Variations for Some Painlev\'e Equations

This paper first discusses irreducibility of a Painlev\'e equation $P$. We explain how the Painlev\'e property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we associate an autonomous Hamiltonian $\mathbb{H}$ to a Painlev\'e equation $P$. Complete integrability of $\mathbb{H}$ is shown to imply that all solutions to $P$ are classical (which includes algebraic), so in particular $P$ is solvable by ''quadratures''. Next, we show that the variational equation of $P$ at a given algebraic solution coincides with the normal variational equation of $\mathbb{H}$ at the corresponding solution. Finally, we test the Morales-Ramis theorem in all cases $P_{2}$ to $P_{5}$ where algebraic solutions are present, by showing how our results lead to a quick computation of the component of the identity of the differential Galois group for the first two variational equations. As expected there are no cases where this group is commutative

Helium, neon, and tritium in the Black Sea

Measurements of the 3He/4He ratio, and concentrations of helium, neon, and tritium have been made in samples collected at station 1355 in the Black Sea during the 1975 cruise of R/V Chain. Helium concentrations increase rapidly from 400 m to about 1000 m and then less rapidly below 1000 m. The maximum He concentration excess is about 16% above solubility equilibrium. Neon concentrations are constant, within a few percent of solubility equilibrium, below 400 m. The He-Ne data thus clearly indicate a large component of radiogenic 4He in the deep water from decay of U and Th in the bottom sediments. Tritium concentrations decrease from 67.2 T.U. at the surface to near-zero values at 726 m, 968 m, and 1358 m. Two deeper samples at 1745 m and 1939 m contain some tritium—0.6 ± 0.3 T.U. and 0.7 ± 0.2 T.U. respectively, which shows that a small amount of high-tritium surface water has descended to the bottom during the past twenty years. A one-dimensional three-box model using our tritium concentrations and the geothermal heat flux values measured by Erickson and Simmons (1974) gives vertical exchange times of 440 ± 180 years between the deep water (1000 m-2000 m) and the middle water (400 m-1000 m), and 125 ± 75 years between the middle water and a layer above from 200 m to 400 m in the salinity interval 21.50‰-22.00‰. The fluxes of radiogenic 4He and primordial 3He into the deep water are found to be 1.3 ± 0.5 × 105 atoms cm—2 sec—1 and 1.1 ± 0.6 atoms cm—2 sec—1 respectively which may be compared with world-ocean estimates of Craig et al. (1975)—3 ± 1.5 x 105 atoms cm—2 sec—1 and 4 ± 1 atoms cm—2 sec—1

Exchange processes and watermass modifications along the subarctic front in the North Pacific: Oxygen consumption rates and net carbon flux

Exchange processes along the subarctic front and the modification of subpolar water in the North Pacific are investigated using tracer data from World Ocean Circulation Experiment P14N and P17N lines. The North Pacific Current transports water on both sides of the subarctic front from the western to eastern North Pacific. During this transport, subpolar water from the western subpolar gyre becomes warmer and saltier through the main thermocline via isopycnal mixing with subtropical water. It is shown that this modified subpolar water of western origin is the primary source of well-ventilated water to the eastern subpolar gyre. The isopycnal mixing along the subarctic front is quantified with a two end-member linear mixing analysis using potential temperature, which allowed estimates of oxygen consumption and nitrate remineralization on intermediate layers. Based on the oxygen consumption estimates and temporal information from transient tracers, the vertically integrated oxygen consumption rate is calculated to be 2.1 ± 0.4 M m-2y-1 in the 132-706 m depth range. This implies a net carbon flux of approximately 19 ± 4 gC m-2y-1 out of the euphotic zone

Radiogenic helium in Baffin Bay bottom water

3He-4He ratios, dissolved He and Ne, and tritium have been measured in 87 seawater samples collected at 14 stations in Baffin Bay, Davis Strait, and in the sounds through which Arctic water flows into Baffin Bay…

Comparison of the RNA-amplification based methods RT–PCR and NASBA for the detection of circulating tumour cells

Increasingly, reverse transcriptase polymerase chain reaction (RT–PCR) is used to detect clinically significant tumour cells in blood or bone marrow. This may result in a redefinition of disease-free and clinical relapse. However, its clinical utility may be limited by lack of automation or reproducibility. Recent studies have suggested nucleic acid sequence-based amplification of target RNA may be more robust. In this study, nucleic acid sequence-based amplification was established to detect melanoma, colorectal and prostate cancer cells. Nucleic acid sequence-based amplification and RT–PCR both successfully amplified target RNA in peripheral blood samples from patients with melanoma and colorectal cancer, but only RT–PCR detected PSA in blood samples from patients with prostate cancer. There was relatively good agreement between sample replicates analyzed by RT–PCR (Kappa values of one for tyrosinase, 0.67 for CK-20 and one for PSA), but less agreement when analyzed by nucleic acid sequence-based amplification. This may limit the routine use of NASBA for the detection of clinically significant disease. In summary, RT–PCR appears at present to be the most reliable and reproducible method for the detection of low-level disease in cancer patients, although prospective studies are warranted to assess the clinical utility of different molecular diagnostic methods

Abyssal upwelling in the Indian Ocean: Radiocarbon diagnostics

The GEOSECS Indian Ocean radiocarbon and carbonate chemistry data set are used to estimate the mean upwelling transport of bottom water in the Indian Ocean north of 30S. The study uses an adjusted radiocarbon concentration which is corrected for the effects of addition of particulate radiocarbon to the deep ocean. The cross-basin uniformity in the vertical gradients of adjusted radiocarbon allows quantification of vertical transfer processes using horizontally averaged concentration and fluxes. The estimated total upwelling flux, north of 30S, is 8.2 ± 1.5 × 106 m3 s-1. The mean upwelling velocity and the vertical diffusivity, in the 3000-4500 m depth range, are estimated as 3 × 106 m s-1 and 2.5 × 10-4 m2 s-1, respectively. The results also suggest faster upwelling in the western Indian Ocean

Fauna diversity in pitcher plants at Setiam Hill, Bintulu, Sarawak, Malaysia

A study was carried out to determine the diversity and enumerate the fauna species related to five pitcher plant species at a selected area in Bukit Setiam Forest, Tatau, Bintulu, Sarawak, Malaysia. At the end of the study, six insect orders together with nematodes and Araneae were detected with different existence abundances and diversity. From the 901 total fauna trapped, 58.82% belonged to the order Hymenoptera, mainly of the ant species, followed by Nematodes (21.64%), Diptera (15.87%), Coleoptera (1.66%), Hemiptera (0.89%), Blattaria (0.44%) and finally, Lepidoptera (0.33%) and Araneae (0.33%). Significant differences (p<0.05) in the composition of insect trapped in pitcher plants were observed for the order Hymenoptera, Diptera, Lepidoptera, Hemiptera and even Nematodes. Meanwhile, no significant difference was observed for Coleoptera, Blattaria and Araneae. There is a strong relationship between fauna and Nepenthes pitcher either as a prey, predator, a mutualistic relationship or parasites or also for a habitat to live or to reproduce

Changes in active site histidine hydrogen bonding trigger cryptochrome activation

Cryptochrome (CRY) is the principal light sensor of the insect circadian clock. Photoreduction of the Drosophila CRY (dCRY) flavin cofactor to the anionic semiquinone (ASQ) restructures a C-terminal tail helix (CTT) that otherwise inhibits interactions with targets that include the clock protein Timeless (TIM). All-atom molecular dynamics (MD) simulations indicate that flavin reduction destabilizes the CTT, which undergoes large-scale conformational changes (the CTT release) on short (25 ns) timescales. The CTT release correlates with the conformation and protonation state of conserved His378, which resides between the CTT and the flavin cofactor. Poisson-Boltzmann calculations indicate that flavin reduction substantially increases the His378 pKa. Consistent with coupling between ASQ formation and His378 protonation, dCRY displays reduced photoreduction rates with increasing pH; however, His378Asn/Arg variants show no such pH dependence. Replica-exchange MD simulations also support CTT release mediated by changes in His378 hydrogen bonding and verify other responsive regions of the protein previously identified by proteolytic sensitivity assays. His378 dCRY variants show varying abilities to light-activate TIM and undergo self-degradation in cellular assays. Surprisingly, His378Arg/Lys variants do not degrade in light despite maintaining reactivity toward TIM, thereby implicating different conformational responses in these two functions. Thus, the dCRY photosensory mechanism involves flavin photoreduction coupled to protonation of His378, whose perturbed hydrogen-bonding pattern alters the CTT and surrounding regions

Anaphylaxis: Revision of the Brighton collaboration case definition

The Brighton Collaboration (BC) has formulated a number of case definitions which have primarily been applied to adverse events of special interest in the context of vaccine safety surveillance. This is a revision of the 2007 BC case definition for anaphylaxis. Recently, the BC definition has been widely used for evaluating reports of suspected anaphylaxis following COVID-19 vaccination. This has led to debate about the performance of the BC definition in comparison with those from the US National Institute of Allergy and Infectious Disease/Food Allergy Anaphylaxis Network (NIAID/FAAN) and the World Allergy Organization (WAO). BC convened an expert working group to revise the case definition based on their usual process of literature review and expert consensus. This manuscript presents the outcome of this process and proposes a revised case definition for anaphylaxis. Major and minor criteria have been re-evaluated with an emphasis on the reporting of observable clinical signs, rather than subjective symptoms, and a clearer approach to the ascertainment of levels of certainty is provided. The BC case definition has also been aligned with other contemporary and international case definitions for anaphylaxis