The LIL for UU-statistics in Hilbert spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest

Research and theory for nursing and midwifery: Rethinking the nature of evidence

Background and Rationale: The rise in the principles of evidence-based medicine in the 1990s heralded a re-emerging orthodoxy in research methodologies. The view of the randomised controlled trial (RCT) as a “gold standard” for evaluation of medical interventions has extended recently to evaluation of organisational forms and reforms and of change in complex systems—within health care and in other human services. Relatively little attention has been given to the epistemological assumptions underlying such a hierarchy of research evidence. Aims and Methods: Case studies from research in maternity care are used in this article to describe problems and limitations encountered in using RCTs to evaluate some recent policy-driven and consumer-oriented developments. These are discussed in relation to theory of knowledge and the epistemological assumptions, or paradigms, underpinning health services research. The aim in this discussion is not to advocate, or to reject, particular approaches to research but to advocate a more open and critical engagement with questions about the nature of evidence. Findings and Discussion: Experimental approaches are of considerable value in investigating deterministic and probabilistic cause and effect relationships, and in testing often well-established but unevaluated technologies. However, little attention has been paid to contextual and cultural factors in the effects of interventions, in the culturally constructed nature of research questions themselves, or of the data on which much research is based. More complex, and less linear, approaches to methodology are needed to address these issues. A simple hierarchical approach does not represent the complexity of evidence well and should move toward a more cyclical view of knowledge development

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a basic plasma process of dramatic rearrangement of magnetic topology, often leading to a violent release of magnetic energy. It is important in magnetic fusion and in space and solar physics --- areas that have so far provided the context for most of reconnection research. Importantly, these environments consist just of electrons and ions and the dissipated energy always stays with the plasma. In contrast, in this paper I introduce a new direction of research, motivated by several important problems in high-energy astrophysics --- reconnection in high energy density (HED) radiative plasmas, where radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. I identify the key processes distinguishing HED reconnection: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and Compton resistivity); and, at the most extreme end, QED effects, including pair creation. I then discuss the main astrophysical applications --- situations with magnetar-strength fields (exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares and magnetically-powered central engines and jets of GRBs. Here, magnetic energy density is so high that its dissipation heats the plasma to MeV temperatures. Electron-positron pairs are then copiously produced, making the reconnection layer highly collisional and dressing it in a thick pair coat that traps radiation. The pressure is dominated by radiation and pairs. Yet, radiation diffusion across the layer may be faster than the global Alfv\'en transit time; then, radiative cooling governs the thermodynamics and reconnection becomes a radiative transfer problem, greatly affected by the ultra-strong magnetic field. This overall picture is very different from our traditional picture of reconnection and thus represents a new frontier in reconnection research.Comment: Accepted to Space Science Reviews (special issue on magnetic reconnection). Article is based on an invited review talk at the Yosemite-2010 Workshop on Magnetic Reconnection (Yosemite NP, CA, USA; February 8-12, 2010). 30 pages, no figure

Cluster Analysis of Cardiovascular Phenotypes in Patients With Type 2 Diabetes and Established Atherosclerotic Cardiovascular Disease: A Potential Approach to Precision Medicine

OBJECTIVE Phenotypic heterogeneity among patients with type 2 diabetes mellitus (T2DM) and atherosclerotic cardiovascular disease (ASCVD) is ill defined. We used cluster analysis machine-learning algorithms to identify phenotypes among trial participants with T2DM and ASCVD. RESEARCH DESIGN AND METHODS We used data from the Trial Evaluating Cardiovascular Outcomes with Sitagliptin (TECOS) study (n = 14,671), a cardiovascular outcome safety trial comparing sitagliptin with placebo in patients with T2DM and ASCVD (median follow-up 3.0 years). Cluster analysis using 40 baseline variables was conducted, with associations between clusters and the primary composite outcome (cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina) assessed by Cox proportional hazards models. We replicated the results using the Exenatide Study of Cardiovascular Event Lowering (EXSCEL) trial. RESULTS Four distinct phenotypes were identified: Cluster I included Caucasian men with a high prevalence of coronary artery disease; cluster II included Asian patients with a low BMI; cluster III included women with noncoronary ASCVD disease; and cluster IV included patients with heart failure and kidney dysfunction. The primary outcome occurred, respectively, in 11.6%, 8.6%, 10.3%, and 16.8% of patients in clusters I to IV. The crude difference in cardiovascular risk for the highest versus lowest risk cluster (cluster IV vs. II) was statistically significant (hazard ratio 2.74 [95% CI 2.29–3.29]). Similar phenotypes and outcomes were identified in EXSCEL. CONCLUSIONS In patients with T2DM and ASCVD, cluster analysis identified four clinically distinct groups. Further cardiovascular phenotyping is warranted to inform patient care and optimize clinical trial designs

The On-orbit Calibrations for the Fermi Large Area Telescope

The Large Area Telescope (LAT) on--board the Fermi Gamma ray Space Telescope began its on--orbit operations on June 23, 2008. Calibrations, defined in a generic sense, correspond to synchronization of trigger signals, optimization of delays for latching data, determination of detector thresholds, gains and responses, evaluation of the perimeter of the South Atlantic Anomaly (SAA), measurements of live time, of absolute time, and internal and spacecraft boresight alignments. Here we describe on orbit calibration results obtained using known astrophysical sources, galactic cosmic rays, and charge injection into the front-end electronics of each detector. Instrument response functions will be described in a separate publication. This paper demonstrates the stability of calibrations and describes minor changes observed since launch. These results have been used to calibrate the LAT datasets to be publicly released in August 2009.Comment: 60 pages, 34 figures, submitted to Astroparticle Physic

The Physics of Star Cluster Formation and Evolution

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe

Volume I. Introduction to DUNE

The preponderance of matter over antimatter in the early universe, the dynamics of the supernovae that produced the heavy elements necessary for life, and whether protons eventually decay—these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our universe, its current state, and its eventual fate. The Deep Underground Neutrino Experiment (DUNE) is an international world-class experiment dedicated to addressing these questions as it searches for leptonic charge-parity symmetry violation, stands ready to capture supernova neutrino bursts, and seeks to observe nucleon decay as a signature of a grand unified theory underlying the standard model. The DUNE far detector technical design report (TDR) describes the DUNE physics program and the technical designs of the single- and dual-phase DUNE liquid argon TPC far detector modules. This TDR is intended to justify the technical choices for the far detector that flow down from the high-level physics goals through requirements at all levels of the Project. Volume I contains an executive summary that introduces the DUNE science program, the far detector and the strategy for its modular designs, and the organization and management of the Project. The remainder of Volume I provides more detail on the science program that drives the choice of detector technologies and on the technologies themselves. It also introduces the designs for the DUNE near detector and the DUNE computing model, for which DUNE is planning design reports. Volume II of this TDR describes DUNE\u27s physics program in detail. Volume III describes the technical coordination required for the far detector design, construction, installation, and integration, and its organizational structure. Volume IV describes the single-phase far detector technology. A planned Volume V will describe the dual-phase technology

Systematics of the Neotropical Genus Leptodactylus Fitzinger, 1826 (Anura: Leptodactylidae): Phylogeny, the Relevance of Non-molecular Evidence, and Species Accounts

A phylogeny of the species-rich clade of the Neotropical frog genus Leptodactylus sensu stricto is presented on the basis of a total evidence analysis of molecular (mitochondrial and nuclear markers) and non-molecular (adult and larval morphological and behavioral characters) sampled from > 80% of the 75 currently recognized species. Our results support the monophyly of Leptodactylus sensu stricto, with Hydrolaetare placed as its sister group. The reciprocal monophyly of Hydrolaetare and Leptodactylus sensu stricto does not require that we consider Hydrolaetare as either a subgenus or synonym of Leptodactylus sensu lato. We recognize Leptodactylus sensu stricto, Hydrolaetare, Adenomera, and Lithodytes as valid monophyletic genera. Our results generally support the traditionally recognized Leptodactylus species groups, with exceptions involving only a few species that are easily accommodated without proposing new groups or significantly altering contents. The four groups form a pectinate tree, with the Leptodactylus fuscus group diverging first, followed by the L. pentadactylus group, which is sister to the L. latrans and L. melanonotus groups. To evaluate the impact of non-molecular evidence on our results, we compared our total evidence results with results obtained from analyses using only molecular data. Although non-molecular evidence comprised only 3.5% of the total evidence matrix, it had a strong impact on our total evidence results. Only one species group was monophyletic in the molecular-only analysis, and support differed in 86% of the 54 Leptodactylus clades that are shared by the results of the two analyses. Even though no non-molecular evidence was included for Hydrolaetare, exclusion of that data partition resulted in that genus being nested within Leptodactylus, demonstrating that the inclusion of a small amount of non-molecular evidence for a subset of species can alter not only the placement of those species, but also species that were not scored for those data. The evolution of several natural history and reproductive traits is considered in the light of our phylogenic framework. Invasion of rocky outcrops, larval oophagy, and use of underground reproductive chambers are restricted to species of the Leptodactylus fuscus and L. pentadactylus groups. In contrast, larval schooling, larval attendance, and more complex parental care are restricted to the L. latrans and L. melanonotus groups. Construction of foam nests is plesiomorphic in Leptodactylus but their placement varies extensively (e.g., underground chambers, surface of waterbodies, natural or excavated basins). Information on species synonymy, etymology, adult and larval morphology, advertisement call, and geographic distribution is summarized in species accounts for the 30 species of the Leptodactylus fuscus group, 17 species of the L. pentadactylus group, eight species of the L. latrans group, and 17 species of the L. melanonotus group, as well as the three species that are currently unassigned to any species group.Se presenta una filogenia del género Leptodactylus, un ciado neotropical rico en especies, basada en análises combinados de datos moleculares (marcadores nuclear y mitocondriales) y no moleculares (caracteres de la morfología de adultos y larvas así como de comportamiento) se muestrearon > 80% de las 75 especies reconocidas. Los resultados apoyan la monofília de Leptodactylus sensu stricto, con Hydrolaetare como su grupo hermano. La monofília recíproca de Hydrolaetare y Leptodactylus no requiere considerar a Hydrolaetare como un subgénero o sinónimo de Leptodactylus sensu lato. Se reconocen Leptodactylus sensu stricto, Hydrolaetare, Adenomera y Lithodytes como géneros monofiléticos válidos. Los resultados en general resuelven los grupos tradicionalmente reconocidos de Leptodactylus, con excepciones de algunas especies que son reasignadas sin la necesidad de proponer nuevos grupos o alterar significativamente el contenido de los grupos tradicionales. Los cuatro grupos de especies forman una topología pectinada donde el grupo de L. fuscus tiene una posición basal, seguido por el grupo de L. pentadactylus que es el grupo hermano al clado formado por los grupo de L. latrans y L. melanonotus. Se estimó el impacto de los datos no moleculares en los resultados, comparándose los resultados de evidencia total con los de los análises de datos moleculares solamente. Los datos no moleculares representan un 3.5% de la matriz de evidencia total, pero estos datos tuvieron un impacto significativo en los resultados del análisis de evidencia total. En el análisis estrictamente molecular solamente un grupo de especies resultó monofilético, y el apoyo difirió en 86% de los 54 ciados de Leptodactylus compartidos entre los dos análises. A pesar que datos no moleculares no fueron incluidos para Hydrolaetare, la exclusión de evidencia no molecular resultó en el género estar dentro de Leptodactylus, demostrando que la inclusión de evidencia no molecular pequeña para un subgrupo de especies altera no solamente la posición topológica de esas especies, sino tambien de las especies para las cuales dichos datos no fueron codificados. La evolución de patrones de historia natural y reprodución se evalúan en el contexto filogenético. La invasión de afloramientos rocosos y la construción de cámaras de reprodución subterraneas está limitada a los grupos de Leptodactylus fuscus y L. pentadactylus, mientras que la oofagia larval está restringida al grupo de L. pentadactylus. Por otro lado, los cárdumenes larvales, la proteción del cárdumen, y otros comportamientos parentales complejos carecterizan al clado formado por los grupos de especies de L. latrans y L. melanonotus. Los resúmenes de especies incluyen información de sinonimias, etimología, morfología de adultos y larvas, cantos, y distribución geográfica para las 30 especies del grupo de Leptodactylus fuscus, 17 especies del grupo L. pentadactylus, ocho especies del grupo de L. latrans, 17 especies del grupo de L. melanonotus, así como para las tres especies que actualmente no se encuentran asociadas a ninguno de los grupos de especies.Taran Grant was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico Proc. 307001/2011-3 and Fundação de Amparo à Pesquisa do Estado de São Paulo Proc. 2012/10000-5