What is a pilot or feasibility study? A review of current practice and editorial policy

Background: In 2004, a review of pilot studies published in seven major medical journals during 2000-01 recommended that the statistical analysis of such studies should be either mainly descriptive or focus on sample size estimation, while results from hypothesis testing must be interpreted with caution. We revisited these journals to see whether the subsequent recommendations have changed the practice of reporting pilot studies. We also conducted a survey to identify the methodological components in registered research studies which are described as 'pilot' or 'feasibility' studies. We extended this survey to grant-awarding bodies and editors of medical journals to discover their policies regarding the function and reporting of pilot studies. Methods: Papers from 2007-08 in seven medical journals were screened to retrieve published pilot studies. Reports of registered and completed studies on the UK Clinical Research Network (UKCRN) Portfolio database were retrieved and scrutinized. Guidance on the conduct and reporting of pilot studies was retrieved from the websites of three grant giving bodies and seven journal editors were canvassed. Results: 54 pilot or feasibility studies published in 2007-8 were found, of which 26 (48%) were pilot studies of interventions and the remainder feasibility studies. The majority incorporated hypothesis-testing (81%), a control arm (69%) and a randomization procedure (62%). Most (81%) pointed towards the need for further research. Only 8 out of 90 pilot studies identified by the earlier review led to subsequent main studies. Twelve studies which were interventional pilot/feasibility studies and which included testing of some component of the research process were identified through the UKCRN Portfolio database. There was no clear distinction in use of the terms 'pilot' and 'feasibility'. Five journal editors replied to our entreaty. In general they were loathe to publish studies described as 'pilot'. Conclusion: Pilot studies are still poorly reported, with inappropriate emphasis on hypothesis-testing. Authors should be aware of the different requirements of pilot studies, feasibility studies and main studies and report them appropriately. Authors should be explicit as to the purpose of a pilot study. The definitions of feasibility and pilot studies vary and we make proposals here to clarify terminology

Impact of pressure anisotropy on tokamak equilibria and the toroidal magnetic precession

Using a generalized anisotropic tokamak equilibrium and an exact guiding centre drift formulation, the effect of parallel and perpendicular anisotropy on the toroidal precession drift is investigated. Significant differences between parallel and perpendicular pressure anisotropy are observed. While the Shafranov shift is not sensitive to the ratio of the parallel and perpendicular pressures p ⊥ /p∥ , the deepening of the magnetic well is found to be sensitive to p ⊥ /p∥ . Here, the diamagnetic effect identified by Connor et al 1983 Nucl. Fusion 23 1702 is generalized and found to depend crucially on the deposition of the energetic ions on which the equilibrium depends, and leads to test particle precessional drifts that depend sensitively on pitch angl

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations

Estimating the minimum important difference in the DEMQOL instrument in people with dementia

Purpose The Dementia-Related Quality of Life (DEMQOL) measure and the DEMQOL-Utility Score (DEMQOL-U) are validated tools for measuring quality of life (QOL) in people with dementia. What score changes translate to a clinically significant impact on patients’ lives was unknown. This study establishes the minimal important differences (MID) for these two instruments. Methods Anchor-based and distribution-based methods were used to estimate the MID scores from patients enrolled in a randomised controlled trial. For the anchor-based method, the global QOL (Q29) item from the DEMQOL was chosen as the anchor for DEMQOL and both Q29 and EQ-5D for DEMQOL-U. A one category difference in Q29, and a 0.07 point difference in EQ-5D score, were used to classify improvement and deterioration, and the MID scores were calculated for each category. These results were compared with scores obtained by the distribution-based methods. Results A total of 490 people with dementia had baseline DEMQOL data, of these 386 had 8-month data, and 344 had 12-month DEMQOL data. The absolute change in DEMQOL for a combined 1-point increase or decrease in the Q29 anchor was 5.2 at 8 months and 6.0 at 12 months. For the DEMQOL-U, the average absolute change at 8 and 12 months was 0.032 and 0.046 for the Q29 anchor and 0.020 and 0.024 for EQ-5D anchor. Conclusion We present MID scores for the DEMQOL and DEMQOL-U instruments obtained from a large cohort of patients with dementia. An anchored-based estimate of the MID for the DEMQOL is around 5 to 6 points; and 0.02 to 0.05 points for the DEMQOL-U. The results of this study can guide clinicians and researchers in the interpretation of these instruments comparisons between groups or within groups of people with dementia. Trial Registration Number and date of registration: ISRCTN17993825 on 11th October 2016

Rare-Earth Nuclei: Radii, Isotope-Shifts and Deformation Properties in the Relativistic Mean Field Theory

A systematic study of the ground-state properties of even-even rare earth nuclei has been performed in the framework of the Relativistic Mean-Field (RMF) theory using the parameter set NL-SH. Nuclear radii, isotope shifts and deformation properties of the heavier rare-earth nuclei have been obtained, which encompass atomic numbers ranging from Z=60 to Z=70 and include a large range of isospin. It is shown that RMF theory is able to provide a good and comprehensive description of the empirical binding energies of the isotopic chains. At the same time the quadrupole deformations $\beta_{2}$ obtained in the RMF theory are found to be in good agreement with the available empirical values. The theory predicts a shape transition from prolate to oblate for nuclei at neutron number N=78 in all the chains. A further addition of neutrons up to the magic number 82 brings about the spherical shape. For nuclei above N=82, the RMF theory predicts the well-known onset of prolate deformation at about N=88, which saturates at about N=102. The deformation properties display an identical behaviour for all the nuclear chains. A good description of the above deformation transitions in the RMF theory in all the isotopic chains leads to a successful reproduction of the anomalous behaviour of the empirical isotopic shifts of the rare-earth nuclei. The RMF theory exhibits a remarkable success in providing a unified and microscopic description of various empirical data.Comment: Revtex (50 pages) and 24 figures (available upon request), Nuclear Physics A (in press

Self-adapting method for the localization of quantum critical points using Quantum Monte Carlo techniques

A generalization to the quantum case of a recently introduced algorithm (Y. Tomita and Y. Okabe, Phys. Rev. Lett. {\bf 86}, 572 (2001)) for the determination of the critical temperature of classical spin models is proposed. We describe a simple method to automatically locate critical points in (Quantum) Monte Carlo simulations. The algorithm assumes the existence of a finite correlation length in at least one of the two phases surrounding the quantum critical point. We illustrate these ideas on the example of the critical inter-chain coupling for which coupled antiferromagnetic S=1 spin chains order at T=0. Finite-size scaling relations are used to determine the exponents, $\nu=0.72(2)$ and $\eta=0.038(3)$ in agreement with previous estimates.Comment: 5 pages, 3 figures, published versio

Influence of uniaxial tensile stress on the mechanical and piezoelectric properties of short-period ferroelectric superlattice

Tetragonal ferroelectric/ferroelectric BaTiO3/PbTiO3 superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mechanism for the enhancement of piezoelectricity is discussed

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor

Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students