A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

A Systematic Review of Studies Comparing the Measurement Properties of the Three-Level and Five-Level Versions of the EQ-5D

Background: Since the introduction of the five-level version of the EQ-5D (5L), many studies have comparatively investigated the measurement properties of the original three-level version (3L) with the 5L version. Objective: The aim of this study was to consolidate the available evidence on the performance of both instruments. Methods: A systematic literature search of studies in the English and German languages was conducted (2007–January 2018) using the PubMed, EMBASE, and PsycINFO (EBSCO) databases, as well as the EuroQol Research Foundation website. Data were extracted and assessed on missing values, distributional properties, informativity indices (Shannon’s H′ and J′), inconsistencies, responsiveness, and test–retest reliability. Results: Twenty-four studies were included in the review. Missing values and floor effects (percentage reporting the worst health state) were found to be negligible for both 3L and 5L (< 5%). From 18 studies, inconsistencies ranged from 0 to 10.6%, although they were generally well below 5%, with 9 studies reporting the most inconsistencies for Usual Activities (mean percentage 4.1%). Shannon’s indices were always higher for 5L than for 3L, and all but three studies reported lower ceiling effects (‘11111’) for 5L than for 3L. There is mixed and insufficient evidence on responsiveness and test–retest reliability, although results on index values showed better performance for 5L on test–retest reliability. Conclusion: Overall, studies showed similar or better measurement properties of the 5L compared with the 3L, and evidence indicated moderately better distributional parameters and substantial improvement in informativity for the 5L compared with the 3L. Insufficient evidence on responsiveness and test–retest reliability implies further research is needed

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Magnetization reversal of an individual exchange biased permalloy nanotube

We investigate the magnetization reversal mechanism in an individual permalloy (Py) nanotube (NT) using a hybrid magnetometer consisting of a nanometer-scale SQUID (nanoSQUID) and a cantilever torque sensor. The Py NT is affixed to the tip of a Si cantilever and positioned in order to optimally couple its stray flux into a Nb nanoSQUID. We are thus able to measure both the NT's volume magnetization by dynamic cantilever magnetometry and its stray flux using the nanoSQUID. We observe a training effect and temperature dependence in the magnetic hysteresis, suggesting an exchange bias. We find a low blocking temperature $T_B = 18 \pm 2$ K, indicating the presence of a thin antiferromagnetic native oxide, as confirmed by X-ray absorption spectroscopy on similar samples. Furthermore, we measure changes in the shape of the magnetic hysteresis as a function of temperature and increased training. These observations show that the presence of a thin exchange-coupled native oxide modifies the magnetization reversal process at low temperatures. Complementary information obtained via cantilever and nanoSQUID magnetometry allows us to conclude that, in the absence of exchange coupling, this reversal process is nucleated at the NT's ends and propagates along its length as predicted by theory.Comment: 8 pages, 4 figure

Psychometric properties of the EQ-5D-5L: a systematic review of the literature

Purpose: Although the EQ-5D has a long history of use in a wide range of populations, the newer five-level version (EQ-5D-5L) has not yet had such extensive experience. This systematic review summarizes the available published scientific evidence on the psychometric properties of the EQ-5D-5L. Methods: Pre-determined key words and exclusion criteria were used to systematically search publications from 2011 to 2019. Information on study characteristics and psychometric properties were extracted: specifically, EQ-5D-5L distribution (including ceiling and floor), missing values, reliability (test–retest), validity (convergent, known-groups, discriminate) and responsiveness (distribution, anchor-based). EQ-5D-5L index value means, ceiling and correlation coefficients (convergent validity) were pooled across the studies using random-effects models. Results: Of the 889 identified publications, 99 were included for review, representing 32 countries. Musculoskeletal/orthopedic problems and cancer (n = 8 each) were most often studied. Most papers found missing values (17 of 17 papers) and floor effects (43 of 48 papers) to be unproblematic. While the index was found to be reliable (9 of 9 papers), individual dimensions exhibited instability over time. Index values and dimensions demonstrated moderate to strong correlations with global health measures, other multi-attribute utility instruments, physical/functional health, pain, activities of daily living, and clinical/biological measures. The instrument was not correlated with life satisfaction and cognition/communication measures. Responsiveness was addressed by 15 studies, finding moderate effect sizes when confined to studied subgroups with improvements in health. Conclusions: The EQ-5D-5L exhibits excellent psychometric properties across a broad range of populations, conditions and settings. Rigorous exploration of its responsiveness is needed

Unraveling the complexity of tyrosine kinase inhibitor-resistant populations by ultra-deep sequencing of the BCR-ABL kinase domain

In chronic myeloid leukemia and Philadelphia chromosome-positive acute lymphoblastic leukemia, tyrosine kinase inhibitor (TKI) therapy may select for drug-resistant BCR-ABL mutants. We used an ultra-deep sequencing (UDS) approach to resolve qualitatively and quantitatively the complexity of mutated populations surviving TKIs and to investigate their clonal structure and evolution over time in relation to therapeutic intervention. To this purpose, we performed a longitudinal analysis of 106 samples from 33 patients who had received sequential treatment with multiple TKIs and had experienced sequential relapses accompanied by selection of 1 or more TKI-resistant mutations. We found that conventional Sanger sequencing had misclassified or underestimated BCR-ABL mutation status in 55% of the samples, where mutations with 1% to 15% abundance were detected. A complex clonal texture was uncovered by clonal analysis of samples harboring multiple mutations and up to 13 different mutated populations were identified. The landscape of these mutated populations was found to be highly dynamic. The high degree of complexity uncovered by UDS indicates that conventional Sanger sequencing might be an inadequate tool to assess BCR-ABL kinase domain mutation status, which currently represents an important component of the therapeutic decision algorithms. Further evaluation of the clinical usefulness of UDS-based approaches is warranted

An international standardization programme towards the application of gene expression profiling in routine leukaemia diagnostics: the Microarray Innovations in LEukemia study prephase

Gene expression profiling has the potential to enhance current methods for the diagnosis of haematological malignancies. Here, we present data on 204 analyses from an international standardization programme that was conducted in 11 laboratories as a prephase to the Microarray Innovations in LEukemia (MILE) study. Each laboratory prepared two cell line samples, together with three replicate leukaemia patient lysates in two distinct stages: (i) a 5-d course of protocol training, and (ii) independent proficiency testing. Unsupervised, supervised, and r2 correlation analyses demonstrated that microarray analysis can be performed with remarkably high intra-laboratory reproducibility and with comparable quality and reliability

Sources and Sinks of Diversification and Conservation Priorities for the Mexican Tropical Dry Forest

Elucidating the geographical history of diversification is critical for inferring where future diversification may occur and thus could be a valuable aid in determining conservation priorities. However, it has been difficult to recognize areas with a higher likelihood of promoting diversification. We reconstructed centres of origin of lineages and identified areas in the Mexican tropical dry forest that have been important centres of diversification (sources) and areas where species are maintained but where diversification is less likely to occur (diversity sinks). We used a molecular phylogeny of the genus Bursera, a dominant member of the forest, along with information on current species distributions. Results indicate that vast areas of the forest have historically functioned as diversity sinks, generating few or no extant Bursera lineages. Only a few areas have functioned as major engines of diversification. Long-term preservation of biodiversity may be promoted by incorporation of such knowledge in decision-making

Measurement of the flavour composition of dijet events in pp collisions at root s=7 TeV with the ATLAS detector

This paper describes a measurement of the flavour composition of dijet events produced in pp collisions at &#8730;s=7 TeV using the ATLAS detector. The measurement uses the full 2010 data sample, corresponding to an integrated luminosity of 39 pb−1. Six possible combinations of light, charm and bottom jets are identified in the dijet events, where the jet flavour is defined by the presence of bottom, charm or solely light flavour hadrons in the jet. Kinematic variables, based on the properties of displaced decay vertices and optimised for jet flavour identification, are used in a multidimensional template fit to measure the fractions of these dijet flavour states as functions of the leading jet transverse momentum in the range 40 GeV to 500 GeV and jet rapidity |y|&#60;2.1. The fit results agree with the predictions of leading- and next-to-leading-order calculations, with the exception of the dijet fraction composed of bottom and light flavour jets, which is underestimated by all models at large transverse jet momenta. The ability to identify jets containing two b-hadrons, originating from e.g. gluon splitting, is demonstrated. The difference between bottom jet production rates in leading and subleading jets is consistent with the next-to-leading-order predictions