Wilcoxon-Mann-Whitney odds ratio: A statistical measure for ordinal outcomes such as EDSS

Background: In many clinical situations, ordinal scales afford the primary method of semi-quantifying patient outcomes. In the field of multiple sclerosis, the primary ordinal scale is the Expanded Disability Status Scale. Predominant methods of ordinal scale statistical analysis provide a p-value without effect size or rely heavily on the assumption of proportionality of odds, subjecting them to lack of power and error. The Wilcoxon-Manny-Whitney Odds is a statistical method which provides significant information such as p-value, effect size, number needed to treat, confidence intervals, and is largely assumption-free. However, its utility has not been demonstrated in the field of multiple sclerosis. Methods: Three clinical studies in the field of multiple sclerosis were selected which utilized ordinal scale outcomes at group or individual levels. Data from these studies was extracted using WebPlotDigitizer, and a custom Wilxocon-Mann-Whitney Odds software was applied to each dataset to re-analyze the main outcomes of the studies. Results: Re-analysis of the manuscript by Muraro et al., 2017 demonstrated that autologous stem cell transplantation for relapsing remitting multiple sclerosis resulted in a 65% chance of improving from any Expanded Disability Status Scale category, although not significant. Re-analysis of the manuscript by Songthammawat et al., 2019 demonstrated chance of improvement with intravenous methylprednisolone and concurrent plasma exchange was 185% versus 32% in intravenous methylprednisolone with add-on plasma exchange, although not significant. Re-analysis of Kister et al., 2012 demonstrated the chances of mobility or cognition scores generally favored decline at every 5-year increment of study, and although statistically significant, these were smaller effect sizes ranging from an 11% chance of improvement to a 66% chance of decline over a 5-year interval. Discussion: The Wilcoxon-Mann-Whitney Odds simplifies ordinal data analysis with its robust largely assumption-free nature. In the place of numerous statistical tests, this single test provides effect size estimate, number needed to treat, p-values, and confidence intervals. Importantly, the Wilcoxon-Mann-Whitney Odds effect size calculation is intuitively applicable to both individual and population-levels. Further, the Wilcoxon-Mann-Whitney Odds allows intuitive description of the progression of large cohorts over time, and we were able to clearly convey the odds of mobility and cognitive decline over 30 years in a large multiple sclerosis cohort. Overall, the Wilcoxon-Mann-Whitney Odds is a powerful and robust statistical test with significant promise within the field of multiple sclerosis

On the origin of irregular structure in Saturn's rings

We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal forces and the yield stress of these assemblies; the required tensile strength of ~10^5 dyn/cm^2 is consistent with the sticking forces observed in laboratory simulations of frosted ice particles. These assemblies could be the nonlinear outcome of a linear instability that occurs in a rotating fluid disk in which the shear stress is a decreasing function of the shear. We show that a simple model of an incompressible, non-Newtonian fluid in shear flow leads to the Cahn-Hilliard equation, which is widely used to model the formation of structure in binary alloys and other systems.Comment: 21 pages, 1 figure, to be published in Astronomical Journa

Spectral density asymptotics for Gaussian and Laguerre β\beta-ensembles in the exponentially small region

The first two terms in the large $N$ asymptotic expansion of the $\beta$ moment of the characteristic polynomial for the Gaussian and Laguerre $\beta$-ensembles are calculated. This is used to compute the asymptotic expansion of the spectral density in these ensembles, in the exponentially small region outside the leading support, up to terms $o(1)$ . The leading form of the right tail of the distribution of the largest eigenvalue is given by the density in this regime. It is demonstrated that there is a scaling from this, to the right tail asymptotics for the distribution of the largest eigenvalue at the soft edge.Comment: 19 page

The globular cluster NGC 2419: a crucible for theories of gravity

We present the analysis of a kinematic data set of stars in the globular cluster NGC 2419, taken with Keck/DEIMOS. Combined with a reanalysis of deep HST and Subaru imaging data, which provide an accurate luminosity profile of the cluster, we investigate the validity of a large set of dynamical models of the system, which are checked for stability via N-body simulations. We find that isotropic models in either Newtonian or Modified Newtonian Dynamics (MOND) are ruled out with extremely high confidence. However, a simple Michie model in Newtonian gravity with anisotropic velocity dispersion provides an excellent representation of the luminosity profile and kinematics. In contrast, with MOND we find that Michie models that reproduce the luminosity profile either over-predict the velocity dispersion on the outskirts of the cluster if the mass to light ratio is kept at astrophysically-motivated values, or else they under-predict the central velocity dispersion if the mass to light ratio is taken to be very small. We find that the best Michie model in MOND is a factor of 10000 less likely than the Newtonian model that best fits the system. A likelihood ratio of 350 is found when we investigate more general models by solving the Jeans equation with a Markov-Chain Monte Carlo scheme. We verified with N-body simulations that these results are not significantly different when the MOND external field effect is accounted for. If the assumptions that the cluster is in dynamical equilibrium, spherical, not on a peculiar orbit, and possesses a single dynamical tracer population of constant M/L are correct, we conclude that the present observations provide a very severe challenge for MOND. [abridged]Comment: 25 pages, 19 figures, accepted for publication in Ap

General Relativistic Contributions in Transformation Optics

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important.Comment: 14 pages, 3 figures. Latest version has expanded analysis, corresponds to published versio

Pitch angles of distant spiral galaxies

We have studied the pitch angles of spiral arms for 31 distant galaxies at z~0.7 from three Hubble Deep Fields (HDF-N, HDF-S, HUDF). Using the pitch angle - rotation velocity relation calibrated from nearby galaxies, we have estimated the rotation velocities of galaxies from the deep fields. These estimates have a low accuracy (~50 km/s), but they allow low-mass and giant galaxies to be distinguished. The Tully-Fisher relation constructed using our velocity estimates shows satisfactory agreement with the actually observed relations for distant galaxies and provides evidence for the luminosity evolution of spiral galaxies.Comment: 9 pages, 6 figure

Synergistic Formation of Radicals by Irradiation with Both Vacuum Ultraviolet and Atomic Hydrogen: A Real-Time In Situ Electron Spin Resonance Study

We report on the surface modification of polytetrafluoroethylene (PTFE) as an example of soft- and bio-materials that occur under plasma discharge by kinetics analysis of radical formation using in situ real-time electron spin resonance (ESR) measurements. During irradiation with hydrogen plasma, simultaneous measurements of the gas-phase ESR signals of atomic hydrogen and the carbon dangling bond (C-DB) on PTFE were performed. Dynamic changes of the C-DB density were observed in real time, where the rate of density change was accelerated during initial irradiation and then became constant over time. It is noteworthy that C-DBs were formed synergistically by irradiation with both vacuum ultraviolet (VUV) and atomic hydrogen. The in situ real-time ESR technique is useful to elucidate synergistic roles during plasma surface modification.Comment: 14 pages, 4 figure

Formation Mechanisms for Spirals in Barred Galaxies

We consider a scenario of formation of the spiral structure in barred galaxies. This scenario includes the new non-resonant mechanism of elongation of spirals, due to the characteristic behaviour of the gravitational potential beyond the principal spiral arms

Primary skin fibroblasts as a model of Parkinson's disease

Parkinson's disease is the second most frequent neurodegenerative disorder. While most cases occur sporadic mutations in a growing number of genes including Parkin (PARK2) and PINK1 (PARK6) have been associated with the disease. Different animal models and cell models like patient skin fibroblasts and recombinant cell lines can be used as model systems for Parkinson's disease. Skin fibroblasts present a system with defined mutations and the cumulative cellular damage of the patients. PINK1 and Parkin genes show relevant expression levels in human fibroblasts and since both genes participate in stress response pathways, we believe fibroblasts advantageous in order to assess, e.g. the effect of stressors. Furthermore, since a bioenergetic deficit underlies early stage Parkinson's disease, while atrophy underlies later stages, the use of primary cells seems preferable over the use of tumor cell lines. The new option to use fibroblast-derived induced pluripotent stem cells redifferentiated into dopaminergic neurons is an additional benefit. However, the use of fibroblast has also some drawbacks. We have investigated PARK6 fibroblasts and they mirror closely the respiratory alterations, the expression profiles, the mitochondrial dynamics pathology and the vulnerability to proteasomal stress that has been documented in other model systems. Fibroblasts from patients with PARK2, PARK6, idiopathic Parkinson's disease, Alzheimer's disease, and spinocerebellar ataxia type 2 demonstrated a distinct and unique mRNA expression pattern of key genes in neurodegeneration. Thus, primary skin fibroblasts are a useful Parkinson's disease model, able to serve as a complement to animal mutants, transformed cell lines and patient tissues