3,186 research outputs found
RLLA: Surviving as a Small National Lifesaving Organisation - Progress in Lesotho: From 2004 to 2018
Modelling mitral valvular dynamics–current trend and future directions
Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed
Max-Margin Works while Large Margin Fails: Generalization without Uniform Convergence
A major challenge in modern machine learning is theoretically understanding
the generalization properties of overparameterized models. Many existing tools
rely on uniform convergence (UC), a property that, when it holds, guarantees
that the test loss will be close to the training loss, uniformly over a class
of candidate models. Nagarajan and Kolter (2019) show that in certain simple
linear and neural-network settings, any uniform convergence bound will be
vacuous, leaving open the question of how to prove generalization in settings
where UC fails. Our main contribution is proving novel generalization bounds in
two such settings, one linear, and one non-linear. We study the linear
classification setting of Nagarajan and Kolter, and a quadratic ground truth
function learned via a two-layer neural network in the non-linear regime. We
prove a new type of margin bound showing that above a certain signal-to-noise
threshold, any near-max-margin classifier will achieve almost no test loss in
these two settings. Our results show that near-max-margin is important: while
any model that achieves at least a -fraction of the max-margin
generalizes well, a classifier achieving half of the max-margin may fail
terribly. Building on the impossibility results of Nagarajan and Kolter, under
slightly stronger assumptions, we show that one-sided UC bounds and classical
margin bounds will fail on near-max-margin classifiers. Our analysis provides
insight on why memorization can coexist with generalization: we show that in
this challenging regime where generalization occurs but UC fails,
near-max-margin classifiers simultaneously contain some generalizable
components and some overfitting components that memorize the data. The presence
of the overfitting components is enough to preclude UC, but the near-extremal
margin guarantees that sufficient generalizable components are present
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