Translated points for prequantization spaces over monotone toric manifolds

We prove a version of Sandon's conjecture on the number of translated points of contactomorphisms for the case of a prequantization bundle over a closed monotone toric manifold. Namely we show that any contactomorphism of this prequantization bundle lying in the identity component of the contactomorphism group possesses at least $N$ translated points, where $N$ is the minimal Chern number of the toric manifold. The proof relies on the theory of generating functions coupled with equivariant cohomology, whereby we adapt Givental's approach to the Arnold conjecture for rational symplectic toric manifolds to the context of prequantization bundles.Comment: Corrected typos; added discussion in the introduction, explanations, and reference

A topological data analysis-based method for gait signals with an application to the study of multiple sclerosis

International audienceIn the past few years, light, affordable wearable inertial measurement units have been providing to clinicians and researchers the possibility to quantitatively study motor degeneracy by comparing gait trials from patients and/or healthy subjects. To do so, standard gait features can be used but they fail to detect subtle changes in several pathologies including multiple sclerosis. Multiple sclerosis is a demyelinating disease of the central nervous system whose symptoms include lower limb impairment, which is why gait trials are commonly used by clinicians for their patients' follow-up. This article describes a method to compare pairs of gait signals, visualize the results and interpret them, based on topological data analysis techniques. Our method is non-parametric and requires no data other than gait signals acquired with inertial measurement units. We introduce tools from topological data analysis (sublevel sets, persistence barcodes) in a practical way to make it as accessible as possible in order to encourage its use by clinicians. We apply our method to study a cohort of patients suffering from progressive multiple sclerosis and healthy subjects. We show that it can help estimate the severity of the disease and also be used for longitudinal follow-up to detect an evolution of the disease or other phenomena such as asymmetry or outliers

Evaluation methods to assess the e cacy of equinovarus foot surgery on the gait of post-stroke hemiplegic patients: A literature review

International audienceEvaluation methods to assess the e cacy of equinovarus foot surgery on the gait of post-stroke hemiplegic patients: A literature review

A new score combining compound muscle action potential (CMAP) amplitudes and motor score is predictive of motor outcome after AVXS-101 (Onasemnogene Abeparvovec) SMA therapy

International audienceSpinal muscular atrophy 1 (SMA1) is a severe early genetic disease with degeneration of motor neurons. Motor development is still suboptimal after gene replacement therapy in symptomatic patients. In this study, compound muscle action potential (CMAP) amplitudes were explored as predictors of motor recovery after gene therapy. Thirteen symptomatic SMA1 patients were prospectively included at the Necker Enfants Malades Hospital, Paris, France (Cohort 1) and 12 at the other pediatric neuromuscular reference centers of the French Filnemus network (Cohort 2). In Cohort 1, median CMAP amplitudes showed the best improvement between baseline and the 12 months visit compared to the other tested nerves (ulnar, fibular and tibial). High median CMAP amplitudes at baseline was associated with unaided sitting achievement at M6 (AUC 90%). None of the patients with CHOPINTEND at M0 < 30/64 and median CMAP < 0.5 mV achieved unaided sitting at M6 and this result was confirmed on Cohort 2 used as an independent validation data. Thus, median CMAP amplitude is a valid biomarker for routine practice to predict sitting at M6. A median CMAP amplitude over 0.5 mV at baseline may predict better motor recovery