Andrea Natale

Eran Zvuloni, Sheina Gendelman, Sanghamitra Mohanty et al.

Introduction: 12-lead electrocardiogram (ECG) is recorded during atrial fibrillation (AF) catheter ablation procedure (CAP). It is not easy to determine if CAP was successful without a long follow-up assessing for AF recurrence (AFR). Therefore, an AFR risk prediction algorithm could enable a better management of CAP patients. In this research, we extracted features from 12-lead ECG recorded before and after CAP and train an AFR risk prediction machine learning model. Methods: Pre- and post-CAP segments were extracted from 112 patients. The analysis included a signal quality criterion, heart rate variability and morphological biomarkers engineered from the 12-lead ECG (804 features overall). 43 out of the 112 patients (n) had AFR clinical endpoint available. These were utilized to assess the feasibility of AFR risk prediction, using either pre or post CAP features. A random forest classifier was trained within a nested cross validation framework. Results: 36 features were found statistically significant for distinguishing between the pre and post surgery states (n=112). For the classification, an area under the receiver operating characteristic (AUROC) curve was reported with AUROC_pre=0.64 and AUROC_post=0.74 (n=43). Discussion and conclusions: This preliminary analysis showed the feasibility of AFR risk prediction. Such a model could be used to improve CAP management.

Andrea Natale, Jemma Shipton, Colin J. Cotter

Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties.

Andrea Natale, Colin J. Cotter

We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a nonholonomic variational principle and an appropriately defined Lagrangian, where finite element H(div) vector fields are identified with advection operators; this is the first successful extension of the structure-preserving discretisation of Pavlov et al. (2009) to the finite element setting. The resulting algorithm coincides with the energy-conserving scheme presented in Guzmán et al. (2016). Through the variational derivation, we discover that it also satisfies a discrete analogous of Kelvin's circulation theorem. Further, we propose an upwind-stabilised version of the scheme which dissipates enstrophy whilst preserving energy conservation and the discrete Kelvin's theorem. We prove error estimates for this version of the scheme, and we study its behaviour through numerical tests.

Andrea Natale, Colin J. Cotter

We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the Streamline Upwind/Petrov-Galerkin (SUPG) discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.