Fuzzy characterization of spike synchrony in parallel spike trains

We present a framework for characterizing spike (and spike-train) synchrony in parallel neuronal spike trains that is based on the identification of spikes with what we call influence maps : real-valued functions that describe an influence region around the corresponding spike times within which possibly graded (i.e., fuzzy) synchrony with other spikes is defined. We formalize two models of synchrony in this framework: the bin-based model (the almost exclusively applied model in the field) and a novel, alternative model based on a continuous, graded notion of synchrony, aimed at overcoming the drawbacks of the bin-based model. We study the task of identifying frequent (and synchronous) neuronal patterns from parallel spike trains in our framework, formalized as an instance of what we call the fuzzy frequent pattern mining problem (a generalization of standard frequent pattern mining) and briefly evaluate our synchrony models on this task.