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Generators of a Picard modular group in two complex dimensions (2011)
Journal Article
Falbel, E., Francsics, G., Lax, P. D., & Parker, J. R. (2011). Generators of a Picard modular group in two complex dimensions. Proceedings of the American Mathematical Society, 139, 2439-2447. https://doi.org/10.1090/s0002-9939-2010-10653-6

The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space.... Read More about Generators of a Picard modular group in two complex dimensions.

Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage (2011)
Journal Article
Einbeck, J. (2011). Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage. Journal of pattern recognition research, 6(2), 175-192. https://doi.org/10.13176/11.288

The mean shift is a simple but powerful tool emerging from the computer science literature which shifts a point to the local center of mass around this point. It has been used as a building block for several nonparametric unsupervised learning techni... Read More about Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage.

The simple harmonic urn (2011)
Journal Article
Crane, E., Georgiou, N., Volkov, S., Wade, A. R., & Waters, R. J. (2011). The simple harmonic urn. Annals of Probability, 39(6), 2119-2177. https://doi.org/10.1214/10-aop605

We study a generalized Pólya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, t... Read More about The simple harmonic urn.

Mertens' theorem for toral automorphisms (2011)
Journal Article
Jaidee, S., Stevens, S., & Ward, T. (2011). Mertens' theorem for toral automorphisms. Proceedings of the American Mathematical Society, 139(05), 1819-1824. https://doi.org/10.1090/s0002-9939-2010-10632-9

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer, periodic orbit... Read More about Mertens' theorem for toral automorphisms.