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.

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.

A Mixture of Regressions Model of COVID-19 Death Rates and Population Comorbidities

As the COVID-19 pandemic spread worldwide, it has become clearer that prevalence of certain comorbidities in a given population could make it more vulnerable to serious outcomes of that disease, including fatality. Indeed, it might be insightful from a health policy perspective to identify clusters of populations in terms of the associations between their prevalent comorbidities and the observed COVID-19 specific death rates. In this study, we described a mixture of polynomial time series (MoPTS) model to simultaneously identify (a) three clusters of 86 U.S. cities in terms of their dynamic death rates, and (b) the different associations of those rates with 5 key comorbidities among the populations in the clusters. We also described an EM algorithm for efficient maximum likelihood estimation of the model parameters

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

Beyond the 1984 Perspective: Narrow Focus on Modern Wildfire Trends Underestimates Future Risks to Water Security

The western United States remains well below historical wildfire activity, yet misconceptions abound in the public and news media that the area burning by wildfire each year in the American West is unprecedented. We submit that short‐term records of wildfire and a disproportionate focus on recent fire trends within high‐profile science stoke these misconceptions. Furthermore, we highlight serious risks to long‐term water security (encompassing water supply, storage, and quality) that have only recently been recognized and are underestimated as the result of skewed perspectives of wildfire. Compiling several data sets, we illustrate a comprehensive history of western wildfire, demonstrate that the majority of western settlement occurred during an artificially and anomalously low period of wildfire in the twentieth century, and discuss the troubling implications the misalignment of wildfire activity and human development may have for the long‐term projections of water security. A crucial first step toward realigning public perspectives will require scientists and journalists to present recent increases in wildfire area within the context and scale of longer‐term trends. Second, proper housing development and resource management will require an appreciation for the differing western ecosystems and the flexibility to adopt varied approaches. These actions are critical for realigning public understanding of both the direct and indirect risks associated with wildfire and ensuring adequate and appropriate measures are taken as we navigate a future of increasing fire in the West

Cosmic Microwave Background anisotropies from second order gravitational perturbations

This paper presents a complete analysis of the effects of second order gravitational perturbations on Cosmic Microwave Background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collision-less fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyse the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations, that is known to give a few percent contribution to the anisotropies at small angular scales.Comment: 15 pages, revtex, no figures. Version to be published in Phys. Rev.

Practical and clinical approaches using pacing to improve selfregulation in special populations such as children and people with mental health or learning disabilities

For special populations such as people with a mental health issue or learning disability, a disconnect between the ability to accurately monitor and regulate exercise behaviour can lead to reduced levels of physical activity, which, in turn, is associated with additional physical or mental health problems. Activity pacing is a strategy used in clinical settings to address issues of pain amelioration, while self-pacing research is now well addressed in sport and exercise science literature. It has been proposed recently that these overlapping areas of investigation collectively support the development of self-regulatory, lifestyle exercise skills across broad population groups. Activity pacing appears to have substantial application in numerous development and rehabilitation settings and, therefore, the purpose of this short communication is to articulate how an activity pacing approach could be utilized among population groups in whom self-regulatory skills may require development. This paper provides specific examples of exercise practice across 2 discrete populations: children, and people with mental health and learning difficulties. In these cases, homeostatic regulatory processes may either be altered, or the individual may require extrinsic support to appropriately self-regulate exercise performance. A support-based exercise environment or approach such as programmatic activity (lifestyle) pacing would be beneficial to facilitate supervised and education-based self-regulation until such time as fully self-regulated exercise is feasible. [Abstract copyright: Journal Compilation © 2021 Foundation of Rehabilitation Information.

Regulation of cell survival by sphingosine-1-phosphate receptor S1P1 via reciprocal ERK-dependent suppression of bim and PI-3-kinase/protein kinase C-mediated upregulation of Mcl-1

Although the ability of bioactive lipid sphingosine-1-phosphate (S1P) to positively regulate anti-apoptotic/pro-survival responses by binding to S1P1 is well known, the molecular mechanisms remain unclear. Here we demonstrate that expression of S1P1 renders CCL39 lung fibroblasts resistant to apoptosis following growth factor withdrawal. Resistance to apoptosis was associated with attenuated accumulation of pro-apoptotic BH3-only protein Bim. However, although blockade of extracellular signal-regulated kinase (ERK) activation could reverse S1P1-mediated suppression of Bim accumulation, inhibition of caspase-3 cleavage was unaffected. Instead S1P1-mediated inhibition of caspase-3 cleavage was reversed by inhibition of phosphatidylinositol-3-kinase (PI3K) and protein kinase C (PKC), which had no effect on S1P1 regulation of Bim. However, S1P1 suppression of caspase-3 was associated with increased expression of anti-apoptotic protein Mcl-1, the expression of which was also reduced by inhibition of PI3K and PKC. A role for the induction of Mcl-1 in regulating endogenous S1P receptor-dependent pro-survival responses in human umbilical vein endothelial cells was confirmed using S1P receptor agonist FTY720-phosphate (FTY720P). FTY720P induced a transient accumulation of Mcl-1 that was associated with a delayed onset of caspase-3 cleavage following growth factor withdrawal, whereas Mcl-1 knockdown was sufficient to enhance caspase-3 cleavage even in the presence of FTY720P. Consistent with a pro-survival role of S1P1 in disease, analysis of tissue microarrays from ER+ breast cancer patients revealed a significant correlation between S1P1 expression and tumour cell survival. In these tumours, S1P1 expression and cancer cell survival were correlated with increased activation of ERK, but not the PI3K/PKB pathway. In summary, pro-survival/anti-apoptotic signalling from S1P1 is intimately linked to its ability to promote the accumulation of pro-survival protein Mcl-1 and downregulation of pro-apoptotic BH3-only protein Bim via distinct signalling pathways. However, the functional importance of each pathway is dependent on the specific cellular context