In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez ( 2009 ) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

In the insect olfactory system, odor-evoked transient synchronization of antennal lobe (AL) projection neurons (PNs) is phase-locked to the oscillations of the local field potential. Sensory information is contained in the spatiotemporal synchronization pattern formed by the identities of the phase-locked PNs. This article investigates the role of feedback inhibition from the local neurons (LNs) in this coding. First, experimental biological results are reproduced with a reduced computational spiking neural network model of the AL. Second, the low complexity of the model leads to a mathematical analysis from which a lower bound on the phase-locking probability is derived. Parameters involved in the bound indicate that PN phase locking depends not only on the number of LN-evoked inhibitory postsynaptic potentials (IPSPs) previously received, but also on their temporal jitter. If the inhibition received by a PN at the current oscillatory cycle is both perfectly balanced (i.e., equal to the mean inhibitory drive) and precise (without any jitter), then the PN will be phase-locked at the next oscillatory cycle with probability one.

A novel unsupervised learning rule, called Boundary Adaptation Rule (BAR), is introduced for scalar quantization. It is shown that the rule maximizes information-theoretic entropy and thus yields equiprobable quantizations of univariate probability density functions. It is shown by simulations that BAR outperforms other unsupervised competitive learning rules in generating equiprobable quantizations. It is also shown that our rule can do better or worse than the Lloyd I algorithm in minimizing average mean square error, depending on the input distribution. Finally, an application to adaptive non-uniform analog to digital (A/D) conversion is considered.