Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

Parametrization of the Driven Betatron Oscillation

An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam motion in a synchrotron. By observing this coherent motion, the optical parameters can be directly measured at the beam position monitor locations. The driven oscillation induced by an AC dipole will generate a phase space ellipse which differs from that of the free oscillation. If not properly accounted for, this difference can lead to a misinterpretation of the actual optical parameters, for instance, of 6% or more in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the linear optics parameters is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. Beam position data taken under the influence of an AC dipole, with this new interpretation in mind, can lead to more precise measurements of the normal Courant-Snyder parameters. This new parameterization of the driven motion is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.Comment: 8 pages, 8 figures, and 1 tabl

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

Stratified decision forests for accurate anatomical landmark localization in cardiac images

Accurate localization of anatomical landmarks is an important step in medical imaging, as it provides useful prior information for subsequent image analysis and acquisition methods. It is particularly useful for initialization of automatic image analysis tools (e.g. segmentation and registration) and detection of scan planes for automated image acquisition. Landmark localization has been commonly performed using learning based approaches, such as classifier and/or regressor models. However, trained models may not generalize well in heterogeneous datasets when the images contain large differences due to size, pose and shape variations of organs. To learn more data-adaptive and patient specific models, we propose a novel stratification based training model, and demonstrate its use in a decision forest. The proposed approach does not require any additional training information compared to the standard model training procedure and can be easily integrated into any decision tree framework. The proposed method is evaluated on 1080 3D highresolution and 90 multi-stack 2D cardiac cine MR images. The experiments show that the proposed method achieves state-of-theart landmark localization accuracy and outperforms standard regression and classification based approaches. Additionally, the proposed method is used in a multi-atlas segmentation to create a fully automatic segmentation pipeline, and the results show that it achieves state-of-the-art segmentation accuracy

Partial Dynamical Symmetry and Mixed Dynamics

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space foliated by tori. This clarifies the suppression of classical chaos associated with partial dynamical symmetry. The results are used to divide the states of a mixed system into ``chaotic'' and ``regular'' classes.Comment: 10 pages, Revtex, 3 figures, Phys. Rev. Lett. in pres

Particle acceleration

Data is compiled from Solar Maximum Mission and Hinothori satellites, particle detectors in several satellites, ground based instruments, and balloon flights in order to answer fundamental questions relating to: (1) the requirements for the coronal magnetic field structure in the vicinity of the energization source; (2) the height (above the photosphere) of the energization source; (3) the time of energization; (4) transistion between coronal heating and flares; (5) evidence for purely thermal, purely nonthermal and hybrid type flares; (6) the time characteristics of the energization source; (7) whether every flare accelerates protons; (8) the location of the interaction site of the ions and relativistic electrons; (9) the energy spectra for ions and relativistic electrons; (10) the relationship between particles at the Sun and interplanetary space; (11) evidence for more than one acceleration mechanism; (12) whether there is single mechanism that will accelerate particles to all energies and also heat the plasma; and (13) how fast the existing mechanisms accelerate electrons up to several MeV and ions to 1 GeV

RoboCup 2D Soccer Simulation League: Evaluation Challenges

We summarise the results of RoboCup 2D Soccer Simulation League in 2016 (Leipzig), including the main competition and the evaluation round. The evaluation round held in Leipzig confirmed the strength of RoboCup-2015 champion (WrightEagle, i.e. WE2015) in the League, with only eventual finalists of 2016 competition capable of defeating WE2015. An extended, post-Leipzig, round-robin tournament which included the top 8 teams of 2016, as well as WE2015, with over 1000 games played for each pair, placed WE2015 third behind the champion team (Gliders2016) and the runner-up (HELIOS2016). This establishes WE2015 as a stable benchmark for the 2D Simulation League. We then contrast two ranking methods and suggest two options for future evaluation challenges. The first one, "The Champions Simulation League", is proposed to include 6 previous champions, directly competing against each other in a round-robin tournament, with the view to systematically trace the advancements in the League. The second proposal, "The Global Challenge", is aimed to increase the realism of the environmental conditions during the simulated games, by simulating specific features of different participating countries.Comment: 12 pages, RoboCup-2017, Nagoya, Japan, July 201

Explainable Anatomical Shape Analysis through Deep Hierarchical Generative Models

Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimer's disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging

Quantum theory of electronic double-slit diffraction

The phenomena of electron, neutron, atomic and molecular diffraction have been studied by many experiments, and these experiments are explained by some theoretical works. In this paper, we study electronic double-slit diffraction with quantum mechanical approach. We can obtain the results: (1) When the slit width $a$ is in the range of $3\lambda\sim 50\lambda$ we can obtain the obvious diffraction patterns. (2) when the ratio of $\frac{d+a}{a}=n (n=1, 2, 3,\cdot\cdot\cdot)$, order $2n, 3n, 4n,\cdot\cdot\cdot$ are missing in diffraction pattern. (3)When the ratio of $\frac{d+a}{a}\neq n (n=1, 2, 3,\cdot\cdot\cdot)$, there isn't missing order in diffraction pattern. (4) We also find a new quantum mechanics effect that the slit thickness $c$ has a large affect to the electronic diffraction patterns. We think all the predictions in our work can be tested by the electronic double-slit diffraction experiment.Comment: 9pages, 14figure