Modal Logic, Temporal Models and Neural Circuits: What Connects Them

“Processes” that temporally choreograph a large number of players appear pervasively in many situations, but pose particular challenges when one attempts to understand how these processes are orchestrated at an elemental level, namely, how may one learn what rules are used by the players to bring about this precise evolution of the process? What topologies are used by the network in codifying the rules of interaction? A particular example we study in this paper deals with the analysis of synthetic data simulating Microelectrode array(MEA) recordings. By computing statistically significant temporal patterns expressed in a propositional modal logic, we extract from it functional connectivity among neurons in an ensemble. For this purpose, we propose a novel algorithm founded upon many ideas from temporal logic, model inference and time-series data analysis, all aimed at the MEA inference problem. The approach, described here, has been validated by several examples in this domain with highly promising results.

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