Machine learning outperforms clinical experts in classification of hip fractures.

Hip fractures are a major cause of morbidity and mortality in the elderly, and incur high health and social care costs. Given projected population ageing, the number of incident hip fractures is predicted to increase globally. As fracture classification strongly determines the chosen surgical treatment, differences in fracture classification influence patient outcomes and treatment costs. We aimed to create a machine learning method for identifying and classifying hip fractures, and to compare its performance to experienced human observers. We used 3659 hip radiographs, classified by at least two expert clinicians. The machine learning method was able to classify hip fractures with 19% greater accuracy than humans, achieving overall accuracy of 92%.

Multi-layered folding with voids.

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper, we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free-boundary problem and compare them with the periodic solutions observed experimentally.

Grazing and border-collision in piecewise-smooth systems: a unified analytical framework.

A comprehensive derivation is presented of normal form maps for grazing bifurcations in piecewise smooth models of physical processes. This links grazings with border-collisions in nonsmooth maps. Contrary to previous literature, piecewise linear maps correspond only to nonsmooth discontinuity boundaries. All other maps have either square-root or (3/2)-type singularities.