Integrable Combinatorics

We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)Comment: 21 pages, 16 figures, proceedings of ICMP1

Qubit Entanglement Breaking Channels

This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as classical-quantum channels. We also review the complete positivity conditions in a canonical parameterization and show how they lead to entanglement-breaking conditions.Comment: Contains main results from section 2 of quant-ph/0207100 Version 2 corrects minor typos. Final version to appear in Rev. Math. Phy

Octahedron-based Projections as Intermediate Representations for Computer Imaging: TOAST, TEA, and More

This paper defines and discusses a set of rectangular all-sky projections that have no singular points, notably the Tesselated Octahedral Adaptive Spherical Transformation (or TOAST) developed initially for the WorldWide Telescope. These have proven to be useful as intermediate representations for imaging data where the application transforms dynamically from a standardized internal format to a specific format (projection, scaling, orientation, etc.) requested by the user. TOAST is strongly related to the Hierarchical Triangular Mesh pixelization and is particularly well adapted to situations where one wishes to traverse a hierarchy of images increasing in resolution. Because it can be recursively computed using a very simple algorithm it is particularly adaptable to use with graphical processing units

Suppression of Octahedral Tilts and Associated Changes of Electronic Properties at Epitaxial Oxide Heterostructure Interfaces

Epitaxial oxide interfaces with broken translational symmetry have emerged as a central paradigm behind the novel behaviors of oxide superlattices. Here, we use scanning transmission electron microscopy to demonstrate a direct, quantitative unit-cell-by-unit-cell mapping of lattice parameters and oxygen octahedral rotations across the BiFeO3-La0.7Sr0.3MnO3 interface to elucidate how the change of crystal symmetry is accommodated. Combined with low-loss electron energy loss spectroscopy imaging, we demonstrate a mesoscopic antiferrodistortive phase transition and elucidate associated changes in electronic properties in a thin layer directly adjacent to the interface