Computer algebra: symbolic and algebraic computation (2nd ed.)
Exact simulation of integrate-and-fire models with synaptic conductances
Neural Computation
Simple model of spiking neurons
IEEE Transactions on Neural Networks
Simplicity and efficiency of integrate-and-fire neuron models
Neural Computation
Fast and exact simulation methods applied on a broad range of neuron models
Neural Computation
ACM SIGARCH Computer Architecture News
A Markovian event-based framework for stochastic spiking neural networks
Journal of Computational Neuroscience
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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.