The Effect of Non-tightness on Bayesian Estimation of PCFGs

Probabilistic context-free grammars have the unusual property of not always defining tight distributions (i.e., the sum of the “probabilities” of the trees the grammar generates can be less than one). This paper reviews how this non-tightness can arise and discusses its impact on Bayesian estimation of PCFGs. We begin by presenting the notion of “almost everywhere tight grammars ” and show that linear CFGs follow it. We then propose three different ways of reinterpreting non-tight PCFGs to make them tight, show that the Bayesian estimators in Johnson et al. (2007) are correct under one of them, and provide MCMC samplers for the other two. We conclude with a discussion of the impact of tightness empirically.

Composition changes in the lower thermosphere

Chemical heating above polar thermosphere and formation of helium bulge during winte

Imaging and quantum efficiency measurement of chromium emitters in diamond

We present direct imaging of the emission pattern of individual chromium-based single photon emitters in diamond and measure their quantum efficiency. By imaging the excited state transition dipole intensity distribution in the back focal plane of high numerical aperture objective, we determined that the emission dipole is oriented nearly orthogonal to the diamond-air interface. Employing ion implantation techniques, the emitters were engineered with various proximities from the diamond-air interface. By comparing the decay rates from the single chromium emitters at different depths in the diamond crystal, an average quantum efficiency of 28% was measured.Comment: 11 pages and 4 figure

Geometry of Banach spaces and biorthogonal systems

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system