Patent ID: 8515886

Claim:
A computer implemented method for implementing a neural field a with simulated Amari dynamics, the Amari dynamics being specified by the equation τ {dot over (a)} ( {right arrow over (x)},t )=− a ( {right arrow over (x)},t )+ i ( {right arrow over (x)},t )+ F ( {right arrow over (x)} )* f[a ( {right arrow over (x)},t )]+ h where {right arrow over (x)} is a vector is a spatial coordinate in at least two dimensions, t is a temporal coordinate indicating a time at which the neural field a is evaluated, {dot over (a)} is a derivative of the neural field a with respect to the coordinate t, a({right arrow over (x)}, t) is a state of the neural field a, represented in a spatial domain (SR) using coordinates {right arrow over (x)}, t i({right arrow over (x)}, t) is a function stating an input to the neural field a at time t, f[.] is a bounded monotonic transfer function having values between 0 and 1, F({right arrow over (x)}) is an interaction kernel, τ specifies a time scale on which the neural field a changes and h is a constant specifying a global excitation or inhibition of the neural field a, the method comprising: simulating an application of the transfer function f to the neural field a in a discrete convolution, via a computing device, wherein a total number of iterations for an evolution of a simulation is determined by the application, and the step of simulating the application of the transfer functions f comprises smoothing the neural field a by applying a smoothing operator (S), and the state of the neural field a and the interaction kernel F({right arrow over (x)}) are transformed in a Fourier representation in order to carry out the discrete convolution, wherein the step of applying a smoothing operator (S) to the neural field a comprises: i) a transforming the neural field a to a frequency domain (FR); ii) transforming an input to the neural field a to the frequency domain (FR); iii) cutting out a central part of the obtained representation in the frequency domain F(FR); iv) transforming the central part back to the spatial domain (SR); v) applying the transfer function f to the obtained representation of the central part in the spatial domain (SR); vi) transforming the result of applying the transfer function back to the frequency domain (FR); vii) multiplying the obtained representation of the result in the frequency domain (FR) with the interaction kernel (F); viii) upsampling the result of multiplying with the interaction kernel (F); ix) performing the remaining update steps in the up-sampled frequency domain (FR); x) transforming the neural field a obtained from upsampling the result to the spatial domain (SR); and xi) outputting an actual state of the neural field a transformed to the spatial domain, wherein steps iii to viii are repeated k times before a new input is applied to the neural field a, k being a positive integer.