Design of linear kernels. *A* demonstrates how the linear kernels and rate vector (*R*_{ob}) were constructed for the random dot data. Discrete time steps were obtained by binning the entire duration of the experiment with suitable time bins. The *n*th entry in the rate vector array equals the number of spikes during the *n*th time step. *X*_{ab} and *X*_{ac} are two 1 pixel × 1 pixel kernels that span pixels at coordinates (*a*,*b*) and (*a*,*c*), respectively. The *n*th entry of each vector equals the number of dots within the areas spanned by the vectors during the *n*th time step. During the 1st illustrated frame, there is a dot at (*a*,*b*) but no dot at (*a*,*c*). Hence the corresponding entries in vectors *X*_{ab} and *X*_{ac} during this time step are 1 and 0, respectively. During the 2nd illustrated frame, there are no dots at (*a*,*b*) but a dot at (*a*,*c*). Hence the entries in the 2 vectors at this time step are 0 and 1, respectively. *B* shows construction of the quadratic kernels. The *n*th entry of each vector equaled the product of the number of dots in the 2 subregions (*i*,*j*) and (*i*,*k*) spanned by that vector during the *n*th time step.

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