Semiclassical Transition from an Elliptical to an Oval Billiard

Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many situations, however, action differences can be arbitrarily small and then uniform approximations are more appropriate. In the present paper we examine different uniform approximations for describing the spectra of integrable systems and systems with mixed phase space. This is done on the example of two billiard systems, an elliptical billiard and a deformation of it, an oval billiard. We derive a trace formula for the ellipse which involves a uniform approximation for the Maslov phases near the separatrix, and a uniform approximation for tori of periodic orbits close to a bifurcation. We then examine how the trace formula is modified when the ellipse is deformed into an oval. This involves uniform approximations for the break-up of tori and uniform approximations for bifurcations of periodic orbits. Relations between different uniform approximations are discussed.Comment: LaTeX, 33 pages including 10 PostScript figures, submitted to J. Phys.

Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems

We consider the semiclassical approximation to the spectral form factor K(tau) for two-dimensional uniformly hyperbolic systems, and derive the first off-diagonal correction for small tau. The result agrees with the tau^2-term of the form factor for the GOE random matrix ensemble.Comment: 8 pages, 3 figure

Regulation of podocyte survival and endoplasmic reticulum stress by fatty acids and its modification by Stearoyl-CoA desaturases and cyclic AMP

Podocyte apoptosis is a hallmark in the development and progression of diabetic nephropathy (DN). Several factors of the diabetic milieu are known to induce podocyte apoptosis. Currently, the role of free fatty acids (FFAs) for podocytopathy and podocyte cell death is unknown, although FFAs are considered to be crucially involved in the development of diabetes mellitus type II. It is well known that FFAs are toxic to several cell types including pancreatic § cells and they may contribute to the development of insulin resistance. The aims of this study were to elucidate the role of the saturated palmitic acid and the monounsaturated palmitoleic and oleic acid on podocyte cell death and endoplasmic reticulum (ER)-stress, to investigate more specifically the impact of ER-stress on podocyte survival as well as to elaborate strategies to protect podocytes from lipotoxicity. The present study uncovered that palmitic acid induces podocyte apoptosis and necrosis and leads to ER-stress as reflected by induction of the unfolded protein response (UPR), i.e. upregulation of the ER chaperone immunoglobulin heavy chain binding protein (BiP), X-box protein 1 (XBP-1) mRNA splicing, and a strong upregulation of the proapoptotic transcription factor C/EBP homologous protein (CHOP). Gene silencing experiments of CHOP support a crucial involvment of CHOP and ER-stress in mediating the proapoptotic effect of palmitic acid in podocytes. Contrariwise, monounsaturated FFAs (MUFAs) such as palmitoleic and oleic acid prevent palmitic acid-induced podocyte death and attenuate ER-stress. This study further revealed that the liver X receptor (LXR) agonist TO901317 (TO) ameliorates survival of palmitic acid-treated podocytes. Mechanistically, this beneficial effect can be explained mainly by the induction of stearoyl-CoA desaturase (SCD-) 1 and 2 as shown by gene silencing experiments and further supported from overexpression studies of SCD-1. Moreover, palmitic acid tracing experiments revealed a higher incorporation of palmitic acid into the triglyceride (TG) fraction in podocytes treated with TO or oleic acid, which is at least compatible with a benefit of increased fatty acid storage, by TO, i.e. SCDs, and MUFAs, respectively. In addition, this study provides some preliminary data that adenylate cyclases (AC) may be an interesting target to protect podocytes from ER-stress in general and in particular from palmitic acid-induced podocytopathy and cell death. Experiments with forskolin, a specific AC agonist, and cyclic AMP (cAMP) analogons protect from palmitic acid-induced podocyte lipotoxicity. The effect cannot be explained by an involvment of PKA-CREB signaling as overexpression of a dominant negative CREB mutant could not abrogate the protective effect of forskolin. Furthermore, the beneficial impact of forskolin is not influencing the intrinisic (mitochondrial) apoptotic pathway. However, in addition to the protection from palmitic acid-induced cell death, forskolin is suppressing podocyte death caused by other independent ER-stressors such as tunicamycin and thapsigargin. These findings suggest a direct role of forskolin and increased cAMP levels for a protection from ER-stress in podocytes. In summary, this study unveiled antagonistic effects of palmitic acid versus monounsaturated FFAs for podocyte survival, ER-stress and the UPR. They support an important role of CHOP in the regulation of podocyte death by FFAs. Similarly to exogenous MUFAs, induction of SCDs partially protects podocytes from palmitic acid-induced ER-stress and podocyte death. The protective effect of MUFAs may be related to increased incorporation of palmitic acid into TGs. Additional, preliminary data indicate that AC agonists such as forskolin may be interesting compounds to protect podocytes from ER-stress and from the toxic effects of FFAs. The results of this study offer a rationale for interventional studies aimed at testing whether dietary shifting of the FFA balance toward MUFAs, or tissue- (podocyte-) specific stimulation or overexpression of SCDs can delay the progression of DN. Similarly, the results of this study should encourage more studies to evaluate the therapeutic potential of AC agonists or phosphodiesterase inhibitors for the prevention and treatment of DN

[Review of] Wilbur S. Nye. Plains Indian Raiders

Published in 1968, reprinted in 1974, and a third printing in 1984, this volume contains a collection of 112 superb photographs, mostly by William S. Soule. Born in Maine in 1836, he was wounded in the Civil War and in 1865 entered the photography business, but sold this to become chief clerk in the sutler store operated by John Tappan at Fort Dodge (Kansas), where he resumed his photographic activity during off-duty hours. Soule probably made most of his photographs of Cheyennes and Araphoes [Arapahos] at Fort Dodge, some others at Camp Supply and Fort Sill (Indian Territory). All of the pictures are probably from the period 1867-1875, and they, perhaps more than the text, explain the need for the third printing of this volume

[Review of] Anthony D. Brown, et al. New Directions in Federal Indian Policy

This volume consists of an introduction and ten articles which were originally presented as papers at the second annual conference (sponsored by the American Indian Studies Center, UCLA) held to examine contemporary issues of importance to Indian Americans. The conference of 1978 focused on a review of the recently completed work of the American Indian Policy Review Commission (AIPRC), which Congress had created in 1975 in order to study past Indian/federal government relationships and to recommend new national policies and programs

[Review of] Jack D. Forbes. Native Americans and Nixon: Presidential Politics and Minority Self-Determination 1969-1972

In Native Americans and Nixon, Jack D. Forbes, author of several monographs on the Indian in America\u27s past, has undertaken an important subject, one also difficult because essential sources are lacking. Forbes therefore employs a number of hedges such as we can only guess (116) in his conjecture about the motives and actions of the Nixon administration relative to Indian Americans. In a foreword taking twenty-three of the 124 pages of text, Roxanne Dunbar Ortiz of California State University, Hayward, sets the theme of neocolonialism. Explaining the background of post-World War II techniques of colonial control, she states that Hundreds of thousands of democratic groups were executed or imprisoned by United States forces directly or through military training and aid to puppet regimes (7). Readers receptive to this statement will have little difficulty in speculating with these writers that Nixon\u27s words were hollow when he stated in 1970 that We must assure the Indian that he can assume control of his own life without being separated involuntarily from the tribal group (5)