Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Genomic adaptations of Campylobacter jejuni to long-term human colonization

Background Campylobacter is a genus of bacteria that has been isolated from the gastrointestinal tract of humans and animals, and the environments they inhabit around the world. Campylobacter adapt to new environments by changes in their gene content and expression, but little is known about how they adapt to long-term human colonization. In this study, the genomes of 31 isolates from a New Zealand patient and 22 isolates from a United Kingdom patient belonging to Campylobacter jejuni sequence type 45 (ST45) were compared with 209 ST45 genomes from other sources to identify the mechanisms by which Campylobacter adapts to long-term human colonization. In addition, the New Zealand patient had their microbiota investigated using 16S rRNA metabarcoding, and their level of inflammation and immunosuppression analyzed using biochemical tests, to determine how Campylobacter adapts to a changing gastrointestinal tract. Results There was some evidence that long-term colonization led to genome degradation, but more evidence that Campylobacter adapted through the accumulation of non-synonymous single nucleotide polymorphisms (SNPs) and frameshifts in genes involved in cell motility, signal transduction and the major outer membrane protein (MOMP). The New Zealand patient also displayed considerable variation in their microbiome, inflammation and immunosuppression over five months, and the Campylobacter collected from this patient could be divided into two subpopulations, the proportion of which correlated with the amount of gastrointestinal inflammation. Conclusions This study demonstrates how genomics, phylogenetics, 16S rRNA metabarcoding and biochemical markers can provide insight into how Campylobacter adapts to changing environments within human hosts. This study also demonstrates that long-term human colonization selects for changes in Campylobacter genes involved in cell motility, signal transduction and the MOMP; and that genetically distinct subpopulations of Campylobacter evolve to adapt to the changing gastrointestinal environment

Tests of the Equivalence Principle with Neutral Kaons

We test the Principle of Equivalence for particles and antiparticles, using CPLEAR data on tagged K0 and K0bar decays into pi^+ pi^-. For the first time, we search for possible annual, monthly and diurnal modulations of the observables |eta_{+-}| and phi_{+-}, that could be correlated with variations in astrophysical potentials. Within the accuracy of CPLEAR, the measured values of |eta_{+-}| and phi_{+-} are found not to be correlated with changes of the gravitational potential. We analyze data assuming effective scalar, vector and tensor interactions, and we conclude that the Principle of Equivalence between particles and antiparticles holds to a level of 6.5, 4.3 and 1.8 x 10^{-9}, respectively, for scalar, vector and tensor potentials originating from the Sun with a range much greater than the distance Earth-Sun. We also study energy-dependent effects that might arise from vector or tensor interactions. Finally, we compile upper limits on the gravitational coupling difference between K0 and K0bar as a function of the scalar, vector and tensor interaction range.Comment: 15 pages latex 2e, five figures, one style file (cernart.csl) incorporate

Test of CPT Symmetry and Quantum Mechanics with Experimental data from CPLEAR

We use fits to recent published CPLEAR data on neutral kaon decays to $\pi^+\pi^-$ and $\pi e\nu$ to constrain the CPT--violation parameters appearing in a formulation of the neutral kaon system as an open quantum-mechanical system. The obtained upper limits of the CPT--violation parameters are approaching the range suggested by certain ideas concerning quantum gravity.Comment: 9 pages of uuencoded postscript (includes 3 figures

Calculation of the Flux of Atmospheric Neutrinos

Atmospheric neutrino-fluxes are calculated over the wide energy range from 30 MeV to 3,000 GeV for the study of neutrino-physics using the data from underground neutrino-detectors. The atmospheric muon-flux at high altitude and at sea level is studied to calibrate the neutrino-fluxes at low energies and high energies respectively. The agreement of our calculation with observations is satisfactory. The uncertainty of atmospheric neutrino-fluxes is also studied.Comment: 51 page

Experimental tests of CPT symmetry and quantum mechanics at CPLEAR

We review a phenomenological parametrization of an open quantum-mechanical formalism for CPT violation in the neutral kaon system, and constrain the parameters using fits to recent CPLEAR data

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