Fermat Potentials for Non-Perturbative Gravitational Lensing

The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which relates the placement and distortion of the images to the real source position in the thin-lens scenario, is obtained by extremizing the time of arrival among all the null paths from the source to the observer (Fermat's principle). We show that the construction of envelopes of certain families of null surfaces consitutes an alternative variational principle or version of Fermat's principle that leads naturally to a lens equation in a generic spacetime with any given metric. We illustrate the construction by deriving the lens equation for static asymptotically flat thin lens spacetimes. As an application of the approach, we find the bending angle for moving thin lenses in terms of the bending angle for the same deflector at rest. Finally we apply this construction to cosmological spacetimes (FRW) by using the fact they are all conformally related to Minkowski space.Comment: accepted for publication in Phys. Rev.

Oxidation of acyclic alkenes and allyl and benzyl ethers with DIB/t-BuOOH/Mg(OAc)<inf>2</inf>

Oxidation of (11Z)-1′,2′-didehydrostemofoline with DIB/TBHP/Mg(OAc)2·4H2O resulted in oxidative cleavage of the C-11-C-12 double bond instead of the desired allylic oxidation of the 1-butenyl side chain. Stemofoline gave a similar result. The oxidation of more simple terminal alkenes was regioselective and gave vinyl ketones while allyl and benzyl ethers gave acrylate and benzoate esters, respectively. Allyl and benzyl ethers could be chemoselectively oxidized in the presence of a terminal alkene or benzyl group. Oxidation of an internal alkene was poorly regioselective, in contrast to the oxidation of 1-substituted cyclohexenes. © 2011 Elsevier Ltd. All rights reserved

Dynamics of Fermat potentials in non-perturbative gravitational lensing

We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we derive two lens equations: one for the case of thick compact lenses and the other one for lensing by gravitational waves. These equations in principle generalize the astrophysical scheme for lensing by removing the thin-lens approximation while retaining the weak fields.Comment: Accepted for publication in Phys. Rev.

Iterative Approach to Gravitational Lensing Theory

We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic equations can be completely integrated, such as Minkowski space-time, Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate the method, we construct the iterative gravitational lens equations and time of arrival equation for a single Schwarzschild lens. This example motivates a discussion of the relationship between the iterative approach, the standard thin lens formulation, and an exact formulation of gravitational lensing.Comment: 27 pages, 2 figures, submitted to Phys.Rev.D, minor revisions, new reference

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl

Mast cell clones: a model for the analysis of cellular maturation.

Cloned mouse mast cells resemble, by ultrastructure, immature mast cells observed in vivo. These mast cell clones can be grown in the absence of any other cells, facilitating direct investigations of their biochemistry and function. We find that cloned mast cells express plasma membrane receptors (Fc epsilon R) that bind mouse IgE with an equilibrium constant (KA) similar to that of normal mouse peritoneal mast cells. In addition, cloned mast cells do not display detectable la antigens and cannot enhance lg secretion when added to lymphocyte cultures or mediate natural killer lysis. In the presence of 1 mM sodium butyrate, cloned mast cells stop dividing and acquire abundant electron-dense cytoplasmic granules similar to those of mature mast cells. Their histamine content increases concomitant with cytoplasmic granule maturation and may exceed that of untreated mast cells by 50-fold. Unlike peritoneal mast cells, cloned mast cells incorporate 35SO4 into chondroitin sulfates rather than heparin. These findings demonstrate that, unlike fully differentiated mouse peritoneal mast cells, cloned immature mouse mast cells contain no heparin and low levels of histamine. In addition, they establish that high-affinity Fc epsilon R are expressed early in mast cell maturation, well before completion of cytoplasmic granule synthesis and mediator storage

Lactobacillus fermentum (PCC®) supplementation and gastrointestinal and respiratory-tract illness symptoms: a randomised control trial in athletes

BACKGROUND Probiotics purportedly reduce symptoms of gastrointestinal and upper respiratory-tract illness by modulating commensal microflora. Preventing and reducing symptoms of respiratory and gastrointestinal illness are the primary reason that dietary supplementation with probiotics are becoming increasingly popular with healthy active individuals. There is a paucity of data regarding the effectiveness of probiotics in this cohort. The aim of this study was to evaluate the effectiveness of a probiotic on faecal microbiology, self-reported illness symptoms and immunity in healthy well trained individuals. METHODS Competitive cyclists (64 males and 35 females; age 35 ± 9 and 36 ± 9 y, VO2max 56 ± 6 and 52 ± 6 ml.kg-1.min-1, mean ± SD) were randomised to either probiotic (minimum 1 × 109 Lactobacillus fermentum (PCC®) per day) or placebo treatment for 11 weeks in a double-blind, randomised, controlled trial. The outcome measures were faecal L. fermentum counts, self-reported symptoms of illness and serum cytokines. RESULTS Lactobacillus numbers increased 7.7-fold (90% confidence limits 2.1- to 28-fold) more in males on the probiotic, while there was an unclear 2.2-fold (0.2- to 18-fold) increase in females taking the probiotic. The number and duration of mild gastrointestinal symptoms were ~2-fold greater in the probiotic group. However, there was a substantial 0.7 (0.2 to 1.2) of a scale step reduction in the severity of gastrointestinal illness at the mean training load in males, which became more pronounced as training load increased. The load (duration×severity) of lower respiratory illness symptoms was less by a factor of 0.31 (99%CI; 0.07 to 0.96) in males taking the probiotic compared with placebo but increased by a factor of 2.2 (0.41 to 27) in females. Differences in use of cold and flu medication mirrored these symptoms. The observed effects on URTI had too much uncertainty for a decisive outcome. There were clear reductions in the magnitude of acute exercise-induced changes in some cytokines. CONCLUSION L. fermentum may be a useful nutritional adjunct for healthy exercising males. However, uncertainty in the effects of supplementation on URTI and on symptoms in females needs to be resolved. TRIAL REGISTRATION The trial was registered in the Australia and New Zealand Clinical Trials Registry (ACTRN12611000006943).The study was funded by Christian Hansen A/S, Probiomics and the Australian Institute of Sport

Quasar Proper Motions and Low-Frequency Gravitational Waves

We report observational upper limits on the mass-energy of the cosmological gravitational-wave background, from limits on proper motions of quasars. Gravitational waves with periods longer than the time span of observations produce a simple pattern of apparent proper motions over the sky, composed primarily of second-order transverse vector spherical harmonics. A fit of such harmonics to measured motions yields a 95%-confidence limit on the mass-energy of gravitational waves with frequencies <2e-9 Hz, of <0.11/h*h times the closure density of the universe.Comment: 15 pages, 1 figure. Also available at http://charm.physics.ucsb.edu:80/people/cgwinn/cgwinn_group/index.htm

Deep Drilling with the ANDRILL Program in Antarctica

ANDRILL (ANtarctic geological DRILLing) is a new international, multi-disciplinary drilling program that targets geological records that lie hidden beneath the icy blanket of Antarctica. The primary objective is to investigate Antarctica’s role in global environmental change over the past sixty-fi ve million years, at various scales of age resolution, and thereby enhance our understanding of Antarctica’s potential response to future global changes. Efforts to understand the infl uence of Antarctica on global climate change require a fundamental knowledge of how the Antarctic cryosphere (ice sheets, ice shelves, and sea ice) has evolved, not only in recent times but also during earlier geological periods when global temperature and atmospheric CO2 levels were similar to what might be reached by the end of this century. ANDRILL’s integrated science approach will use stratigraphic drilling, coring, and multi-proxy core analysis combined with geophysical surveys and numerical modeling to study the Cenozoic history of Antarctic climate and ice sheets, the evolution of polar biota, Antarctic tectonism, and Antarctica’s role in the evolution of Earth’s ocean–climate system

Therapeutic potential of targeting sphingosine kinases and sphingosine 1-phosphate in hematological malignancies

Sphingolipids, such as ceramide, sphingosine and sphingosine 1-phosphate (S1P) are bioactive molecules that have important functions in a variety of cellular processes, which include proliferation, survival, differentiation and cellular responses to stress. Sphingolipids have a major impact on the determination of cell fate by contributing to either cell survival or death. Although ceramide and sphingosine are usually considered to induce cell death, S1P promotes survival of cells. Sphingosine kinases (SPHKs) are the enzymes that catalyze the conversion of sphingosine to S1P. There are two isoforms, SPHK1 and SPHK2, which are encoded by different genes. SPHK1 has recently been implicated in contributing to cell transformation, tumor angiogenesis and metastatic spread, as well as cancer cell multidrug-resistance. More recent findings suggest that SPHK2 also has a role in cancer progression. This review is an overview of our understanding of the role of SPHKs and S1P in hematopoietic malignancies and provides information on the current status of SPHK inhibitors with respect to their therapeutic potential in the treatment of haematological cancers