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Exact Simulation of Integrate-and-Fire Models with Exponential Currents

brette{at}di.ens.fr Odyssee Lab (ENPC Certis/ENS Paris/INRIA Sophia), Département d'Informatique, Ecole Normale Supérieure, 75230 Paris Cedex 05, France

Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.