  Codifying memories is one of the fundamental problems of modern Neuroscience.
The functional mechanisms behind this phenomenon remain largely unknown.
Experimental evidence suggests that some of the memory functions are performed
by stratified brain structures such as, e.g., the hippocampus. In this
particular case, single neurons in the CA1 region receive a highly
multidimensional input from the CA3 area, which is a hub for information
processing. We thus assess the implication of the abundance of neuronal
signalling routes converging onto single cells on the information processing.
We show that single neurons can selectively detect and learn arbitrary
information items, given that they operate in high dimensions. The argument is
based on Stochastic Separation Theorems and the concentration of measure
phenomena. We demonstrate that a simple enough functional neuronal model is
capable of explaining: i) the extreme selectivity of single neurons to the
information content, ii) simultaneous separation of several uncorrelated
stimuli or informational items from a large set, and iii) dynamic learning of
new items by associating them with already "known" ones. These results
constitute a basis for organization of complex memories in ensembles of single
neurons. Moreover, they show that no a priori assumptions on the structural
organization of neuronal ensembles are necessary for explaining basic concepts
of static and dynamic memories.
