Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Proceedings of the Fourth International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Biological Shape Variability Modeling (MFCA 2013), Nagoya, Japan

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the first edition of this workshop in 2006, second edition in New-York in 2008, the third edition in Toronto in 2011, the forth edition was held in Nagoya Japan on September 22 2013

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

This Week's Finds in Mathematical Physics (1-50)

These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of $n$-categories to these subjects. However, there are also digressions into Lie algebras, elliptic curves, linear logic and other subjects. They were typeset in 2020 by Tim Hosgood. If you see typos or other problems please report them. (I already know the cover page looks weird).Comment: 242 page

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

The application of b-mode ultrasonography for analysis of human skeletal muscle

Skeletal muscles control the joints of the skeletal system and they allow human movement and interaction with the environment. They are vital for stability in balance, walking and running, and many other skilled motor tasks. To understand how muscles operate in general and specific situations there are a variety of tools at the disposal of research scientists and clinicians for analysing muscle function. Strain gauges for example allow the quantification of forces exerted during joint rotation. However, skeletal muscles are multilayer systems and often different muscles are responsible for the overall force generated during joint rotation. Therefore, strain gauges do not reveal the extent of the contribution of individual muscles during muscle function. The most widely-used and accepted muscle analysis tool is electromyography (EMG), which can measure the activation level of individual muscles by measuring the electrical potential propagating through muscle resulting from local activations of motor units. However, EMG does not linearly relate to any real physical forces, meaning that without prior knowledge of the force exertion on the level of the muscle, force cannot be estimated. EMG can measure superficial layers of muscle non-invasively by attaching surface electrodes (surface EMG) to the skin over the belly of the muscle. To measure the activity of individual muscle beneath the superficial muscle, a needle or thin-wire electrode must be inserted through the skin and into the muscle volume (intramuscular EMG), which is invasive and not practical in many situations. Furthermore, intramuscular EMG can only provide measurement of a very small volume (<1mm3) which can have varying amounts of active motor units. Ultrasonography is a powerful cost-effective non-invasive imaging technology which allows real-time observation of cross-sections of multiple layers of dynamic skeletal muscle. Recent advances in automated skeletal muscle ultrasound analysis techniques, and advances in image processing techniques make ultrasound a valuable line of investigation for analysis of dynamic skeletal muscle. This aim of this thesis is to study and develop advanced image analysis techniques applicable to the analysis of dynamic skeletal muscle. The broader aim is to understand the capacity/limits of ultrasound as a skeletal muscle analysis tool. The ideas presented within offer new approaches to modelling complex muscle architecture and function via ultrasound. Tools have also been developed here that will contribute to, and promote ultrasound skeletal muscle analysis as a new and emerging technology which may be used by clinicians and research scientists to develop our understanding of skeletal muscle function. The main findings of this thesis are that automated segmentation of architecturally simple and complex skeletal muscle groups is possible and accurate, and that information about joint angles and muscle activity/force can be automatically extracted directly from ultrasound images without the explicit knowledge of how to extract it. The techniques used offer new possibilities for non-invasive information extraction from complex muscle groups such as the muscles in the human posterior neck