Lossless Information Transmission

Before presenting our results on structural implications of the observed and predicted levels of activity in the MB and of the requirement of lossless information transmission, some explanation of our probabilistic approach seems warranted. The probability Ppn of activity in a given PN mainly reflects properties of the input space (odor space) and different patterns of PN activity are diced out for every LFP cycle. The connection probabilities pn- kc and kc bkc, on the other hand, refer to the random connectivity of each locust, i.e., the connectivity is determined only once for each animal. In building distributions (and taking averages) with respect to both probability spaces, we are making statements about the distribution of (and the typical value of) properties for all locusts in response to all possible odors, in a sense. 

Using the above assumptions of independently chosen random connections and independently and randomly active PNs we can directly calculate the probability for a given KC to be active. 

Because all KCs look at the same PN activity patterns at any given time, their activity is not independent, such that the probability distribution for the number of 

The expectation value for the number of active KCs depends critically on 

In summary, the activity level in the MB depends essentially on the connectivity degree and the firing threshold of KCs as expected. More surprising is the extremely wide distribution of possible activity levels which may introduce the necessity of gain control mechanisms. 

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