Computational Methods for the Construction of a Class of Noetherian Operators

This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer algebra packages such as CoCoA and Singular

Judicially Modified Democracy: Court and State Pre-Emption of Local GMO Regulation in Hawaii and Beyond

The federal framework for regulating genetically modified organisms (GMOs) has long been criticized as fragmented and inadequate to protect against various health, environmental, and economic concerns. Yet, despite having the legal authority to augment the federal framework, the overwhelming majority of states have failed to enact any substantive legislation governing GMOs at the state-level. In the wake of this regulatory vacuum, a small but growing number of local governments have attempted to regulate GMOs locally. However, local GMO regulations face significant challenges by the GMO industry, which has sought to undo local regulatory authority both through the courts and through industry lobbying of state legislators to expressly pre-empt local regulation. Today, roughly 17 states have now expressly pre-empted local authority to regulate GMOs, largely due to industry influence. Hawaii is a high-stakes battleground for the genetically modified debate, and in 2013-2014, three local counties—Maui County, Hawaii County, and Kauai County—all attempted to regulate GMOs at the local level. Although the counties purportedly had broad statutory authority to regulate to protect local health, life, and property, as well as conservation obligations under the Hawaii Constitution, the local GMO ordinances were quickly challenged in court by the GMO industry and soon invalidated by the federal district court in Hawaii on novel state and federal pre-emption grounds. As the very first local GMO regulations struck down on state and federal pre-emption grounds, the Hawaii pre-emption decisions will likely have a significant adverse impact on local GMO regulation across the country if allowed to stand. This article argues that the recent pre-emption decisions were wrongly decided under traditional pre-emption principles, and further argues that in the absence of state or federal comprehensive regulatory schemes sufficient to address mounting health, environmental, and economic concerns, courts and states should refrain from denying local authority to regulate GMOs. Permitting local regulation of GMOs not only fosters and supports legitimate local democracy, but it may also be what is most needed to find innovative solutions to acknowledged GMO risks and realities

Ingress observations of the 1980 eclipse of the symbiotic star CI Cyngni

One of the major results from the IUE may prove to be the knowledge gained by studies of the ultraviolet spectra of symbiotic stars. Symbiotics combine spectral features of a cool M giant like photosphere with strong high excitation emission lines of nebular origin, superposed. The UV spectra are dominated by intense permitted and semiforbidden emission lines and weak continua indicative of hot compact objects and accretion disks. Two symbiotics, AR Pav and CI Cyg are thought to be eclipsing binaries and IUE observations during the 1980 eclipse of CI Cygni are discussed

Logical pre- and post-selection paradoxes are proofs of contextuality

If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Luders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without Luders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 kHz per root Hz with only 2 mW of continuous wave, single mode input power. We describe the measurement of a weak value and show how even higher frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.Comment: 4 pages, 3 figures, published in PR

Complementary weak-value amplification with concatenated postselections

We measure a transverse momentum kick in a Sagnac interferometer using weak-value amplification with two postselections. The first postselection is controlled by a polarization dependent phase mismatch between both paths of a Sagnac interferometer and the second postselection is controlled by a polarizer at the exit port. By monitoring the darkport of the interferometer, we study the complementary amplification of the concatenated postselections, where the polarization extinction ratio is greater than the contrast of the spatial interference. In this case, we find an improvement in the amplification of the signal of interest by introducing a second postselection to the system

All-Optical Delay of Images using Slow Light

Two-dimensional images carried by optical pulses (2 ns) are delayed by up to 10 ns in a 10 cm cesium vapor cell. By interfering the delayed images with a local oscillator, the transverse phase and amplitude profiles of the images are shown to be preserved. It is further shown that delayed images can be well preserved even at very low light levels, where each pulse contains on average less than one photon.Comment: 4 pages, 5 figure

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers

EPR Steering Inequalities from Entropic Uncertainty Relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.Comment: 10 pages, 2 figure