Analysis of perfect mappings of the stimuli through neural temporal sequences

The analysis of an optimal neural system that maps stimuli into unique sequences of activations of fundamental atoms or functional clusters (FCs) is carried out. We say that it is perfect because the system maps with an injective function every stimulus in minimum time with the least number of FCs, such that every FC is activated only once. The neural system has the possibility to sustain several sequences in parallel. In this framework, we study the capacity achievable by the system, minimal completion time and complexity in terms of the number of parallel sequences. We show that the maximum capacity of the system is achieved without using parallel sequences at the expense of long completion times. However, when the capacity value is fixed, the largest possible number of parallel sequences is optimal because it requires short completion times. The complexity measure adds to important points: (i) the largest complexity of the system is achieved without parallel sequences, and (ii) the capacity estimation is a good estimation of the complexity of the system.