Spectrum of non-Hermitian heavy tailed random matrices

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some additional smoothness assumptions on the law of X_{jk}, we prove that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability measure mu_alpha on C depending only on alpha such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1} (X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our approach combines Aldous & Steele's objective method with Girko's Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of mu_alpha. In contrast with the Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in Mathematical Physics 307, 513-560 (2011

Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point

We report the details and revised analysis of an experiment to measure the specific heat of helium with subnanokelvin temperature resolution near the lambda point. The measurements were made at the vapor pressure spanning the region from 22 mK below the superfluid transition to 4 uK above. The experiment was performed in earth orbit to reduce the rounding of the transition caused by gravitationally induced pressure gradients on earth. Specific heat measurements were made deep in the asymptotic region to within 2 nK of the transition. No evidence of rounding was found to this resolution. The optimum value of the critical exponent describing the specific heat singularity was found to be a = -0.0127+ - 0.0003. This is bracketed by two recent estimates based on renormalization group techniques, but is slightly outside the range of the error of the most recent result. The ratio of the coefficients of the leading order singularity on the two sides of the transition is A+/A- =1.053+ - 0.002, which agrees well with a recent estimate. By combining the specific heat and superfluid density exponents a test of the Josephson scaling relation can be made. Excellent agreement is found based on high precision measurements of the superfluid density made elsewhere. These results represent the most precise tests of theoretical predictions for critical phenomena to date.Comment: 27 Pages, 20 Figure

Global surveillance of cancer survival 1995-2009: analysis of individual data for 25,676,887 patients from 279 population-based registries in 67 countries (CONCORD-2)

BACKGROUND: Worldwide data for cancer survival are scarce. We aimed to initiate worldwide surveillance of cancer survival by central analysis of population-based registry data, as a metric of the effectiveness of health systems, and to inform global policy on cancer control. METHODS: Individual tumour records were submitted by 279 population-based cancer registries in 67 countries for 25·7 million adults (age 15-99 years) and 75,000 children (age 0-14 years) diagnosed with cancer during 1995-2009 and followed up to Dec 31, 2009, or later. We looked at cancers of the stomach, colon, rectum, liver, lung, breast (women), cervix, ovary, and prostate in adults, and adult and childhood leukaemia. Standardised quality control procedures were applied; errors were corrected by the registry concerned. We estimated 5-year net survival, adjusted for background mortality in every country or region by age (single year), sex, and calendar year, and by race or ethnic origin in some countries. Estimates were age-standardised with the International Cancer Survival Standard weights. FINDINGS: 5-year survival from colon, rectal, and breast cancers has increased steadily in most developed countries. For patients diagnosed during 2005-09, survival for colon and rectal cancer reached 60% or more in 22 countries around the world; for breast cancer, 5-year survival rose to 85% or higher in 17 countries worldwide. Liver and lung cancer remain lethal in all nations: for both cancers, 5-year survival is below 20% everywhere in Europe, in the range 15-19% in North America, and as low as 7-9% in Mongolia and Thailand. Striking rises in 5-year survival from prostate cancer have occurred in many countries: survival rose by 10-20% between 1995-99 and 2005-09 in 22 countries in South America, Asia, and Europe, but survival still varies widely around the world, from less than 60% in Bulgaria and Thailand to 95% or more in Brazil, Puerto Rico, and the USA. For cervical cancer, national estimates of 5-year survival range from less than 50% to more than 70%; regional variations are much wider, and improvements between 1995-99 and 2005-09 have generally been slight. For women diagnosed with ovarian cancer in 2005-09, 5-year survival was 40% or higher only in Ecuador, the USA, and 17 countries in Asia and Europe. 5-year survival for stomach cancer in 2005-09 was high (54-58%) in Japan and South Korea, compared with less than 40% in other countries. By contrast, 5-year survival from adult leukaemia in Japan and South Korea (18-23%) is lower than in most other countries. 5-year survival from childhood acute lymphoblastic leukaemia is less than 60% in several countries, but as high as 90% in Canada and four European countries, which suggests major deficiencies in the management of a largely curable disease. INTERPRETATION: International comparison of survival trends reveals very wide differences that are likely to be attributable to differences in access to early diagnosis and optimum treatment. Continuous worldwide surveillance of cancer survival should become an indispensable source of information for cancer patients and researchers and a stimulus for politicians to improve health policy and health-care systems

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

The relationship between riverine U-series disequilibria and erosion rates in a basaltic terrain

U-series isotopes have been measured in the dissolved phase, suspended load and bedload of the main rivers draining basaltic catchments in Iceland. For the dissolved phase, (234U/238U) and (238U/230Th) range between 1.08 and 2.2, and 7.4 and 516, respectively. For the suspended load and bedload, (234U/238U) and (238U/230Th) range from 0.97 to 1.09 and from 0.93 to 1.05, respectively. Chemical erosion rates, calculated from dissolved major elements, range between 13 and 333 t km− 2 yr− 1. Physical erosion rates have also been estimated, from existing data, and range between 21 and 4864 t/km2/yr, with an average of 519 t km− 2 yr− 1. U-series disequilibria indicate that weathering in Iceland operates at close to steady-state conditions. A model of continuous weathering indicates a maximum weathering timescale of 10 kyr, with an average rate of uranium release into water of 1.6 · 10− 4 yr− 1, which is significant when compared to granitic terrains located at similar latitudes and to tropical basaltic terrains. All river waters display (234U/238U) greater than secular equilibrium, consistent with the effects of alpha-recoil. The same dissolved phase (234U/238U) exhibit a negative trend with physical erosion rates, explained by the dominant effect of close-to-congruent chemical weathering of hyaloclastites in the younger basaltic terrains. Therefore, chemical erosion rate and mineral weathering susceptibility play a major role in determining 234U–238U disequilibria in basaltic river waters. Comparison of global data for river basins in which weathering was recently strongly limited indicates a negative correlation between silicate weathering rates estimated with major elements and the age of weathering estimated with U-series disequilibria. This strongly suggests a key role of time and soil thickness on the chemical erosion of silicates

Sedimentary Fe-Mn oxyhydroxides as paleoceanographic archives and the role of aeolian flux in regulating oceanic dissolved REE

In the marine environment, authigenic ferromanganese (Fe–Mn) oxides precipitate from seawater, incorporating many dissolved trace elements (such as Nd, Pb) whose isotopic composition is a direct proxy for ambient seawater. Thus, isotopic studies of the Fe–Mn oxyhydroxide component leached from sedimentary records can provide information on changes in erosional input or ocean circulation changes. Such studies may be complicated, however, by the presence of detrital material containing a Fe–Mn oxide component, which may mask the true ‘seawater’ signal. In addition, the formation of Fe–Mn oxyhydroxides in the marine environment remains poorly understood. In particular, the phase (carbonates, detrital particles) that controls the delivery of authigenic Fe–Mn oxides to the sediments has not yet been determined. In this study, we have analysed the REE and Nd isotopic compositions of Fe–Mn oxyhydroxide fractions dispersed in marine sediment cores from the Cape and Angola basins, in the SE Atlantic (cruise IMAGES II). For the Angola Basin deep-sea core, located at ~1000 km south of the Congo River mouth, both the REE and Nd isotopic compositions (Nd) measured in recent Fe–Mn oxyhydroxide fractions are typical of Congo River-borne Fe–Mn oxides. This shows that ‘preformed’ Fe–Mn oxides associated with detrital fractions can locally contaminate the ‘seawater’ signal recorded by ‘authigenic’ oxyhydroxides. By contrast, examination of REE distributions, Nd isotope data and mass accumulation rates in Cape Basin sediments shows paradoxically that the flux of Fe–Mn oxides to sediments is controlled by aeolian particles from the nearby Namib Desert, even though their REE and Nd compositions point clearly to an ‘authigenic’ origin. It is proposed that partial dissolution of aeolian dust occurs in the water column, releasing into solution its easily leachable Fe–Mn component. The dissolved Fe2+ and Mn2+ would then fuel the reprecipitation of authigenic Fe–Mn oxyhydroxides, scavenging additional dissolved trace elements from the ocean, most probably from deep water masses. In this case, calculations suggest that aeolian deposition acts as a net sink for dissolved Nd in the Cape Basin, rather than a source, and allows us to estimate the rate of removal of dissolved Nd associated with atmospheric deposition, yielding a global oceanic residence time for Nd (Nd) of between 500 and 1400 years