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Fig. 7 Robust reconstruction of stimuli encoded by complex cells with stochastic ion channels.

Here, we evaluate the decoding of stimuli encoded by complex cells with BSGs modeled as Hodgkin–Huxley neurons.

These results suggest that stimuli encoded by complex cells can be decoded with a significantly lower number of measurements than that required by Algorithm 1.

Complex cells with a nucleus (eukaryotes) display a tightly controlled multistage cell division cycle.

HMAX is a multiple layer system with simple and complex cell layers alternating that sets up connections to simple cells based on randomly chosen exemplars, and a MAX function performed by the complex cells of their simple cell inputs.

Therefore, we can cast the problem of reconstructing temporal stimuli encoded by neural circuits with complex cells as a feasibility problem, that is, finding all positive semidefinite Hermitian matrices that satisfy (29) and have rank 1.

Example of reconstructed video encoded by a neural circuit with complex cells.

Snapshots of the original videos encoded by a neural circuit with complex cells are shown on the left.

The encoding of stimulus by the neural circuit with complex cells is a particular case of the low-rank DSP of the form given in (76).

When using an algorithm similar to Algorithm 1 to reconstruct spatio-temporal stimuli encoded by a neural circuit with complex cells, at least (operatorname{dim}({mathcal {H}}^{p}_{1}) ( operatorname{dim}({mathcal {H}}^{p}_{1})+1 ) /2) measurements are required.

Assuming that the spike times ((t_{k}^{i}), kin mathbb{I}^{i}), (i=1,2,ldots,M) , are known, by Lemma 1 the neural circuit with complex cells encodes the stimulus via a set of linear functionals acting on (u_{2}) (see equation (7)).