Hempstead Union Free School District and United Public Service Employees Union

In the matter of the fact-finding between the Hempstead Union Free School District, employer, and the United Public Service Employees Union, union. PERB case no. M2009-300. Before: Stuart L. Bass, fact finder

Optimal and Robust Quantum Metrology Using Interaction-Based Readouts

Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram{\'e}r-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry \emph{or} to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal \emph{and} robust quantum metrology is achievable in current spin-squeezing experiments.Comment: 7 pages, 3 figure

A Multiscale Investigation of Habitat Use and Within-river Distribution of Sympatric Sand Darter Species

The western sand darter Ammocrypta clara, and eastern sand darter Ammocrypta pellucida are sand-dwelling fishes of conservation concern. Past research has emphasized the importance of studying individual populations of conservation concern, while recent research has revealed the importance of incorporating landscape scale processes that structure habitat mosaics and local populations. We examined habitat use and distributions of western and eastern sand darters in the lower Elk River of West Virginia. At the sandbar habitat use scale, western sand darters were detected in sandbars with greater area, higher proportions of coarse grain sand and faster bottom current velocity, while the eastern sand darter used a wider range of sandbar habitats. The landscape scale analysis revealed that contributing drainage area was an important predictor for both species, while sinuosity, which presumably represents valley type also contributed to the western sand darter’s habitat suitability. Sandbar quality (area, grain size, and velocity) and fluvial geomorphic variables (drainage area and valley type) are likely key driving factors structuring sand darter distributions in the Elk River. This multiscale study of within-river species distribution and habitat use is unique, given that only a few sympatric populations are known of western and eastern sand darters

Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case

In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. Here the theory is developed for conditioned Gaussian processes for which the resulting SPDE is linear. Applications include the Kalman-Bucy filter/smoother. A companion paper studies the nonlinear case, building on the linear analysis provided here

Redshifted 21cm Signatures Around the Highest Redshift Quasars

The Ly-alpha absorption spectrum of the highest redshift quasars indicates that they are surrounded by giant HII regions, a few Mpc in size. The neutral gas around these HII regions should emit 21cm radiation in excess of the Cosmic Microwave Background, and enable future radio telescopes to measure the transverse extent of these HII regions. At early times, the HII regions expand with a relativistic speed. Consequently, their measured sizes along the line-of-sight (via Ly-alpha absorption) and transverse to it (via 21 cm emission) should have different observed values due to relativistic time-delay. We show that the combined measurement of these sizes would directly constrain the neutral fraction of the surrounding intergalactic medium (IGM) as well as the quasar lifetime. Based on current number counts of luminous quasars at z>6, an instrument like LOFAR should detect >2 redshifted 21cm shells per field (with a radius of 11 degrees) around active quasars as bright as those already discovered by SDSS, and >200 relic shells of inactive quasars per field. We show that Ly-alpha photons from the quasar are unable to heat the IGM or to couple the spin and kinetic temperatures of atomic hydrogen beyond the edge of the HII region. The detection of the IGM in 21cm emission around high redshift quasars would therefore gauge the presence of a cosmic Ly-alpha background during the reionization epoch.Comment: 11 pages, 6 figures. Submitted to Ap

Emergence of the Shackleton Range from beneath the Antarctic Ice Sheet due to glacial erosion

This paper explores the long-term evolution of a subglacial fjord landscape in the Shackleton Range, Antarctica. We propose that prolonged ice-sheet erosion across a passive continental margin caused troughs to deepen and lower the surrounding ice-sheet surface, leaving adjacent mountains exposed. Geomorphological evidence suggests a change in the direction of regional ice flow accompanied emergence. Simple calculations suggest that isostatic compensation caused by the deepening of bounding ice-stream troughs lowered the ice-sheet surface relative to the mountains by ~800m. Use of multiple cosmogenic isotopes on bedrock and erratics (26Al, 10Be, 21Ne) provides evidence that overriding of the massif and the deepening of the adjacent troughs occurred earlier than the Quaternary. Perhaps this occurred in the mid-Miocene, as elsewhere in East Antarctica in the McMurdo Dry Valleys and the Lambert basin. The implication is that glacial erosion instigates feedback that can change ice-sheet thickness, extent, and direction of flow. Indeed, as the subglacial troughs evolve over millions of years, they increase topographic relief; and this changes the dynamics of the ice sheet. © 2013 Elsevier B.V