Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning associations between clinical information and motion-based descriptors using a large scale MR-derived cardiac motion atlas

The availability of large scale databases containing imaging and non-imaging data, such as the UK Biobank, represents an opportunity to improve our understanding of healthy and diseased bodily function. Cardiac motion atlases provide a space of reference in which the motion fields of a cohort of subjects can be directly compared. In this work, a cardiac motion atlas is built from cine MR data from the UK Biobank (~ 6000 subjects). Two automated quality control strategies are proposed to reject subjects with insufficient image quality. Based on the atlas, three dimensionality reduction algorithms are evaluated to learn data-driven cardiac motion descriptors, and statistical methods used to study the association between these descriptors and non-imaging data. Results show a positive correlation between the atlas motion descriptors and body fat percentage, basal metabolic rate, hypertension, smoking status and alcohol intake frequency. The proposed method outperforms the ability to identify changes in cardiac function due to these known cardiovascular risk factors compared to ejection fraction, the most commonly used descriptor of cardiac function. In conclusion, this work represents a framework for further investigation of the factors influencing cardiac health.Comment: 2018 International Workshop on Statistical Atlases and Computational Modeling of the Hear

Nonuniqueness in spin-density-functional theory on lattices

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive.Comment: 4 pages, 1 figur

A Population of Radio-loud Narrow Line Seyfert 1 Galaxies with Blazar-like Properties?

(abridged) We present a comprehensive study of a sample of 23 genuine radio-loud NLS1 galaxies which have the radio-loudness parameters greater than 100. The radio sources of the sample are ubiquitously compact. A significant fraction of these objects show interesting radio to X-ray properties that are unusual to most of the previously known radio-loud NLS1 AGN, but are reminiscent of blazars. These include flat radio spectra, large amplitude flux and spectral variability, compact VLBI cores, very high brightness temperatures derived from variability, enhanced optical emission in excess of the normal ionising continuum, flat X-ray spectra, and blazar-like SEDs. We interpret them as evidence for the postulated blazar nature of these very radio-loud NLS1 AGN, which might possess at least moderately relativistic jets. Intrinsically, some of the objects have relatively low radio power and would have been classified as radio-intermediate AGN. The black hole masses are estimated to be within 10^{6-8}Msun, and the inferred Eddington ratios are around unity. The results imply that radio-loud AGN may be powered by black holes with moderate masses (10^{6-7}Msun) accreting at high rates. We find that a significant fraction of the objects, despite having strong emission lines, resemble high-energy peaked BL Lacs (HBL) in their SED. Given the peculiarities of blazar-like NLS1 galaxies, questions arise as to whether they are plain downsizing extensions of normal radio-loud AGN, or whether they form a previously unrecognised population.Comment: Comments: 29 pages, 16 figures, 4 tables, accepted for publication in Ap

Deep learning for cardiac image segmentation: A review

Deep learning has become the most widely used approach for cardiac image segmentation in recent years. In this paper, we provide a review of over 100 cardiac image segmentation papers using deep learning, which covers common imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound (US) and major anatomical structures of interest (ventricles, atria and vessels). In addition, a summary of publicly available cardiac image datasets and code repositories are included to provide a base for encouraging reproducible research. Finally, we discuss the challenges and limitations with current deep learning-based approaches (scarcity of labels, model generalizability across different domains, interpretability) and suggest potential directions for future research

XMM-Newton View of PKS 2155-304: Characterizing the X-ray Variability Properties with EPIC-PN

Starting from XMM-Newton EPIC-PN data, we present the X-ray variability characteristics of PKS 2155-304 using a simple analysis of the excess variance, \xs, and of the fractional rms variability amplitude, fvar. The scatter in \xs\ and \fvar, calculated using 500 s long segments of the light curves, is smaller than the scatter expected for red noise variability. This alone does not imply that the underlying process responsible for the variability of the source is stationary, since the real changes of the individual variance estimates are possibly smaller than the large scatters expected for a red noise process. In fact the averaged \xs and \fvar, reducing the fluctuations of the individual variances, chang e with time, indicating non-stationary variability. Moreover, both the averaged \sqxs (absolute rms variability amplitude) and \fvar show linear correlation with source flux but in an opposite sense: \sqxs correlates with flux, but \fvar anti-correlates with flux. These correlations suggest that the variability process of the source is strongly non-stationary as random scatters of variances should not yield any correlation. \fvar spectra were constructed to compare variability amplitudes in different energy bands. We found that the fractional rms variability amplitude of the source, when significant variability is observed, increases logarithmically with the photon energy, indicating significant spectral variability. The point-to-point variability amplitude may also track this trend, suggesting that the slopes of the power spectral density of the source are energy-independent. Using the normalized excess variance the black hole mass of \pks was estimated to be about $1.45 \times 10^8 M_{\bigodot}$. This is compared and contrasted with the estimates derived from measurements of the host galaxies.Comment: Accepted for publication in The Astrophysical Journa

Large-scale Quality Control of Cardiac Imaging in Population Studies: Application to UK Biobank

In large population studies such as the UK Biobank (UKBB), quality control of the acquired images by visual assessment is unfeasible. In this paper, we apply a recently developed fully-automated quality control pipeline for cardiac MR (CMR) images to the first 19,265 short-axis (SA) cine stacks from the UKBB. We present the results for the three estimated quality metrics (heart coverage, inter-slice motion and image contrast in the cardiac region) as well as their potential associations with factors including acquisition details and subject-related phenotypes. Up to 14.2% of the analysed SA stacks had sub-optimal coverage (i.e. missing basal and/or apical slices), however most of them were limited to the first year of acquisition. Up to 16% of the stacks were affected by noticeable inter-slice motion (i.e. average inter-slice misalignment greater than 3.4 mm). Inter-slice motion was positively correlated with weight and body surface area. Only 2.1% of the stacks had an average end-diastolic cardiac image contrast below 30% of the dynamic range. These findings will be highly valuable for both the scientists involved in UKBB CMR acquisition and for the ones who use the dataset for research purposes