Symmetry Breaking and Bifurcations in the Periodic Orbit Theory; 1, Elliptic Billiard

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of the circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We show that the circular disk limit of the diameter-orbit contribution is also reached through contributions from closed (periodic and non-periodic) orbits of hyperbolic type with an even number of reflections from the boundary. We obtain the Maslov indices depending on deformation and energy in terms of the phases of the complex error and Airy functions. We find enhancement of the amplitudes near the common bifurcation points of both short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones

Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

Sex and sexuality: An evolutionary view

In this article, I first offer a summary of Darwin’s main ideas, especially relating to sex, and explain how these have been elaborated by more recent evolutionary scholars. I then give an account of the historical divergence between psychoanalysis and classical Darwinian thought, and describe how the early psychoanalyst Sabina Spielrein tried to counter this by addressing some biological themes in her work. Following a review of some contemporary attempts to bring psychoanalysis and evolutionary thought into alignment with each other, I make some suggestions regarding a view of sex and sexuality that would be sound in evolutionary terms while also being helpful in psychoanalytic ones

Ethanol Negatively Regulates Hepatic Differentiation of hESC by Inhibition of the MAPK/ERK Signaling Pathway In Vitro

Alcohol insult triggers complex events in the liver, promoting fibrogenic/inflammatory signals and in more advanced cases, aberrant matrix deposition. It is well accepted that the regenerative capacity of the adult liver is impaired during alcohol injury. The liver progenitor/stem cells have been shown to play an important role in liver regeneration -in response to various chronic injuries; however, the effects of alcohol on stem cell differentiation in the liver are not well understood.We employed hepatic progenitor cells derived from hESCs to study the impact of ethanol on hepatocyte differentiation by exposure of these progenitor cells to ethanol during hepatocyte differentiation.We found that ethanol negatively regulated hepatic differentiation of hESC-derived hepatic progenitor cells in a dose-dependent manner. There was also a moderate cell cycle arrest at G1/S checkpoint in the ethanol treated cells, which is associated with a reduced level of cyclin D1 in these cells. Ethanol treatment specifically inhibited the activation of the ERK but not JNK nor the p38 MAP signaling pathway. At the same time, the WNT signaling pathway was also reduced in the cells exposed to ethanol. Upon evaluating the effects of the inhibitors of these two signaling pathways, we determined that the Erk inhibitor replicated the effects of ethanol on the hepatocyte differentiation and attenuated the WNT/β-catenin signaling, however, inhibitors of WNT only partially replicated the effects of ethanol on the hepatocyte differentiation.Our results demonstrated that ethanol negatively regulated hepatic differentiation of hESC-derived hepatic progenitors through inhibiting the MAPK/ERK signaling pathway, and subsequently attenuating the WNT signaling pathway. Thus, our finding provides a novel insight into the mechanism by which alcohol regulates cell fate selection of hESC-derived hepatic progenitor cells, and the identified pathways may provide therapeutic targets aimed at promoting liver repair and regeneration during alcoholic injury