Test Statistics for the Identification of Assembly Neurons in Parallel Spike Trains

Figure 2

Example: A collection of spike trains for neurons that contain a neuronal assembly formed by —three injected coincidences in the example, circled in blue. The window set (i.e., time binning) is considered in our example (yielding a partition with ten windows). We are interested in testing whether neuron is part of an assembly. : in order to compute we consider the number of spikes of neurons in each window and sum over. We get, for our example, . We proceed in a similar way to assess by only considering those windows in which neuron fires, which yields . We thus get that (concluding that is an assembly neuron depends on the significance of the value —see Section 5.1). : we have that and and that and (for the other two pairs—i.e., and —its number of coincidences is lower than its expected one under independence). These numbers yield . : on one hand we have, for the cardinalities of the patterns, where neuron does not necessarily occur, , , , and and, on the other hand, , , , and . For such values and we have that . : for this test statistic we only consider the windows that contain a spike of neuron . Of those, only three of them—that is, those containing an instance of the assembly —yield pairwise intersections of cardinality bigger than . Each such intersection contributes with a cardinality of to the total value of our statistic, yielding .