Permutation Inference for Canonical Correlation Analysis

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 reference

Static inverters which sum a plurality of waves Patent

Describing static inverter with single or multiple phase outpu

Meteorological impacts of the total solar eclipse of 21 August 2017

A solar eclipse presents many opportunities for examining the impact of the reduction in solar radiation upon meteorological conditions, particularly so as accurate predictions of the circumstances and extent of the eclipse well before the event enable bespoke observing programmes to be set out in advance. The total solar eclipse of 21 August 2017 traversed the United States from north-west to south-east (Figure 1) and a partial eclipse (at least) was visible in every state. According to news reports, the path of totality was lined with more than 10 million people, making this probably the largest audience for any total solar eclipse in human history. The time of year and time of day was favourable for both good viewing conditions along much of the eclipse path, and for the detection of eclipse-related impacts on surface meteorological variables

Tobacco Control Progress in Low and Middle Income Countries in Comparison to High Income Countries

The study aimed to describe worldwide levels and trends of tobacco control policy by comparing low and middle income countries with other income categories from 2007 to 2014 and to analyze the corresponding relation to recent changes in smoking prevalence. Policy measure data representing years 2007 to 2014 were collected from all available World Health Organization (WHO) reports on the global tobacco epidemic. Corresponding policy percentage scores (PS) were calculated based on MPOWER measures. Age-standardized smoking prevalence data for years 2010 and 2015 were collected from the WHO Global Health Observatory Data Repository. Trends of PS were analysed with respect to WHO region and OECD country income category. Scatter plots and regression analysis were used to depict the relationship between tobacco control policy of 2010 and change in smoking prevalence between 2015 and 2010 by sex and income category. Combined PS for all countries increased significantly from 47% in 2007 to 61% by 2014 (p < 0.001). When grouped by income category and region, policies were strengthened in all categories, albeit with varying progression. By 2014, tobacco control policy legislation had reached 45% in the Least Developed Countries (LDCs), 59% in Low Middle Income Countries (LMICs), 66% in Upper Middle Income Countries (UMICs) and 70% in High Income Countries (HICs). Overall, there was a negative relationship between higher policy scores and change in smoking prevalence. Although policy strengthening had been conducted between 2007 and 2014, room for considerable global improvement remains, particularly in LDCs. View Full-Tex

Standing wave oscillations in binary mixture convection: from onset via symmetry breaking to period doubling into chaos

Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients. Galerkin as well as finite-difference simulations were used. They were augmented by simple control methods to obtain also unstable SW states. For sufficiently negative Soret coefficients unstable SWs bifurcate subcritically out of the quiescent conductive state. They become stable via a saddle-node bifurcation when lateral phase pinning is exerted. Eventually their invariance under time-shift by half a period combined with reflexion at midheight of the fluid layer gets broken. Thereafter they terminate by undergoing a period-doubling cascade into chaos

Non-spiky density of states of an icosahedral quasicrystal

The density of states of the ideal three-dimensional Penrose tiling, a quasicrystalline model, is calculated with a resolution of 10 meV. It is not spiky. This falsifies theoretical predictions so far, that spikes of width 10-20 meV are generic for the density of states of quasicrystals, and it confirms recent experimental findings. The qualitative difference between our results and previous calculations is partly explained by the small number of k points that has usually been included in the evaluation of the density of states of periodic approximants of quasicrystals. It is also shown that both the density of states of a small approximant of the three-dimensional Penrose tiling and the density of states of the ideal two-dimensional Penrose tiling do have spiky features, which also partly explains earlier predictions.Comment: 8 pages, 4 figures. Changes in this version: longer introduction, details of figures shown in inset

False Discovery Rate and Localizing Power

False discovery rate (FDR) is commonly used for correction for multiple testing in neuroimaging studies. However, when using two-tailed tests, making directional inferences about the results can lead to vastly inflated error rate, even approaching 100% in some cases. This happens because FDR only provides weak control over the error rate, meaning that the proportion of error is guaranteed only globally over all tests, not within subsets, such as among those in only one or another direction. Here we consider and evaluate different strategies for FDR control with two-tailed tests, using both synthetic and real imaging data. Approaches that separate the tests by direction of the hypothesis test, or by the direction of the resulting test statistic, more properly control the directional error rate and preserve FDR benefits, albeit with a doubled risk of errors under complete absence of signal. Strategies that combine tests in both directions, or that use simple two-tailed p-values, can lead to invalid directional conclusions, even if these tests remain globally valid. To enable valid thresholding for directional inference, we suggest that imaging software should allow the possibility that the user sets asymmetrical thresholds for the two sides of the statistical map. While FDR continues to be a valid, powerful procedure for multiple testing correction, care is needed when making directional inferences for two-tailed tests, or more broadly, when making any localized inference

Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath

Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed through the application of a large magnetic field that splits the energy levels of the electron spin and prevents depolarization. However, dephasing decoherence resulting from a dynamical nuclear spin bath cannot be removed in this way. Fluctuations of the nuclear field lead to uncertainty of the electron's precessional frequency in a process known as spectral diffusion. This article considers the effect of the electron's wavefunction shape upon spectral diffusion and provides wavefunction dependent decoherence time formulas for free induction decay as well as spin echoes and concatenated dynamical decoupling schemes for enhancing coherence. We also discuss dephasing of a qubit encoded in singlet-triplet states of a double quantum dot. A central theoretical result of this work is the development of a continuum approximation for the spectral diffusion problem which we have applied to GaAs and InAs materials specifically

Mega-analysis methods in ENIGMA : the experience of the generalized anxiety disorder working group

The ENIGMA group on Generalized Anxiety Disorder (ENIGMA-Anxiety/GAD) is part of a broader effort to investigate anxiety disorders using imaging and genetic data across multiple sites worldwide. The group is actively conducting a mega-analysis of a large number of brain structural scans. In this process, the group was confronted with many methodological challenges related to study planning and implementation, between-country transfer of subject-level data, quality control of a considerable amount of imaging data, and choices related to statistical methods and efficient use of resources. This report summarizes the background information and rationale for the various methodological decisions, as well as the approach taken to implement them. The goal is to document the approach and help guide other research groups working with large brain imaging data sets as they develop their own analytic pipelines for mega-analyses