Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions

We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical L-values we obtain a conjecture for the first two terms in the ratio of the number of vanishings of twists sorted according to arithmetic progressions.Comment: 16 pages, many figure

Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Room reflections and constancy in speech-like sounds: within-band effects

The experiment asks whether constancy in hearing precedes or follows grouping. Listeners heard speech-like sounds comprising 8 auditory-filter shaped noise-bands that had temporal envelopes corresponding to those arising in these filters when a speech message is played. The „context‟ words in the message were “next you‟ll get _to click on”, into which a “sir” or “stir” test word was inserted. These test words were from an 11-step continuum that was formed by amplitude modulation. Listeners identified the test words appropriately and quite consistently, even though they had the „robotic‟ quality typical of this type of 8-band speech. The speech-like effects of these sounds appears to be a consequence of auditory grouping. Constancy was assessed by comparing the influence of room reflections on the test word across conditions where the context had either the same level of reflections, or where it had a much lower level. Constancy effects were obtained with these 8-band sounds, but only in „matched‟ conditions, where the room reflections were in the same bands in both the context and the test word. This was not the case in a comparison „mismatched‟ condition, and here, no constancy effects were found. It would appear that this type of constancy in hearing precedes the across-channel grouping whose effects are so apparent in these sounds. This result is discussed in terms of the ubiquity of grouping across different levels of representation

Interview with Lloyd Watkins, President Emeritus

Oral history interview with Illinois State University Emeritus President Lloyd Watkins. The interview was conducted on January 23, 2007, by Kate O\u27Toole, as part of the Illinois State University Oral History Project.https://ir.library.illinoisstate.edu/soh/1013/thumbnail.jp

Maximizing the hyperpolarizability of one-dimensional systems

Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of conjugation, that could potentially be adjusted to improve the nonlinear-optical response. However, there were no conditions set on the optimized potential energy function to ensure that the resulting energies were consistent with what is observed in real molecules. Furthermore, the system was placed into a one-dimensional box with infinite walls, forcing the wavefunctions to vanish at the ends of the molecule. In the present work, the walls are separated by a distance much larger than the molecule's length; and, the variations of the potential energy function are restricted to levels that are more typical of a real molecule. In addition to being a more physically-reasonable model, our present approach better approximates the bound states and approximates the continuum states - which are usually ignored. We find that the same universal properties continue to be important for optimizing the nonlinear-optical response, though the details of the wavefunctions differ from previous result.Comment: 10 pages, 5 figure

Photovoltaic Cooking in the Developing World

The challenge of clean cooking is faced by hundreds of millions of people worldwide. We present a cooking technology consisting of a solar panel directly connected to an electric heater in a well-insulated chamber. Assuming continued decrease in solar panel prices, we anticipate that in a few decades Solar Electric Cooking technologies will be the most common cooking technology for the poor. Appropriate use of insulation reduces the power demand making low-power Insulated Solar Electric Cooking systems already cost competitive