Abstract
Our contribution in this paper is threefold. First, we present a framework for characterizing spike synchrony in neuronal spike-train recordings that is based on the identification of spikes (also called electrical impulses or action potentials) with what we call influence maps: real-valued functions that describe an influence region around the corresponding spike times within which a continuous and possibly graded notion of synchrony among spikes is defined. Second, we provide a model of synchrony within our framework that is based on a continuous, two-valued (i.e., bivalent) measure of synchrony, aimed at overcoming the drawbacks of time discretization in the bin-based one (the almost exclusively applied model in the field), which we also describe within our framework. Third, in connection with the assessment of synchrony in our continuous model, we provide methodology and algorithms for the identification of frequent parallel episodes in sequences of events (i.e., sets of items, normally required to occur within a certain time span in the sequence). Special attention is given to the notion of frequency of parallel episodes and its computation.