The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Gene Expression Differences between Enriched Normal and Chronic Myelogenous Leukemia Quiescent Stem/Progenitor Cells and Correlations with Biological Abnormalities

In comparing gene expression of normal and CML CD34+ quiescent (G0) cell, 292 genes were downregulated and 192 genes upregulated in the CML/G0 Cells. The differentially expressed genes were grouped according to their reported functions, and correlations were sought with biological differences previously observed between the same groups. The most relevant findings include the following. (i) CML G0 cells are in a more advanced stage of development and more poised to proliferate than normal G0 cells. (ii) When CML G0 cells are stimulated to proliferate, they differentiate and mature more rapidly than normal counterpart. (iii) Whereas normal G0 cells form only granulocyte/monocyte colonies when stimulated by cytokines, CML G0 cells form a combination of the above and erythroid clusters and colonies. (iv) Prominin-1 is the gene most downregulated in CML G0 cells, and this appears to be associated with the spontaneous formation of erythroid colonies by CML progenitors without EPO

Upper limits on the extent of seafloor anoxia during the PETM from uranium isotopes

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: All data generated or analyzed during this study are included in this published article (and its Supplementary information files). Source data are provided with this paper.The Paleocene Eocene Thermal Maximum (PETM) represents a major carbon cycle and climate perturbation that was associated with ocean de-oxygenation, in a qualitatively similar manner to the more extensive Mesozoic Oceanic Anoxic Events. Although indicators of ocean de-oxygenation are common for the PETM, and linked to biotic turnover, the global extent and temporal progression of de-oxygenation is poorly constrained. Here we present carbonate associated uranium isotope data for the PETM. A lack of resolvable perturbation to the U-cycle during the event suggests a limited expansion of seafloor anoxia on a global scale. We use this result, in conjunction with a biogeochemical model, to set an upper limit on the extent of global seafloor de-oxygenation. The model suggests that the new U isotope data, whilst also being consistent with plausible carbon emission scenarios and observations of carbon cycle recovery, permit a maximum ~10-fold expansion of anoxia, covering <2% of seafloor area.European Union Horizon 2020Natural Environment Research Council (NERC

Constraining large scale HI bias using redshifted 21-cm signal from the post-reionization epoch

In the absence of complex astrophysical processes that characterize the reionization era, the 21-cm emission from neutral hydrogen (HI) in the post-reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k,z), which relates HI to the dark matter distribution and (ii) a mean neutral fraction (x_{HI}) which sets its amplitude. In this paper, we investigate the nature of large scale HI bias. The post-reionization HI is modelled using gravity only N-Body simulations and a suitable prescription for assigning gas to the dark matter halos. Using the simulated bias as the fiducial model for HI distribution at z\leq 4, we have generated a hypothetical data set for the 21-cm angular power spectrum (C_{l}) using a noise model based on parameters of an extended version of the GMRT. The binned C_{l} is assumed to be measured with SNR \gtrsim 4 in the range 400 \leq l \leq 8000 at a fiducial redshift z=2.5. We explore the possibility of constraining b(k) using the Principal Component Analysis (PCA) on this simulated data. Our analysis shows that in the range 0.2 < k < 2 Mpc^{-1}, the simulated data set cannot distinguish between models exhibiting different k dependences, provided 1 \lesssim b(k) \lesssim 2 which sets the 2-sigma limits. This justifies the use of linear bias model on large scales. The largely uncertain x_{HI} is treated as a free parameter resulting in degradation of the bias reconstruction. The given simulated data is found to constrain the fiducial x_{HI} with an accuracy of \sim 4% (2-sigma error). The method outlined here, could be successfully implemented on future observational data sets to constrain b(k,z) and x_{HI} and thereby enhance our understanding of the low redshift Universe.Comment: 10 pages, 11 figures, 2 tables. Accepted in MNRAS. Revised to match the accepted versio

A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter $w$ and a very accurate approximation for the Ansatz $w(a)=w_0+w_a(1-a)$. We compute the growth index \gamma=\log f(a)/\log\Om_m(a), and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as $\gamma(a)=\gamma_0+\gamma_a(1-a)$ in most cases. We then compare four different types of dark energy (DE) models: $w\Lambda$CDM, DGP, $f(R)$ and a LTB-large-void model, which have very different behaviors at z\gsim1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like Euclid, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift $z\simeq 2$. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin for a Euclid-like survey. We use as observables the complete and marginalized power spectrum of galaxies $P(k)$ and the Weak Lensing (WL) power spectrum. We find that, using $P(k)$, one can reach (2%, 5%) errors in $(w_0, w_a)$, and (4%, 12%) errors in $(\gamma_0, \gamma_a)$, while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, $f(R)$ models and $\Lambda$CDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.}Comment: 29 pages, 7 figures, 6 table

Ocean acidification and the Permo-Triassic mass extinction.

Ocean acidification triggered by Siberian Trap volcanism was a possible kill mechanism for the Permo-Triassic Boundary mass extinction, but direct evidence for an acidification event is lacking. We present a high-resolution seawater pH record across this interval, using boron isotope data combined with a quantitative modeling approach. In the latest Permian, increased ocean alkalinity primed the Earth system with a low level of atmospheric CO2 and a high ocean buffering capacity. The first phase of extinction was coincident with a slow injection of carbon into the atmosphere, and ocean pH remained stable. During the second extinction pulse, however, a rapid and large injection of carbon caused an abrupt acidification event that drove the preferential loss of heavily calcified marine biota

Dynamic anoxic ferruginous conditions during the end-Permian mass extinction and recovery

The end-Permian mass extinction, ~252 million years ago, is notable for a complex recovery period of ~5 Myr. Widespread euxinic (anoxic and sulfidic) oceanic conditions have been proposed as both extinction mechanism and explanation for the protracted recovery period, yet the vertical distribution of anoxia in the water column and its temporal dynamics through this time period are poorly constrained. Here we utilize Fe–S–C systematics integrated with palaeontological observations to reconstruct a complete ocean redox history for the Late Permian to Early Triassic, using multiple sections across a shelf-to-basin transect on the Arabian Margin (Neo-Tethyan Ocean). In contrast to elsewhere, we show that anoxic non-sulfidic (ferruginous), rather than euxinic, conditions were prevalent in the Neo-Tethys. The Arabian Margin record demonstrates the repeated expansion of ferruginous conditions with the distal slope being the focus of anoxia at these times, as well as short-lived episodes of oxia that supported diverse biota

Efficiency and safety of varying the frequency of whole blood donation (INTERVAL): a randomised trial of 45 000 donors

Background: Limits on the frequency of whole blood donation exist primarily to safeguard donor health. However, there is substantial variation across blood services in the maximum frequency of donations allowed. We compared standard practice in the UK with shorter inter-donation intervals used in other countries. Methods: In this parallel group, pragmatic, randomised trial, we recruited whole blood donors aged 18 years or older from 25 centres across England, UK. By use of a computer-based algorithm, men were randomly assigned (1:1:1) to 12-week (standard) versus 10-week versus 8-week inter-donation intervals, and women were randomly assigned (1:1:1) to 16-week (standard) versus 14-week versus 12-week intervals. Participants were not masked to their allocated intervention group. The primary outcome was the number of donations over 2 years. Secondary outcomes related to safety were quality of life, symptoms potentially related to donation, physical activity, cognitive function, haemoglobin and ferritin concentrations, and deferrals because of low haemoglobin. This trial is registered with ISRCTN, number ISRCTN24760606, and is ongoing but no longer recruiting participants. Findings: 45 263 whole blood donors (22 466 men, 22 797 women) were recruited between June 11, 2012, and June 15, 2014. Data were analysed for 45 042 (99·5%) participants. Men were randomly assigned to the 12-week (n=7452) versus 10-week (n=7449) versus 8-week (n=7456) groups; and women to the 16-week (n=7550) versus 14-week (n=7567) versus 12-week (n=7568) groups. In men, compared with the 12-week group, the mean amount of blood collected per donor over 2 years increased by 1·69 units (95% CI 1·59–1·80; approximately 795 mL) in the 8-week group and by 0·79 units (0·69–0·88; approximately 370 mL) in the 10-week group (p&lt;0·0001 for both). In women, compared with the 16-week group, it increased by 0·84 units (95% CI 0·76–0·91; approximately 395 mL) in the 12-week group and by 0·46 units (0·39–0·53; approximately 215 mL) in the 14-week group (p&lt;0·0001 for both). No significant differences were observed in quality of life, physical activity, or cognitive function across randomised groups. However, more frequent donation resulted in more donation-related symptoms (eg, tiredness, breathlessness, feeling faint, dizziness, and restless legs, especially among men [for all listed symptoms]), lower mean haemoglobin and ferritin concentrations, and more deferrals for low haemoglobin (p&lt;0·0001 for each) than those observed in the standard frequency groups. Interpretation: Over 2 years, more frequent donation than is standard practice in the UK collected substantially more blood without having a major effect on donors' quality of life, physical activity, or cognitive function, but resulted in more donation-related symptoms, deferrals, and iron deficiency. Funding: NHS Blood and Transplant, National Institute for Health Research, UK Medical Research Council, and British Heart Foundation