On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, non-periodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.Comment: 8 pages, uu-encoded ps-fil

Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within this class of algorithms, Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of DR (resp. ADMM) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when both of the two functions (resp. their conjugates) are partly smooth relative to their respective manifolds, we show that DR (resp. ADMM) identifies these manifolds in finite time. Moreover, when these manifolds are affine or linear, we prove that DR/ADMM is locally linearly convergent. When $J$ and $G$ are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified manifolds. This is illustrated by several concrete examples and supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth International Conference on Scale Space and Variational Methods in Computer Visio

A continuous low star formation rate in IZw 18 ?

Deep long-slit spectroscopic observations of the blue compact galaxy IZw 18 obtained with the CFH 3.6 m Telescope are presented. The very low value of oxygen abundance previously reported is confirmed and a very homogeneous abundance distribution is found (no variation larger than 0.05 dex) over the whole ionized region. We concur with Tenorio-Tagle (1996) and Devost et al. (1997) that the observed abundance level cannot result from the material ejected by the stars formed in the current burst, and propose that the observed metals were formed in a previous star formation episode. Metals ejected in the current burst of star formation remain most probably hidden in a hot phase and are undetectable using optical spectroscopy. We discuss different scenarios of star formation in IZw 18. Combining various observational facts, for instance the faint star formation rate observed in low surface brightness galaxies van Zee et al. (1997), it is proposed that a low and continuous rate of star formation occurring during quiescent phases between bursts could be a significant source of metal enrichment of the interstellar medium.Comment: 10 pages, 4 Postscript figures, to be published in Astronomy and Astrophysics main journa

Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field

Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov–Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium

Improving the nutritive value of rice seeds: elevation of cysteine and methionine contents in rice plants by ectopic expression of a bacterial serine acetyltransferase

With the aim of increasing the cysteine level in rice (Oryza sativa L.) and thus improving its nutritional quality, transgenic rice plants were generated expressing an Escherichia coli serine acetyltransferase isoform (EcSAT), the enzyme synthesizing O-acetylserine, the precursor of cysteine. The gene was fused to the transit peptide of the Arabidopsis Rubisco and driven by a ubiquitin promoter to target the enzyme to plastids. Twenty-two transgenic plants were examined for transgene protein expression, and five lines with a high expression level and enzymatic activity, respectively, were selected for further analysis. In these lines, the contents of cysteine and glutathione increased 2.4-fold and 2-fold, respectively. More important is the increase in free methionine and methionine incorporated into the water-soluble protein fraction in seeds. Free methionine increased in leaves up to 2.7-fold, in seeds up to 1.4-fold, and bound to seed proteins up to 4.8-fold, respectively, while the bound methionine level remained constant or even decreased in leaves. Notably, the transgenic lines exhibited higher isoleucine, leucine, and valine contents (each up to 2-fold depending on tissue, free, or bound), indicating a potential conversion of methionine via methionine -lyase to isoleucine. As the transgenic rice plants overexpressing EcSAT had significantly higher levels of both soluble and protein-bound methionine, isoleucine, cysteine, and glutathione in rice they may represent a model and target system for improving the nutritional quality of cereal crops

Characterizations of Super-regularity and its Variants

Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of optimization problems with correspondingly weak assumptions on the value functions. Indeed, one of the earliest classes of nonconvex sets for which convergence results were obtainable, the class of so-called super-regular sets introduced by Lewis, Luke and Malick (2009), has no functional counterpart. In this work, we amend this gap in the theory by establishing the equivalence between a property slightly stronger than super-regularity, which we call Clarke super-regularity, and subsmootheness of sets as introduced by Aussel, Daniilidis and Thibault (2004). The bridge to functions shows that approximately convex functions studied by Ngai, Luc and Th\'era (2000) are those which have Clarke super-regular epigraphs. Further classes of regularity of functions based on the corresponding regularity of their epigraph are also discussed.Comment: 15 pages, 2 figure