A new method of checking the consistency of precedence matrices is demonstrated. The method is based on the theorem that a precedence matrix is consistent if and only ff every principal submatrix has at least one zero row or zero column. Because this method recognizes inconsistencies in their implicit form whereas the conventional method recognized only explicit contradictions, a considerable saving in time and effort can be effected, since the process of making explicit all the implicatmns of a precedence matrix, particularly a larger one, is a tedious time-consuimng operation.
In a recent paper Fuortes & Hodgkin (1964) proposed a non-linear electrical filter model for the Limulus (horseshoe crab) visual response. This model, with modifications to improve its agreement with the data, has been studied by means of the computer program NIH-OMR 9 B 21 developed by Berman, which, given a model and a set of experimental data, finds the values of the model parameters which give a least squares fit to the data. The Fuortes-Hodgkin model consists of a cascade of identical stages, each composed of a series isolating or amplifying unit, and a shunt resistance and capacitance. The necessary non-linearity is introduced by a feed-back loop, which makes the shunt resistors decrease as the output increases. Since this model gave good qualitative agreement with the data obtained on Limulus (Fuortes & Hodgkin, 1964) and also with some data on the human visual system (J. G. Robson, Cambridge, personal communication) it seemed worth while to investigate its properties further by means of the computer program 9B21.The general conclusions are that the behaviour is not, within limits, very sensitive to the number of stages in the chain-nine, ten, and eleven stage chains gave almost equally good fits. However, changing the location of the feed-back loop alters the system behaviour substantially, and the fit was greatly improved by making the shunt resistances depend not on the output of the last stage, but of the stage preceding it.
METHODSFuorte8 and Hodgkin Model. The experiments are described in detail by Fuortes & Hodgkin (1964) and Fuortes (1959), but a brief summary will be given here. The stimuli were short pulses and steps of light of varying amplitudes, and the responses were the generator potentials measured by micro-electrodes in the eccentric cells of the Limulu8 ommatidiuxm in conditions of dark and light adaptation, at 8°C. Fuortes and Hodgkin observed that with background light, or pre-exposure, both the time constant and sensitivity of the system decreased, the latter by a far larger factor than the former. This type of
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