An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques

Soliton Dynamics in Computational Anatomy

Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be singular solutions of a partial differential equation that is called the geodesic EPDiff equation. A recently discovered momentum map for singular solutions of EPDiff yields their canonical Hamiltonian formulation, which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta. The momentum map provides an isomorphism between landmarks (and outlines) for images and singular soliton solutions of the EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as well as new data representation.Comment: published in NeuroImag

Averaged Lagrangians and the mean dynamical effects of fluctuations in continuum mechanics

We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincar\'e (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then derive a set of approximate small amplitude GLM equations (glm) that express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The new glm EP motion equations for compressible and incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure (THC). The glm equations lead to generalizations of the Euler-alpha models to include compressibility and magnetic fields.Comment: 95 pages, no figures, submitted to Physica

Developing a Machine Learning-Based Clinical Decision Support Tool for Uterine Tumor Imaging

Uterine leiomyosarcoma (LMS) is a rare but aggressive malignancy. On imaging, it is difficult to differentiate LMS from, for example, degenerated leiomyoma (LM), a prevalent but benign condition. We curated a data set of 115 axial T2-weighted MRI images from 110 patients (mean [range] age=45 [17-81] years) with UTs that included five different tumor types. These data were randomly split stratifying on tumor volume into training (n=85) and test sets (n=30). An independent second reader (reader 2) provided manual segmentations for all test set images. To automate segmentation, we applied nnU-Net and explored the effect of training set size on performance by randomly generating subsets with 25, 45, 65 and 85 training set images. We evaluated the ability of radiomic features to distinguish between types of UT individually and when combined through feature selection and machine learning. Using the entire training set the mean [95% CI] fibroid DSC was measured as 0.87 [0.59-1.00] and the agreement between the two readers was 0.89 [0.77-1.0] on the test set. When classifying degenerated LM from LMS we achieve a test set F1-score of 0.80. Classifying UTs based on radiomic features we identify classifiers achieving F1-scores of 0.53 [0.45, 0.61] and 0.80 [0.80, 0.80] on the test set for the benign versus malignant, and degenerated LM versus LMS tasks. We show that it is possible to develop an automated method for 3D segmentation of the uterus and UT that is close to human-level performance with fewer than 150 annotated images. For distinguishing UT types, while we train models that merit further investigation with additional data, reliable automatic differentiation of UTs remains a challenge

Attentional Processing in C57BL/6J Mice Exposed to Developmental Vitamin D Deficiency

Epidemiological evidence suggests that Developmental Vitamin D (DVD) deficiency is associated with an increased risk of schizophrenia. DVD deficiency in mice is associated with altered behaviour, however there has been no detailed investigation of cognitive behaviours in DVD-deficient mice. The aim of this study was to determine the effect of DVD deficiency on a range of cognitive tasks assessing attentional processing in C57BL/6J mice. DVD deficiency was established by feeding female C57BL/6J mice a vitamin D-deficient diet from four weeks of age. After six weeks on the diet, vitamin D-deficient and control females were mated with vitamin D-normal males and upon birth of the pups, all dams were returned to a diet containing vitamin D. The adult offspring were tested on a range of cognitive behavioural tests, including the five-choice serial reaction task (5C-SRT) and five-choice continuous performance test (5C-CPT), as well as latent inhibition using a fear conditioning paradigm. DVD deficiency was not associated with altered attentional performance on the 5C-SRT. In the 5C-CPT DVD-deficient male mice exhibited an impairment in inhibiting repetitive responses by making more perseverative responses, with no changes in premature or false alarm responding. DVD deficiency did not affect the acquisition or retention of cued fear conditioning, nor did it affect the expression of latent inhibition using a fear conditioning paradigm. DVD-deficient mice exhibited no major impairments in any of the cognitive domains tested. However, impairments in perseverative responding in DVD-deficient mice may indicate that these animals have specific alterations in systems governing compulsive or reward-seeking behaviour

Bauxite residue (Red mud) as a pulverised fuel ash substitute in the manufacture of lightweight aggregate

This study looked at the potential of bauxite residue or red mud to be used in the manufacture of lightweight aggregate in replacement of pulverised fuel ash (PFA), commonly used as a way of recycling problematic wastes. The percentage replacements of red mud with PFA were as follows: 25, 31, 38, 44 and 50%. These were blended in a mix with waste excavated clay and sewage sludge – all from the Chongqing municipality in China. Lightweight pellets were produced using a Trefoil rotary kiln and were sintered to 1200 °C. Results showed that 44 % bauxite residue replacement produced lightweight pellets with the highest compressive strength, highest density and largest water holding capacity. This would be expected in materials with a low level of silicates, which causes insufficient glass phase viscosity and therefore poor bloating during firing; producing an aggregate with a higher density but with open pores that allowed for larger water absorption. All ratios of red mud aggregates were significantly reduced in pH after firing to around pH 8, and this reduced the leachability of the aggregates to levels below those set by the European landfill directive (2003/33/EC)

Genetic Drivers of Heterogeneity in Type 2 Diabetes Pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P \u3c 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care

Genetic drivers of heterogeneity in type 2 diabetes pathophysiology

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes1,2 and molecular mechanisms that are often specific to cell type3,4. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P &lt; 5 × 10-8) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores5 in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care.</p