The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)

Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first antiderivatives. We recall earlier results of one of us on the Holder continuity of these continuous functions and relate them to results of other authors; this involves a generalization of classical theorems on Fourier series by S. Bernstein and Hardy-Littlewood. We then show that the antiderivatives are non-differentiable at all irrational points, as well as all, or in certain cases, some rational points. We include graphs of several of these functions, which clearly display a high degree of oscillation. Our investigations are motivated in part by properties of "Riemann's nondifferentiable function", also known as "Weierstrass' function".Comment: 27 pages, 6 Figures; version 2 corrects misprints and updates reference

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

Neutrino Interferometry In Curved Spacetime

Gravitational lensing introduces the possibility of multiple (macroscopic) paths from an astrophysical neutrino source to a detector. Such a multiplicity of paths can allow for quantum mechanical interference to take place that is qualitatively different to neutrino oscillations in flat space. After an illustrative example clarifying some under-appreciated subtleties of the phase calculation, we derive the form of the quantum mechanical phase for a neutrino mass eigenstate propagating non-radially through a Schwarzschild metric. We subsequently determine the form of the interference pattern seen at a detector. We show that the neutrino signal from a supernova could exhibit the interference effects we discuss were it lensed by an object in a suitable mass range. We finally conclude, however, that -- given current neutrino detector technology -- the probability of such lensing occurring for a (neutrino-detectable) supernova is tiny in the immediate future.Comment: 25 pages, 1 .eps figure. Updated version -- with simplified notation -- accepted for publication in Phys.Rev.D. Extra author adde

The growth of different body length dimensions is not predictive for the peak growth velocity of sitting height in the individual child

The aim of this study was to determine whether the differences in timing of the peak growth velocity (PGV) between sitting height, total body height, subischial leg length, and foot length can be used to predict whether the individual patient with adolescent idiopathic scoliosis is before or past his or her PGV of sitting height. Furthermore, ratios of growth of different body parts were considered in order to determine their value in prediction of the PGV of sitting height in the individual patient. Ages of the PGV were determined for sitting height (n = 360), total body height (n = 432), subischial leg length (n = 357), and foot length (n = 263), and compared for the whole group and for the individual child in particular. Furthermore, the ages of the highest and lowest ratios between the body length dimensions were determined and compared to the age of the PGV of sitting height. The mean ages of the highest and lowest ratios were significantly different from the mean age of the PGV of sitting height in 3 out of 12 ratios in girls and 8 out of 12 ratios in boys. The variation over children was large and the ratios were too small, leading to a too large influence of measurement errors. The mean ages of the PGV all differed significantly from the mean age of the PGV of sitting height. However, the variation over individual children of the age differences in PGV between body dimensions was large, and the differences in timing of the PGV were not useful to predict whether the individual child is before or past his or her PGV of sitting height

The cost-effectiveness of procalcitonin for guiding antibiotic prescribing in individuals hospitalized with COVID-19: part of the PEACH study

\ua9 The Author(s) 2024. Published by Oxford University Press on behalf of British Society for Antimicrobial Chemotherapy.Background: Many hospitals introduced procalcitonin (PCT) testing to help diagnose bacterial coinfection in individuals with COVID-19, and guide antibiotic decision-making during the COVID-19 pandemic in the UK. Objectives: Evaluating cost-effectiveness of using PCT to guide antibiotic decisions in individuals hospitalized with COVID-19, as part of a wider research programme. Methods: Retrospective individual-level data on patients hospitalized with COVID-19 were collected from 11 NHS acute hospital Trusts and Health Boards from England and Wales, which varied in their use of baseline PCT testing during the first COVID-19 pandemic wave. A matched analysis (part of a wider analysis reported elsewhere) created groups of patients whose PCT was/was not tested at baseline. A model was created with combined decision tree/Markov phases, parameterized with quality-of-life/unit cost estimates from the literature, and used to estimate costs and quality-adjusted life years (QALYs). Cost-effectiveness was judged at a \ua320000/QALY threshold. Uncertainty was characterized using bootstrapping. Results: People who had baseline PCT testing had shorter general ward/ICU stays and spent less time on antibiotics, though with overlap between the groups’ 95% CIs. Those with baseline PCT testing accrued more QALYs (8.76 versus 8.62) and lower costs (\ua39830 versus \ua310 700). The point estimate was baseline PCT testing being dominant over no baseline testing, though with uncertainty: the probability of cost-effectiveness was 0.579 with a 1 year horizon and 0.872 with a lifetime horizon. Conclusions: Using PCT to guide antibiotic therapy in individuals hospitalized with COVID-19 is more likely to be cost-effective than not, albeit with uncertainty

Six-minute walking test in children with ESRD: discrimination validity and construct validity

The six-minute walking test (6MWT) may be a practical test for the evaluation functional exercise capacity in children with end-stage renal disease (ESRD). The aim of this study was to investigate the 6MWT performance in children with ESRD compared to reference values obtained in healthy children and, secondly, to study the relationship between 6MWT performance with anthropometric variables, clinical parameters, aerobic capacity and muscle strength. Twenty patients (13 boys and seven girls; mean age 14.1 ± 3.4 years) on dialysis participated in this study. Anthropometrics were taken in a standardized manner. The 6MWT was performed in a 20-m-long track in a straight hallway. Aerobic fitness was measured using a cycle ergometer test to determine peak oxygen uptake \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\mathop {\text{V}}\limits^\cdot {{\text{O}}_{\text{2peak}}}} \right)$$\end{document}, peak rate (Wpeak) and ventilatory threshold (VT). Muscle strength was measured using hand-held myometry. Children with ESRD showed a reduced 6MWT performance (83% of predicted, p < 0.0001), irrespective of the reference values used. The strongest predictors of 6MWT performance were haematocrit and height. Regression models explained 59% (haematocrit and height) to 60% (haematocrit) of the variance in 6MWT performance. 6MWT performance was not associated with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathop {\text{V}}\limits^\cdot {{\text{O}}_{\text{2peak}}}}$$\end{document}, strength, or other anthropometric variables, but it was significantly associated with haematocrit and height. Children with ESRD scored lower on the 6MWT than healthy children. Based on these results, the 6MWT may be a useful instrument for monitoring clinical status in children with ESRD, however it cannot substitute for other fitness tests, such as a progressive exercise test to measure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathop {\text{V}}\limits^\cdot {{\text{O}}_{\text{2peak}}}}$$\end{document} or muscle strength tests

Identification of regulatory variants associated with genetic susceptibility to meningococcal disease

Non-coding genetic variants play an important role in driving susceptibility to complex diseases but their characterization remains challenging. Here, we employed a novel approach to interrogate the genetic risk of such polymorphisms in a more systematic way by targeting specific regulatory regions relevant for the phenotype studied. We applied this method to meningococcal disease susceptibility, using the DNA binding pattern of RELA - a NF-kB subunit, master regulator of the response to infection - under bacterial stimuli in nasopharyngeal epithelial cells. We designed a custom panel to cover these RELA binding sites and used it for targeted sequencing in cases and controls. Variant calling and association analysis were performed followed by validation of candidate polymorphisms by genotyping in three independent cohorts. We identified two new polymorphisms, rs4823231 and rs11913168, showing signs of association with meningococcal disease susceptibility. In addition, using our genomic data as well as publicly available resources, we found evidences for these SNPs to have potential regulatory effects on ATXN10 and LIF genes respectively. The variants and related candidate genes are relevant for infectious diseases and may have important contribution for meningococcal disease pathology. Finally, we described a novel genetic association approach that could be applied to other phenotypes