Quantitative Methods for Analyzing Information Processing in the Mammalian Cortex

In chapter 2, \Ve study the finite sampling problem in measures of information, discussing previously introduced correction procedures, and describing our own method, based on the analytical evaluation of the aYerage error and its subtraction form raw estimates. The analytical evaluation is carried out for different regularizations of the responses, like pure binning, convolutions with continuous distributions and regularization with neural networks. The last sections of the chapter report the results of computer simulations. which shed light on the relative effectiveness and on the range of validity of our and of other methods. Chapter 3 is devoted to discuss how to apply information theoretical analyses to neuronal data. In particular two different aspects are considered. The first is the evaluation of the amount of information contained in the firing rates of single cells. We w~ll discuss how to use the high precision of information measures from low dimensional codes to study the contribution of different properties of the neuronal responses, such as noise or the graded nature of responses, to information processing at different time scales. Furthermore, we discuss the important fact that the initial rate at which a neuron transmits information depends only on the mean firing rates (Skaggs et al. 1993), and is simply related to the sparseness of the neuronal representation. The second problem considered is the calculation of information from high dimensional response spaces, as the principal components of the spike train, or the response vector of a population of simultaneously recorded neurons. It is shown that the limit of dimensions that can lead to reasonably accurate direct measures is low, 2-:3, whereas changes of variables that transforms the response space into the stimulus seL by applying a decoding algorithm that reconstructs a predicted stimulus from the response vector, can give sensible results for higher dimensional codes. This discussion on single cell and multiple cell analysis is corroborated by computer simulations, and by the detailed presentation of original results on the analysis of real data: coding of spatial vie\v by cells in the primate hippocampus, and coding of simple somatosensory stimulations in the rat SI cortical region. In chapter -1 we present a quantitative model of information processing within hippocampus. \Ye take into account the entorhinal-CA3-CA1 system, focusing on the role of the Schaffer collaterals and the direct perforant path connections from entorhinal cortex to CAI. The model is quantitatiYe in that the relevant details of the biological circuitry are taken into account, and the parameters characterizing the network can be related to experimental quantities. The goal of the chapter is to provide an analytical evaluation of the amount of information present: at the firing rate level, in the model CAI output about the firing activity of the celh in entorhinal cortex. For this purpose we use standard techniques of statistical mechc.nics, like mean field theory and the replica trick. \Ye discuss also hm\· to use experimental data to validate some of the building hypotheses of the model, and to check its quantitative predictions.