Subdivision schemes are widely used in numerical mathematics such as signal/image approximation, analysis and control of data or analysis. However, to develop their full power, subdivision should be incorporated into a multiresolution that, mimicking wavelet analyses, provides multi-scale decomposition function, curve, surface. The ingredients needed define associated scheme decimation detail o...

Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire model. The method is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with ...

Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire model. The method is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with ...

Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier-Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the Full Approximation Scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: enteri...