Precise n-gram Probabilities from Stochastic Context-free Grammars

We present an algorithm for computing n-gram probabilities from stochastic context-free grammars, a procedure that can alleviate some of the standard problems associated with n-grams (estimation from sparse data, lack of linguistic structure, among others). The method operates via the computation of substring expectations, which in turn is accomplished by solving systems of linear equations derived from the grammar. We discuss efficient implementation of the algorithm and report our practical experience with it.Comment: 12 pages, to appear in ACL-9

The Fourier extension operator on large spheres and related oscillatory integrals

We obtain new estimates for a class of oscillatory integral operators with folding canonical relations satisfying a curvature condition. The main lower bounds showing sharpness are proved using Kakeya set constructions. As a special case of the upper bounds we deduce optimal $L^p(mathbb{S}^2)\to L^q(R \mathbb{S}^2)$ estimates for the Fourier extension operator on large spheres in $\mathbb{R}^3$, which are uniform in the radius $R$. Two appendices are included, one concerning an application to Lorentz space bounds for averaging operators along curves in $R^3$, and one on bilinear estimates

The application of regional-scale geochemical data in defining the extent of aeolian sediments : the Late Pleistocene loess and coversand deposits of East Anglia, UK

The ‘European Coversand Sheet’ is a discontinuous ‘sheet’ of aeolian (windblown) loess and coversand that extends through eastern and southern England, across the English Channel into northern France, Belgium and the Netherlands (Kasse, 1997; Antoine et al., 2003). Whilst some of the earlier aeolian sediments date from the Middle Pleistocene, most correspond to the Late Pleistocene Weichselian / Devensian and earliest Holocene stages. East Anglia contains considerable accumulations of aeolian sediment. Although several valuable studies have attempted to determine the spatial extent of aeolian material (e.g. Catt, 1977, 1985), defining their margins has proved largely difficult because aeolian material is highly susceptible to reworking and removal by various natural and anthropogenic agents. Within this study, we use regional‐scale geochemical data from soils to reconstruct the extent of aeolian sediments in East Anglia. A specific geochemical signature, defined by elevated concentrations of Hafnium (Hf) and Zirconium (Zr), is strongly characteristic of soils developed on aeolian deposits within the United States, China, Europe and New Zealand (Taylor et al., 1983). The data suggests that the approach is sufficiently sensitive to identify a residual aeolian component within soils even where deposits may be thin and unmappable by conventional methods, or if the material has been largely eroded

Quantum network communication -- the butterfly and beyond

We study the k-pair communication problem for quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (i) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (ii) For two particular networks (including the butterfly network) routing is proved optimal, and the free assisting classical communication can at best be used to modify the directions of quantum channels in the network. Consequently, the achievable rate regions are given by counting edge avoiding paths, and precise achievable rate regions in all four assisting scenarios can be obtained. (iii) Optimality of routing can also be proved in classes of networks. The first class consists of directed unassisted networks in which (1) the receivers are information sinks, (2) the maximum distance from senders to receivers is small, and (3) a certain type of 4-cycles are absent, but without further constraints (such as on the number of communicating and intermediate parties). The second class consists of arbitrary backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair communication problem, observations are made on quantum multicasting and a static version of network communication related to the entanglement of assistance.Comment: 15 pages, 17 figures. Final versio

Noise and loss of superconducting aluminium resonators at single photon energies

The loss and noise mechanisms of superconducting resonators are useful tools for understanding decoherence in superconducting circuits. While the loss mechanisms have been heavily studied, noise in superconducting resonators has only recently been investigated. In particular, there is an absence of literature on noise in the single photon limit. Here, we measure the loss and noise of an aluminium on silicon quarter-wavelength ($\lambda/4$) resonator in the single photon regime.Comment: LT28 Conference proceeding, to be published in IOP Conference Serie

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs and heteroscedastic noise. We provide a general theoretical guarantee for TruVaR covering these aspects, and use it to recover and strengthen existing results on BO and LSE. Moreover, we provide a new result for a setting where one can select from a number of noise levels having associated costs. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.Comment: Accepted to NIPS 201

A perception-action strategy for hummingbirds

Many human and animal tasks are thought to be controlled with the tau informational variable. It is widely accepted that controlling the rate of change of tau during decelerative tasks, such as when braking or landing, is one common perceptual control strategy. However, many tasks require accelerating before decelerating to a goal, such as reaching. An advancement of tau theory shows how a single action formula may be used to control the full action unit from initiation to peak velocity, and to rest at the goal, with the same perceptual tau information as before and accounting for the same decelerative kinematics as before. Here, we test the theory against data from high-speed video of a hummingbird flying to its flower feeder. We find that the theory accounts for 97% of the variance in the data, and thus supports it