After Helmholtz.

Varieties of Helmholtz Machine

The Helmholtz machine is a new unsupervised learning architecture that uses top-down connections to build probability density models of input and bottom-up connections to build inverses to those models. The wake-sleep learning algorithm for the machine involves just the purely local delta rule. This paper suggests a number of different varieties of Helmholtz machines, each with its own strength...

Preconditioning Helmholtz linear systems

Linear systems which originate from the simulation of wave propagation phenomena can be very difficult to solve by iterative methods. These systems are typically complex valued and they tend to be highly indefinite, which renders the standard ILU-based preconditioners ineffective. This paper presents a study of ways to enhance standard preconditioners by altering the diagonal by imaginary shift...

Kelvin-Helmholtz Instabilities

Circular concentric Helmholtz resonators

The effect of specific cavity dimensions of circular concentric Helmholtz resonators is investigated theoretically, computationally, and experimentally. Three analytical models are employed in this study: ~1! A two-dimensional model developed to account for the nonplanar wave propagation in both the neck and the cavity; ~2! a one-dimensional solution developed for the limit of small cavity leng...

Elastic Helmholtz resonators

The influence of wall elasticity on the response of a Helmholtz resonator is examined by analyzing the canonical case of a thin elastic spherical shell with a circular aperture subject o plane wave excitation. By neglecting the thickness of the wall and representing the elasticity via a "thin shell" theory the problem is reduced to one of solving an integral equation over the aperture for the p...