We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern Hamiltonian, can be understood as arising from different representations of the one-boundary Temperley–Lieb algebra. For a system of size L these representations a...

Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-d...

The starred for-adverbial in (1a) reflects standard judgments: in the presence of a DP direct object like a cake—which following terminology by Borer (2005) is referred to here as a Q(uantity)-DP— with an incremental theme verb like eat, the VP is telic. In contrast, in (1b), with a mass noun direct object like cake—referred to here as a non-Q-DP—the VP is atelic. Although these are the pattern...

We prove sharp L estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation C ⊂ T ∗ΩL × T ∗ΩR projects to T ∗ΩL and to T ∗ΩR with corank one singularities of type ≤ 2. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line ...

Robotic systems can achieve real-time visual odometry by extracting a fixed number of invariant keypoints from the current camera frame, matching them against keypoints from a previous frame, and calculating camera motion from matching pairs. If keypoints are selected by response only they can become concentrated in a small image region. This decreases the chance for keypoints to match between ...

Regular expressions with back referencing have been used in a variety of software products in common use, such as Emacs and Perl, for many years. In these products, regular expressions have been extended with a naming construct. If a subexpression is named by some variable, whenever this subexpression matches some string, that string is assigned to the variable. Later occurrences of the same va...

Spin glasses is a fascinating field, from which a variety of theoretical models and concepts were invented. As an emergent state from the random magnetic system, it defers from other statistical systems in several ways. In particular, the quenched variables prevent the system to be ergodic, and the competitive interactions gives rise to non-trivial degeneracies of the ground states as well as t...

We describe an O(n) time algorithm for computing the exact probability that two d-dimensional probabilistic point sets are linearly separable, for any fixed d ≥ 2. A probabilistic point in d-space is the usual point, but with an associated (independent) probability of existence. We also show that the d-dimensional separability problem is equivalent to a (d + 1)-dimensional convex hull membershi...

The effect of setting all T=0 two body interaction matrix elements equal to a constant (or zero) in shell model calculations (designated as < T = 0 >= 0) are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using < T = 0 >= 0 in single j shell calculations degeneracies appear e.g. the I =