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need computation-like synchronisation or state update. Synchronisation can be provided by considering "Small World" relationships. (Gao et al., 2001) have shown that a "Small World" network needs only a small fraction of long-range couplings to obtain a great improvement in both stochastic resonance and synchronisation in network connectivity of bistable oscillators. We suggest that the known topology of the visual cortex (Zeki, 1993) if considered as a "Small World" network can provide the foregoing benefits. They would be consistent with the long-range and short-range connectivities of V1 to retinal neurons which have the required bistable oscillator condition provided by on-centre or off-centre neurons responses to light and dark and including those with colour opponency properties. The long and short-range selectivity for connections can be dynamic based on the neuron threshold levels and spatial frequency channels (Dudkin, 1992). The system updates a neuronal state only when new

The cortical implementation of PaSH-FFT was discussed in Section 4.2 where it was argued that the known connectivity of area V1 was sufficient to support its cortical implementation. It was then argued that this implementation could deliver the required convolution in a 'small' number of sequential steps. However, the argument did not rule out the possibility of an alternative mechanism that would deliver the required convolution in fewer steps than PaSH-FFT. It would appear that without a sufficiently developed model of the brain's parallelism, it is unlikely that a mathematical proof of a lower bound for the minimum number of sequential steps could be produced. Currently, the only bound that we can be sure of is that the required convolution could not be completed in one step. The question of determining the

The role of the frequency domain was at the heart of the solution to the cortical convolution conundrum proposed in this paper. However, the possibility of performing the convolution in the spatial domain without resorting to the frequency domain cannot be ruled out by any argument presented in this paper. Although it is unclear how this could be accomplished without resorting to a highly asymmetric model of the distribution of the connectivity of long-range connections. In any case, the search for an explanation of how the dynamic reconfiguration implied by the analysis of this paper is actually accomplished is likely to provide many different conjectures along the way. One possible avenue in this endevour might be provided by further tracer experiments such as those reported in (Angelucci et al.,

This paper reviewed the evidence for long-range contextual modulation and concluded that it implied cortical convolution at the scale of the visual field. This resulted in the need to address the problem of how such long-range convolution could be accounted for with known cortical connectivity and within known time constraints. The paper proposed a solution to the problem that emerged from a mathematical analysis of cortical connectivity to account for the implied constraints of long-range convolution. In particular, it was argued that the known distribution of the long-range patchy connections and extrastriate connections is adequate to provide the means by which the global visual signal can be transformed into frequency space where the convolution can be performed. The main thrust of the argument was that

information indicates a change in the input signal.

minimum lower bound remains an open question.

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2002).

**6. Summary and conclusion**

It was shown that, to a first order approximation, a cortical implementation of PaSH-FFT could account for the large scale convolution implied by known models of contextual modulation. The significance of PaSH-FFT is that it:


It is the conclusion of this paper that the processing of the visual signal in the frequency domain via a fast Fourier transform plays a fundamental role in primate vision.
