An efficient finite volume approach has been used to develop a three dimensional Helmholtz acoustic solver for complex geometries. This acoustic solver was utilized to obtain characteristic mode shapes and frequencies of a baffled combustion chamber. An experimental setup, including stationary and moving sensors, has also been used to measure these quantities for the same model combustion chamb...

1 Polar Biological Oceanography, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, Centre for Natural History (CeNak), Zoological Museum, University of Hamburg, Hamburg, Germany, Wageningen Marine Research, Den Helder, Netherlands, 4 Ecological Chemistry, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, C...

The W-S (Wake-Sleep) algorithm is a simple learning rule for the models with hidden variables. It is shown that this algorithm can be applied to a factor analysis model which is a linear version of the Helmholtz machine. But even for a factor analysis model, the general convergence is not proved theoretically. In this article, we describe the geometrical understanding of the W-S algorithm in co...

Multilayer architectures such as those used in Bayesian belief networks and Helmholtz machines provide a powerful framework for representing and learning higher order statistical relations among inputs. Because exact probability calculations with these models are often intractable, there is much interest in finding approximate algorithms. We present an algorithm that efficiently discovers highe...

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the...

We present a formulation of mean-field approximation for layered feed-forward stochastic networks. In this formulation, one can obtain not only estimates of averages for state variables of the networks but also those of intra-layer correlations, the latter of which cannot be obtained by the conventional mean-jield approximation. Moreovel; this formulation provides a pamework to treat “condition...

Unsupervised training of deep generative models containing latent variables and performing inference remains a challenging problem for complex, high dimensional distributions. One basic approach to this problem is the so called Helmholtz machine and it involves training an auxiliary model that helps to perform approximate inference jointly with the generative model which is to be fitted to the ...

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also...

A. K. Bera, ∗ B. Lake, 2 A. T. M. N. Islam, B. Klemke, E. Faulhaber, † and J. M. Law Helmholtz Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany Helmholtz Zentrum Berlin für Materialien und Energie, Gemeinsame Forschergruppe, D-85747 Garching, Germany Hochfeld Magnetlab D...