Case Report: Color as a Therapeutic Intervention

Peer reviewedFinal Accepted Versio

Nonholonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 200

Two-year results from a phase 2 extension study of oral amiselimod in relapsing multiple sclerosis.

BACKGROUND: Amiselimod, an oral selective sphingosine-1-phosphate 1 receptor modulator, suppressed disease activity dose-dependently without clinically relevant bradyarrhythmia in a 24-week phase 2, placebo-controlled study in relapsing-remitting multiple sclerosis. OBJECTIVE: To assess safety and efficacy of amiselimod over 96 weeks. METHODS: After completing the core study, patients on amiselimod continued at the same dose, whereas those on placebo were randomised 1:1:1 to amiselimod 0.1, 0.2 or 0.4 mg for another 72 weeks. Most patients receiving 0.1 mg were re-randomised to 0.2 or 0.4 mg upon availability of the core study results. RESULTS: Of 415 patients randomised in the core study, 367 (88.4%) entered and 322 (77.6%) completed the extension. One or more adverse events were reported in 303 (82.6%) of 367 patients: 'headache', 'lymphocyte count decreased', 'nasopharyngitis' and 'MS relapse' were most common (14.7%-16.9%). No serious opportunistic infection, macular oedema or malignancy was reported and no bradyarrhythmia of clinical concern was observed by Holter or 12-lead electrocardiogram. The dose-dependent effect of amiselimod on clinical and magnetic resonance imaging-related outcomes from the core study was sustained in those continuing on amiselimod and similarly observed after switching to active drug. CONCLUSION: For up to 2 years of treatment, amiselimod was well tolerated and dose-dependently effective in controlling disease activity

Conformal mechanics inspired by extremal black holes in d=4

A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville.Comment: V2: presentation improved, new material and references added; the version to appear in JHE

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Identifying multiple sclerosis subtypes using unsupervised machine learning and MRI data

Multiple sclerosis (MS) can be divided into four phenotypes based on clinical evolution. The pathophysiological boundaries of these phenotypes are unclear, limiting treatment stratification. Machine learning can identify groups with similar features using multidimensional data. Here, to classify MS subtypes based on pathological features, we apply unsupervised machine learning to brain MRI scans acquired in previously published studies. We use a training dataset from 6322 MS patients to define MRI-based subtypes and an independent cohort of 3068 patients for validation. Based on the earliest abnormalities, we define MS subtypes as cortex-led, normal-appearing white matter-led, and lesion-led. People with the lesion-led subtype have the highest risk of confirmed disability progression (CDP) and the highest relapse rate. People with the lesion-led MS subtype show positive treatment response in selected clinical trials. Our findings suggest that MRI-based subtypes predict MS disability progression and response to treatment and may be used to define groups of patients in interventional trials