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

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

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

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

Allocentric representation in the human amygdala and ventral visual stream

The hippocampus and the entorhinal cortex are considered the main brain structures for allocentric representation of the external environment. Here, we show that the amygdala and the ventral visual stream are involved in allocentric representation. Thirty-one young men explored 35 virtual environments during high-resolution functional magnetic resonance imaging (fMRI) of the medial temporal lobe (MTL) and were subsequently tested on recall of the allocentric pattern of the objects in each environment-in other words, the positions of the objects relative to each other and to the outer perimeter. We find increasingly unique brain activation patterns associated with increasing allocentric accuracy in distinct neural populations in the perirhinal cortex, parahippocampal cortex, fusiform cortex, amygdala, hippocampus, and entorhinal cortex. In contrast to the traditional view of a hierarchical MTL network with the hippocampus at the top, we demonstrate, using recently developed graph analyses, a hierarchical allocentric MTL network without a main connector hub

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

Ultra-high-field imaging reveals increased whole brain connectivity underpins cognitive strategies that attenuate pain

We investigated how the attenuation of pain with cognitive interventions affects brain connectivity using neuroimaging and a whole brain novel analysis approach. While receiving tonic cold pain, 20 healthy participants performed three different pain attenuation strategies during simultaneous collection of functional imaging data at seven tesla. Participants were asked to rate their pain after each trial. We related the trial-by-trial variability of the attenuation performance to the trial-by-trial functional connectivity strength change of brain data. Across all conditions, we found that a higher performance of pain attenuation was predominantly associated with higher functional connectivity. Of note, we observed an association between low pain and high connectivity for regions that belong to brain regions long associated with pain processing, the insular and cingulate cortices. For one of the cognitive strategies (safe place), the performance of pain attenuation was explained by diffusion tensor imaging metrics of increased white matter integrity

Patients with chronic pain exhibit individually unique cortical signatures of pain encoding

Chronic pain is characterised by an ongoing and fluctuating intensity over time. Here, we investigated how the trajectory of the patients\u27 endogenous pain is encoded in the brain. In repeated functional MRI (fMRI) sessions, 20 patients with chronic back pain and 20 patients with chronic migraine were asked to continuously rate the intensity of their endogenous pain. Linear mixed effects models were used to disentangle cortical processes related to pain intensity and to pain intensity changes. At group level, we found that the intensity of pain in patients with chronic back pain is encoded in the anterior insular cortex, the frontal operculum, and the pons; the change of pain in chronic back pain and chronic migraine patients is mainly encoded in the anterior insular cortex. At the individual level, we identified a more complex picture where each patient exhibited their own signature of endogenous pain encoding. The diversity of the individual cortical signatures of chronic pain encoding results bridge between clinical observations and neuroimaging; they add to the understanding of chronic pain as a complex and multifaceted disease