The Hall and longitudinal conductivities of a recently studied holographic model of a quantum Hall ferromagnet are computed using the Karch-OBannon technique. In addition, the low temperature entropy of the model is determined. The holographic model
has a phase transition as the Landau level filling fraction is increased from zero to one. We argue that this phase transition allows the longitudinal conductivity to have features qualitatively similar to those of two dimensional electron gases in the integer quantum Hall regime. The argument also applies to the low temperature limit of the entropy. The Hall conductivity is found to have an interesting structure. Even though it does not exhibit Hall plateaux, it has a flattened dependence on the filling fraction with a jump, analogous to the interpolation between Hall plateaux, at the phase transition.
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another arc, or fro
m three circular arcs [Dubins, 1957]. Dubins original proof uses advanced calculus; later, Dubins result was reproved using control theory techniques [Reeds and Shepp, 1990], [Sussmann and Tang, 1991], [Boissonnat, Cerezo, and Leblond, 1994]. We introduce and study a discrete analogue of curvature-constrained motion. We show that shortest bounded-curvature polygonal paths have the same structure as Dubins paths. The properties of Dubins paths follow from our results as a limiting case---this gives a new, discrete proof of Dubins result.
We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in qua
ntum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid. Conversely, we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant.
This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian observation noise,
with variance strictly greater than zero, Srinivas et al proved that the regret vanishes at the approximate rate of $O(1/sqrt{t})$, where t is the number of observations. To complement their result, we attack the deterministic case and attain a much faster exponential convergence rate. Under some regularity assumptions, we show that the regret decreases asymptotically according to $O(e^{-frac{tau t}{(ln t)^{d/4}}})$ with high probability. Here, d is the dimension of the search space and tau is a constant that depends on the behaviour of the objective function near its global maximum.
