Towards explaining the speed of kk-means

The $k$-means method is a popular algorithm for clustering, known for its speed in practice. This stands in contrast to its exponential worst-case running-time. To explain the speed of the $k$-means method, a smoothed analysis has been conducted. We sketch this smoothed analysis and a generalization to Bregman divergences

Reconstruction of Hidden Symmetries

Representations of a group $G$ in vector spaces over a field $K$ form a category. One can reconstruct the given group $G$ from its representations to vector spaces as the full group of monoidal automorphisms of the underlying functor. This is a special example of Tannaka-Krein theory. This theory was used in recent years to reconstruct quantum groups (quasitriangular Hopf algebras) in the study of algebraic quantum field theory and other applications. We show that a similar study of representations in spaces with additional structure (super vector spaces, graded vector spaces, comodules, braided monoidal categories) produces additional symmetries, called ``hidden symmetries''. More generally, reconstructed quantum groups tend to decompose into a smash product of the given quantum group and a quantum group of ``hidden'' symmetries of the base category.Comment: 42 pages, amslatex, figures generated with bezier.sty, replaced to facilitate mailin

Corrections to Scaling in the Integer Quantum Hall Effect

Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $\nu{}$. In the second lowest Landau level the irrelevant scaling index is $y_{\mathrm{irr}}=-0.38\pm0.04$. At the center of the lowest Landau level an additional periodic potential is found to be irrelevant with the same scaling index. These results suggest that the localization length exponent $\nu$ is universal with respect to Landau level index and an additional periodic potential.Comment: 8 pages, RevTeX 3.0, 7 PostScript figures in uuencoded compressed tar file include

A microscopic Interpretation of the SM Higgs Mechanism

A model is presented where the Higgs mechanism of the Standard Model is deduced from the alignment of a strongly correlated fermion system in an internal space with $A_4$ symmetry. The ground state is constructed and its energy calculated. Finally, it is claimed that the model may be derived from a field theory in 6+1 dimensions.Comment: 24 pages, 3 figure