Analyse numerique pour ingenieurs by André Fortin

By André Fortin

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Taking time t to be measured relative to the time of the switch (either from 01 to a 2 or vice versa), the word distribution P(w(t)) was collected for every time slice t E [-I, 11 s. 17 The input/output relation of the fly motion-sensitive neuron H1 adapts continuously to the local variance. (a). @). The rate measured in response follows log a(t). (c). Input/output relati~n~measured at time bins throughout the response differ considerably in their horizontal scale. (d). However, when the projected stimulus s is normalized by the local standard deviation, the input/output relations overlay.

16b). 16~). While Laughlin's work implies that evolution or development has sculpted the neural response to match the natural environment, it is possible that adaptive processes occur on much faster time scales. For the motion-sensitive neuron H1 in the blowfly, in response to a Gaussian stimulus with a variance a', the input/output relation adapts such that the stimulus appears to be scaled in units of its standard deviation 1121. Furthermore, it was shown that this rescaling, analogous to Laughlin's results, optimizes information transmission through the system [12].

18)),to invert the relationship between stimulus and spikes: where s as before represents the complete stimulus description. In forming our reduced N-dimensional model, we have replaced s with some limited number of dimensions, s l , $ 2 , . . , S N . 31) Ion,spike 5 l o n e spike, so that one has an objective measure of the improvement in quality gained by adding additional dimensions. This was applied to the analysis of the NM neurons described previously; it was found that the ID STA-based model recovers 63% of the direct information, while a 2D model recovers 75% [72].

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