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Recent studies have explored theoretically the ability of populations ofneurons to carry information about a set of stimuli, both in the case of purelydiscrete or purely continuous stimuli, and in the case of multidimensionalcontinuous angular and discrete correlates, in presence of additional quencheddisorder in the distribution. An analytical expression for the mutualinformation has been obtained in the limit of large noise by means of thereplica trick. Here we show that the same results can actually be obtained inmost cases without the use of replicas, by means of a much simpler expansion ofthe logarithm. Fitting the theoretical model to real neuronal data, we showthat the introduction of correlations in the quenched disorder improves thefit, suggesting a possible role of signal correlations-actually detected inreal data- in a redundant code. We show that even in the more difficultanalysis of the asymptotic regime, an explicit expression for the mutualinformation can be obtained without resorting to the replica trick despite thepresence of quenched disorder, both with a gaussian and with a more realisticthresholded-gaussian model. When the stimuli are mixed continuous and discrete,we find that with both models the information seem to grow logarithmically toinfinity with the number of neurons and with the inverse of the noise, eventhough the exact general dependence cannot be derived explicitly for thethresholded gaussian model. In the large noise limit lower values ofinformation were obtained with the thresholded-gaussian model, for a fixedvalue of the noise and of the population size. On the contrary, in theasymptotic regime, with very low values of the noise, a lower information valueis obtained with the gaussian model.Comment: 34 pages, 5 figure

Replica-free evaluation of the neuronal population information with mixed continuous and discrete stimuli: From the linear to the asymptotic regime