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

Capture, analyse, visualise:An exemplar of performance analysis in practice in field hockey

The goal of performance analysis is to capture the multitude of factors that affect sports strategy, and present them in an informative, interpretable, and accessible format. The aim of this study was to outline a performance analysis process in field hockey that captures, analyses and visualises strategy in layers of detail culminating in the creation of an RStudio Shiny application. Computerised notational analysis systems were developed to capture in-game events and ball tracking data of 74 matches from the Women’s Pro League 2019. Game styles were developed using k-means cluster analysis to reduce detailed in-game events into practical profiles to identify the attack types, game actions and tempo of a team’s strategy. Ball movement profiles were developed to identify the predictability (entropy) and direction (progression rates) of ball movements, and consequent distribution of possession in different attacking zones. The Shiny application, an interactive web-platform, links the information from simple game profiles with detailed game variables to understand each teams’ holistic game plan, how they are different, and how to exploit these differences. The process outlined can be applied to any team invasion sport to understand, develop and communicate successful strategies under different match situations

Cloned mouse cells with natural killer function and cloned suppressor T cells express ultrastructural and biochemical features not shared by cloned inducer T cells.

We have examined the morphology, cytochemistry, and biochemistry of mouse leukocyte subsets by analyzing cloned leukocyte populations specialized to perform different immunologic functions. Cloned cells expressing high-affinity plasma membrane receptors for IgE and mediating natural killer (NK) lysis and cloned antigen-specific suppressor T cells contained prominent osmiophilic cytoplasmic granules similar by ultrastructure to those of mouse basophils. Both clones also incorporated 35SO4 into granule-associated sulfated glycosaminoglycans, expressed a characteristic ultrastructural pattern of nonspecific esterase activity, incorporated exogenous [3H]5-hydroxytryptamine, and contained cytoplasmic deposits of particulate glycogen. By contrast, cloned inducer T cells lacked cytoplasmic granules and glycogen, incorporated neither 35SO4 nor [3H]5-hydroxytryptamine, and differed from the other clones in pattern of nonspecific esterase activity. These findings establish that certain cloned cells with NK activity and cloned suppressor T cells express morphologic and biochemical characteristics heretofore associated with basophilic granulocytes. However, these clones differ in surface glycoprotein expression and immunologic function, and the full extent of the similarities and differences among these populations and basophils remains to be determined

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

PEGylated surfaces for the study of DNA-protein interactions by atomic force microscopy

DNA-protein interactions are vital to cellular function, with key roles in the regulation of gene expression and genome maintenance. Atomic force microscopy (AFM) offers the ability to visualize DNA-protein interactions at nanometre resolution in near-physiological buffers, but it requires that the DNA be adhered to the surface of a solid substrate. This presents a problem when working in biologically relevant protein concentrations, where proteins may be present in large excess in solution; much of the biophysically relevant information can therefore be occluded by non-specific protein binding to the underlying substrate. Here we explore the use of PLLx-b-PEGy block copolymers to achieve selective adsorption of DNA on a mica surface for AFM studies. Through varying both the number of lysine and ethylene glycol residues in the block copolymers, we show selective adsorption of DNA on mica that is functionalized with a PLL10-b-PEG113/PLL1000-2000 mixture as viewed by AFM imaging in a solution containing high concentrations of streptavidin. We show - through the use of biotinylated DNA and streptavidin - that this selective adsorption extends to DNA-protein complexes and that DNA-bound streptavidin can be unambiguously distinguished in spite of an excess of unbound streptavidin in solution. Finally, we apply this to the nuclear enzyme PARP1, resolving the binding of individual PARP1 molecules to DNA by in-liquid AFM

Imaging the Effects of Peptide Materials on Phospholipid Membranes by Atomic Force Microscopy

Recent advances in biomolecular design require accurate measurements performed in native or near-native environments in real time. Atomic force microscopy (AFM) is a powerful tool to observe the dynamics of biologically relevant processes at aqueous interfaces with high spatial resolution. Here, we describe imaging protocols to characterize the effects of peptide materials on phospholipid membranes in solution by AFM. These protocols can be used to determine the mechanism and kinetics of membrane-associated activities at the nanoscale

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

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.

Was Sinn Féin dying? A quantitative post-mortem of the party's decline and the emergence of Fianna Fáil

This article calls for a reappraisal of the consensus surrounding the split within Sinn Féin in 1926 that led to the foundation of Fianna Fáil. It demonstrates that quantitative factors cited to demonstrate Sinn Féin’s “terminal” decline – finances, cumann numbers, and election results – and to explain de Valera’s decision to leave Sinn Féin and establish a rival republican organisation, Fianna Fáil, do not provide sufficient objective grounds to explain the republican leader’s actions. This article demonstrates that Sinn Féin’s election results during the period in question (1923-1926) were encouraging and the decline in finances and cumann numbers can be explained by the fact that the base year used to compare progress was 1923, an election year. Moreover, this article compares the performance of Sinn Féin to the first five years of Fianna Fáil (1926-1931) to show that what has been interpreted as terminal decline can also be attributed to normal inter-election lulls in party activity. Correspondingly, subjective factors – e.g. personal rivalries, differences in ideology, organisational style and levels of patience in terms of achieving political power – were most likely the determining factors rather than organisational decline