The moment map on the space of symplectic 3D Monge-Amp\`ere equations

For any second-order scalar PDE $\mathcal{E}$ in one unknown function, that we interpret as a hypersurface of a second-order jet space $J^2$, we construct, by means of the characteristics of $\mathcal{E}$, a sub-bundle of the contact distribution of the underlying contact manifold $J^1$, consisting of conic varieties. We call it the contact cone structure associated with $\mathcal{E}$. We then focus on symplectic Monge-Amp\`ere equations in 3 independent variables, that are naturally parametrized by a 13-dimensional real projective space. If we pass to the field of complex numbers $\mathbb{C}$, this projective space turns out to be the projectivization of the 14-dimensional irreducible representation of the simple Lie group $\mathsf{Sp}(6,\mathbb{C})$: the associated moment map allows to define a rational map $\varpi$ from the space of symplectic 3D Monge-Amp\`ere equations to the projectivization of the space of quadratic forms on a $6$-dimensional symplectic vector space. We study in details the relationship between the zero locus of the image of $\varpi$, herewith called the cocharacteristic variety, and the contact cone structure of a 3D Monge-Amp\`ere equation $\mathcal{E}$: under the hypothesis of non-degenerate symbol, we prove that these two constructions coincide. A key tool in achieving such a result will be a complete list of mutually non-equivalent quadratic forms on a $6$-dimensional symplectic space, which has an interest on its own.Comment: v2, 41 pages, 1 figure, submitte

Using a Quadtree Algorithm To Assess Line of Sight

A matched pair of computer algorithms determines whether line of sight (LOS) is obstructed by terrain. These algorithms were originally designed for use in conjunction with combat-simulation software in military training exercises, but could also be used for such commercial purposes as evaluating lines of sight for antennas or determining what can be seen from a "room with a view." The quadtree preparation algorithm operates on an array of digital elevation data and only needs to be run once for a terrain region, which can be quite large. Relatively little computation time is needed, as each elevation value is considered only one and one-third times. The LOS assessment algorithm uses that quadtree to answer LOS queries. To determine whether LOS is obstructed, a piecewise-planar (or higher-order) terrain skin is computationally draped over the digital elevation data. Adjustments are made to compensate for curvature of the Earth and for refraction of the LOS by the atmosphere. Average computing time appears to be proportional to the number of queries times the logarithm of the number of elevation data points. Accuracy is as high as is possible for the available elevation data, and symmetric results are assured. In the simulation, the LOS query program runs as a separate process, thereby making more random-access memory available for other computations

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamic response in the deeply supercooled regime (T = 180 K) which is typically not accessible through equilibrium methods. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch-Williams-Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalised variance $\chi_T$. Our study provides new insights into X-ray stimulated stress relaxation and the underlying mechanisms behind spatio-temporal fluctuations in biological granular materials

Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump–probe experiments at X-ray free-electron laser sources

A prototype device capable of splitting an X-ray pulse into two adjustable fractions, delaying one of them with the aim of performing split pulse X-ray photon correlation spectroscopy and pump–probe type studies was designed and manufactured. Time delays up to 2.95 ns have been demonstrated. The achieved contrast values of 56% indicate a feasibility of performing coherence-based experiments with the delay line

5-α reductase inhibitors and prostate cancer prevention: where do we turn now?

With the lifetime risk of being diagnosed with prostate cancer so great, an effective chemopreventive agent could have a profound impact on the lives of men. Despite decades of searching for such an agent, physicians still do not have an approved drug to offer their patients. In this article, we outline current strategies for preventing prostate cancer in general, with a focus on the 5-α-reductase inhibitors (5-ARIs) finasteride and dutasteride. We discuss the two landmark randomized, controlled trials of finasteride and dutasteride, highlighting the controversies stemming from the results, and address the issue of 5-ARI use, including reasons why providers may be hesitant to use these agents for chemoprevention. We further discuss the recent US Food and Drug Administration ruling against the proposed new indication for dutasteride and the change to the labeling of finasteride, both of which were intended to permit physicians to use the drugs for chemoprevention. Finally, we discuss future directions for 5-ARI research

Endstation for ultrafast magnetic scattering experiments at the free-electron laser in Hamburg

This content may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This material originally appeared in Review of Scientific Instruments 84, 013906 (2013) and may be found at https://doi.org/10.1063/1.4773543.An endstation for pump–probe small-angle X-ray scattering (SAXS) experiments at the free-electron laser in Hamburg (FLASH) is presented. The endstation houses a solid-state absorber, optical incoupling for pump–probe experiments, time zero measurement, sample chamber, and detection unit. It can be used at all FLASH beamlines in the whole photon energy range offered by FLASH. The capabilities of the setup are demonstrated by showing the results of resonant magnetic SAXS measurements on cobalt-platinum multilayer samples grown on freestanding Si3N4 membranes and pump-laser-induced grid structures in multilayer samples.BMBF, 05K10GU4, Verbundprojekt: FSP 301 - FLASH: Nanoskopische Systeme. Teilprojekt 6: Aufbau einer Plattform für Experimente mit ultimativer Orts- und Zeitauflösung unter Ausnutzung der kohärenten Beugung weicher Röntgenstrahlung an PETRA III und FLASHDFG, 13002249, SFB 668: Magnetismus vom Einzelatom zur NanostrukturDFG, 170620586, SFB 925: Licht-induzierte Dynamik und Kontrolle korrelierter Quantensystem