Quadratic ideals and Rogers–Ramanujan recursions

We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers–Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen

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

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

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

On high moments of strongly diluted large Wigner random matrices

We consider a dilute version of the Wigner ensemble of nxn random matrices $H$ and study the asymptotic behavior of their moments $M_{2s}$ in the limit of infinite $n$, $s$ and $\rho$, where $\rho$ is the dilution parameter. We show that in the asymptotic regime of the strong dilution, the moments $M_{2s}$ with $s=\chi\rho$ depend on the second and the fourth moments of the random entries $H_{ij}$ and do not depend on other even moments of $H_{ij}$. This fact can be regarded as an evidence of a new type of the universal behavior of the local eigenvalue distribution of strongly dilute random matrices at the border of the limiting spectrum. As a by-product of the proof, we describe a new kind of Catalan-type numbers related with the tree-type walks.Comment: 43 pages (version four: misprints corrected, discussion added, other minor modifications

Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

INSIDE: Steering Spatial Attention with Non-Imaging Information in CNNs

We consider the problem of integrating non-imaging information into segmentation networks to improve performance. Conditioning layers such as FiLM provide the means to selectively amplify or suppress the contribution of different feature maps in a linear fashion. However, spatial dependency is difficult to learn within a convolutional paradigm. In this paper, we propose a mechanism to allow for spatial localisation conditioned on non-imaging information, using a feature-wise attention mechanism comprising a differentiable parametrised function (e.g. Gaussian), prior to applying the feature-wise modulation. We name our method INstance modulation with SpatIal DEpendency (INSIDE). The conditioning information might comprise any factors that relate to spatial or spatio-temporal information such as lesion location, size, and cardiac cycle phase. Our method can be trained end-to-end and does not require additional supervision. We evaluate the method on two datasets: a new CLEVR-Seg dataset where we segment objects based on location, and the ACDC dataset conditioned on cardiac phase and slice location within the volume. Code and the CLEVR-Seg dataset are available at https://github.com/jacenkow/inside.Comment: Accepted at International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) 202

Bundles and Hotspots of Multiple Ecosystem Services for Optimized Land Management in Kentucky, United States

Ecosystem services are benefits that the natural environment provides to support human well-being. A thorough understanding and assessment of these services are critical to maintain ecosystem services flow through sustainable land management to optimize bundles of ecosystem services provision. Maximizing one particular ecosystem service may lead to reduction in another. Therefore, identifying ecosystem services tradeoffs and synergies is key in addressing this challenge. However, the identification of multiple ecosystem services tradeoffs and synergies is still limited. A previous study failed to effectively capture the spatial interaction among ecosystem services as it was limited by “space-to-time” substitution method used because of temporal data scarcity. The study was also limited by using land use types in creating ecosystem services, which could lead to some deviations. The broad objective of this study is therefore to examine the bundles and hotspots of multiple ecosystem services and their tradeoffs in Kentucky, U.S. The study combined geographic data and spatially-explicit models to identify multiple ecosystem services bundles and hotspots, and determined the spatial locations of ecosystem services hotspots. Results showed that the spatial interactions among ecosystem services were very high: of the 21 possible pairs of ecosystem services, 17 pairs were significantly correlated. The seven ecosystem services examined can be bundled into three groups, geographically clustered on the landscape. These results support the hypothesis that some groups of ecosystem services provision can present similar spatial patterns at a large mesoscale. Understanding the spatial interactions and bundles of the ecosystem services provides essential information for evidence-based sustainable land management

Numerical modeling of the environment impact of landfill leachate leakage on groundwater quality-A field application

There are more than 372 big uncontrolled landfill areas in China. Waste disposal facilities are mainly responsible for the gradual quality degradation of groundwater. This paper reports an integrated study undertaken to develop an environmental assessment of the uncontrolled sanitary landfill area of the city of Jiaxing, Zhejiang, China. The USGS modular 3D finite difference groundwater flow model (Mod- flow) and Modular 3D Finite Difference Mass Transport Model (MT3D) software were used to simulate groundwater flow and contaminant transport modeling. The results indicated that landfill leachate leakage has significant effect on groundwater quality