Implications of physical symmetries in adaptive image classifiers.

It is demonstrated that rotational invariance and reflection symmetry of image classifiers lead to a reduction in the number of free parameters in the classifier. When used in adaptive detectors, e.g. neural networks, this may be used to decrease the number of training samples necessary to learn a given classification task, or to improve generalization of the neural network. Notably, the symmetrization of the detector does not compromise the ability to distinguish objects that break the symmetry.

Pattern formation of underwater sand ripples with a skewed drive.

In this paper we present an experimental study of the dynamics of underwater sand ripples when a regular pattern of ripples is subjected to a skewed oscillatory flow, i.e., one not perpendicular to the direction of the ripple crests. Striking patterns with new, superposed ripples on top of the original ones occur very quickly with a characteristic angle, which is, in general, not perpendicular to the flow. A slower, more complex transition then follows, leading to the final state where the ripples are again perpendicular to the flow. We investigate the variation of the superposed pattern as a function of the direction, amplitude, and frequency of the drive, and as a function of the viscosity (by changing the temperature). We quantify the dynamics of the entire transition process and finally study the grain motion around idealized (solid) skewed ripples. This leads to a characteristic mean path of a single particle. The path has a shape close to a parallelogram, with no apparent connection to the pattern of real, superposed ripples. On the other hand, a thin layer of sand sprinkled on the solid ripples leads to qualitatively similar patterns.

Response classification in psychological testing using a neural network.

A feedforward neural network with error backpropagation has been designed to recognize hand-drawn patterns in a cognitive test. The architecture uses both position and direction sensitivity in the input layer. The training set consisted of 659 icons which were shifted horizontally and vertically to give a total training set of 5931 icons. In testing on an independent set of 31,192 icons produced by 557 subjects from a Danish standard population sample, the rate of misclassification was 0.12% compared with an average rate of sequence errors of 1.6%.

Stability balloon for two-dimensional vortex ripple patterns.

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A sufficient decrease of f leads to a "freezing" of the pattern, while a sufficient increase of f leads to a supercritical secondary "pearling" instability. Sufficient changes in the amplitude a lead to subcritical secondary "doubling" and "bulging" instabilities. Our findings are summarized in a "stability balloon" for vortex ripple pattern formation.