, and I have no idea how the brain tweaks them! We have {a1,a2,a3,a4,a5}, {t,t1,t2,...,t8}, and then we have the sigmoids {s1,s2,..,s8} Indeed, until we have some idea how to fill in all these parameters we can't actually make use of this model/representation.

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