We undertake a probabilistic analysis of the response of repetitively firing neural populations
to simple pulselike stimuli. Recalling and extending results from the literature, we compute …

In this article, the authors consider optimal decision making in two-alternative forced-choice (TAFC)
tasks. They begin by analyzing 6 models of TAFC decision making and show that all …

We analyse a low-dimensional model for turbulent shear flows. The model is based on Fourier
modes and describes sinusoidal shear flow, in which the fluid between two free-slip walls …

The proper orthogonal decomposition identifies basis functions or modes which optimally
capture the average energy content from numerical or experimental data. By projecting the …

Variational methods are used to determine the optimal currents that elicit spikes in various
phase reductions of neural oscillator models. We show that, for a given reduced neuron …

The well-established method of phase reduction neglects information about a limit-cycle
oscillator's approach towards its periodic orbit. Consequently, phase reduction suffers in …

For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is obtained
by computing the so-called isochrons, ie the sets of points that converge toward the same …

This paper shows that canards, which are periodic orbits for which the trajectory follows
both the attracting and repelling part of a slow manifold, can exist for a two-dimensional …

We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-dimensional
tori. We focus on the effects of symmetry and of the forms of the coupling …

A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase
models, with a single variable describing the phase of the oscillation with respect to some …