Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space

The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the stability of this statement for spaces that can be realized as graphical hypersurfaces in Euclidean space. We prove (under certain technical hypotheses) that if a sequence of complete asymptotically flat graphs of nonnegative scalar curvature has mass approaching zero, then the sequence must converge to Euclidean space in the pointed intrinsic flat sense. The appendix includes a new Gromov-Hausdorff and intrinsic flat compactness theorem for sequences of metric spaces with uniform Lipschitz bounds on their metrics.Comment: 31 pages, 2 figures, v2: to appear in Crelle's Journal, many minor changes, one new exampl

The Null distance encodes causality

A Lorentzian manifold endowed with a time function, $\tau$, can be converted into a metric space using the null distance, $\hat{d}_\tau$, defined by Sormani and Vega. We show that if the time function is a proper regular cosmological time function as studied by Andersson, Galloway and Howard, and also by Wald and Yip, or if, more generally, it satisfies the anti-Lipschitz condition of Chru\'sciel, Grant and Minguzzi, then the causal structure is encoded by the null distance in the following sense: $$\hat{d}_\tau(p,q)=\tau(q)-\tau(p) \iff q \textrm{ lies in the causal future of } p.$$ As a consequence, in dimension $n+1$, $n\ge 2$, we prove that if there is a bijective map between two such spacetimes, $F: M_1\to M_2$, which preserves the cosmological time function, $\tau_2(F(p))= \tau_1(p)$ for any $p \in M_1$, and preserves the null distance, $\hat{d}_{\tau_2}(F(p),F(q))=\hat{d}_{\tau_1}(p,q)$ for any $p,q\in M_1$, then there is a Lorentzian isometry between them, $F_*g_1=g_2$. This yields a canonical procedure allowing us to convert such spacetimes into unique metric spaces with causal structures and time functions. This will be applied in our upcoming work to define Spacetime Intrinsic Flat Convergence.Comment: 24 pages, 4 figure

Candidate Binding Sites for Allosteric Inhibition of the SARS-CoV-2 Main Protease from the Analysis of Large-Scale Molecular Dynamics Simulations

We analyzed a 100 μs MD trajectory of the SARS-CoV-2 main protease by a non-parametric data analysis approach which allows characterizing a free energy landscape as a simultaneous function of hundreds of variables. We identified several conformations that, when visited by the dynamics, are stable for several hundred nanoseconds. We explicitly characterize and describe these metastable states. In some of these configurations, the catalytic dyad is less accessible. Stabilizing them by a suitable binder could lead to an inhibition of the enzymatic activity. In our analysis we keep track of relevant contacts between residues which are selectively broken or formed in the states. Some of these contacts are formed by residues which are far from the catalytic dyad and are accessible to the solvent. Based on this analysis we propose some relevant contact patterns and three possible binding sites which could be targeted to achieve allosteric inhibition

Defining responders to therapies by a statistical modeling approach applied to randomized clinical trial data

Background: Personalized medicine is the tailoring of treatment to the individual characteristics of patients. Once a treatment has been tested in a clinical trial and its effect overall quantified, it would be of great value to be able to use the baseline patients' characteristics to identify patients with larger/lower benefits from treatment, for a more personalized approach to therapy. Methods: We show here a previously published statistical method, aimed at identifying patients' profiles associated to larger treatment benefits applied to three identical randomized clinical trials in multiple sclerosis, testing laquinimod vs placebo (ALLEGRO, BRAVO, and CONCERTO). We identified on the ALLEGRO patients' specific linear combinations of baseline variables, predicting heterogeneous response to treatment on disability progression. We choose the best score on the BRAVO, based on its ability to identify responders to treatment in this dataset. We finally got an external validation on the CONCERTO, testing on this new dataset the performance of the score in defining responders and non-responders. Results: The best response score defined on the ALLEGRO and the BRAVO was a linear combination of age, sex, previous relapses, brain volume, and MRI lesion activity. Splitting patients into responders and non-responders according to the score distribution, in the ALLEGRO, the hazard ratio (HR) for disability progression of laquinimod vs placebo was 0.38 for responders, HR = 1.31 for non-responders (interaction p = 0.0007). In the BRAVO, we had similar results: HR = 0.40 for responders and HR = 1.24 for non-responders (interaction p = 0.006). These findings were successfully replicated in the CONCERTO study, with HR = 0.44 for responders and HR=1.08 for non-responders (interaction p = 0.033). Conclusions: This study demonstrates the possibility to refine and personalize the treatment effect estimated in randomized studies by using the baseline demographic and clinical characteristics of the included patients. The method can be applied to any randomized trial in any medical condition to create a treatment-specific score associated to different levels of response to the treatment tested in the trial. This is an easy and affordable method toward therapy personalization, indicating patient profiles related to a larger benefit from a specific drug, which may have implications for taking clinical decisions in everyday clinical practice

Jeans modelling of the Milky Way's nuclear stellar disc

The nuclear stellar disc (NSD) is a flattened stellar structure that dominates the gravitational potential of the Milky Way at Galactocentric radii 30≲R≲300pc⁠. In this paper, we construct axisymmetric Jeans dynamical models of the NSD based on previous photometric studies and we fit them to line-of-sight kinematic data of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and silicon monoxide (SiO) maser stars. We find that (i) the NSD mass is lower but consistent with the mass independently determined from photometry by Launhardt et al. Our fiducial model has a mass contained within spherical radius r=100pc of M(r 1. Observations and theoretical models of the star-forming molecular gas in the central molecular zone suggest that large vertical oscillations may be already imprinted at stellar birth. However, the finding σz/σR > 1 depends on a drop in the velocity dispersion in the innermost few tens of parsecs, on our assumption that the NSD is axisymmetric, and that the available (extinction corrected) stellar samples broadly trace the underlying light and mass distributions, all of which need to be established by future observations and/or modelling. (iii) We provide the most accurate rotation curve to date for the innermost 500pc of our Galaxy

Cerebellar volume as imaging outcome in progressive multiple sclerosis

Background and purpose: To assess whether cerebellar volumes changes could represent a sensitive outcome measure in primary-progressive MS. Material and methods: Changes in cerebellar volumes over one-year follow-up, estimated in 26 primary-progressive MS patients and 20 controls with Freesurfer longitudinal pipeline, were assessed using Wilcoxon test and tested for their correlation with disability worsening by a logistic regression. Clinical worsening was defined as EDSS score increase or change of >20% for 25-foot walk test or 9-hole peg test scores at follow-up. Sample sizes for given treatment effects and power were calculated. The findings were validated in an independent cohort of 20 primary-progressive MS patients. Results: Significant changes were detected in brain T1 lesion volume (p<0.01), cerebellar T2 and T1 lesion volume (p<0.01 and p<0.05), cerebellar volume, cerebellar cortex volume, and cerebellar WM volume (p<0.001). Only cerebellar volume and cerebellar cortex volume percentage change were significantly reduced in clinically progressed patients when compared to patients who did not progress (p<0.01; respectively AUC of 0.91 and 0.96). Cerebellar volume percentage changes were consistent in the exploration and validation cohorts (cerebellar volume -1.90±1.11% vs -1.47±2.30%; cerebellar cortex volume -1.68±1.41% vs -1.56±2.23%). Based on our results the numbers of patients required to detect a 30% effect are 81 per arm for cerebellar volume and 162 per arm for cerebellar cortex volume (90% power, type 1 error alpha = 0.05). Conclusions: Our results suggest a role for cerebellar cortex volume and cerebellar volume as potential short-term imaging metrics to monitor treatment effect in primary-progressive MS clinical trials

Brain health: time matters in multiple sclerosis

publisher: Elsevier articletitle: Brain health: time matters in multiple sclerosis journaltitle: Multiple Sclerosis and Related Disorders articlelink: http://dx.doi.org/10.1016/j.msard.2016.07.003 content_type: article copyright: © 2016 Oxford PharmaGenesis Ltd. Published by Elsevier B.V

Blood neurofilament light as a potential endpoint in Phase 2 studies in MS

Objectives To assess whether neurofilament light chain (NfL) could serve as an informative endpoint in Phase 2 studies in patients with relapsing-remitting multiple sclerosis (RRMS) and estimate the sample size requirements with NfL as the primary endpoint. Methods Using data from the Phase 3 FREEDOMS study, we evaluated correlation of NfL at Month 6 with 2-year outcomes: relapses, confirmed disability worsening (CDW), new or enlarging T2 lesions (active lesions), and brain volume loss (BVL). We compared the proportion of treatment effect (PTE) on 2-year relapses and BVL explained by 6-month log-transformed NfL levels with the PTE explained by the number of active lesions over 6 months. We estimated sample size requirements for different treatment effects. Results At Month 6, blood NfL levels (pg/mL, median [range]) were lower in the fingolimod arm (fingolimod (n = 132) 18 [8-247]; placebo (n = 114) 26 [8-159], P < 0.001). NfL at 6 months correlated with number of relapses (r = 0.25, P < 0.001), 6-month CDW (hazard ratio 1.83, P = 0.012), active lesions (r = 0.46, P < 0.001), and BVL (r = -0.41, P < 0.001) at Month-24. The PTE (95% CI) on 24-month relapses and BVL explained by 6-month NfL was 25% (8-60%) and 60% (32-132%), and by 6-month active lesions was 28% (11-66%) and 45% (18-115%), respectively. Assuming a 20-40% treatment-related reduction in NfL levels, 143-28 patients per arm will be required. Conclusions Blood NfL may qualify as an informative and easy-to-measure endpoint for future Phase 2 clinical studies that captures both inflammatory- and noninflammatory-driven neuroaxonal injury in RRMS

Learning ability correlates with brain atrophy and disability progression in RRMS

Objective To assess the prognostic value of practice effect on Paced Auditory Serial Addition Test (PASAT) in multiple sclerosis. Methods We compared screening (day a '14) and baseline (day 0) PASAT scores of 1009 patients from the FTY720 Research Evaluating Effects of Daily Oral therapy in Multiple Sclerosis (FREEDOMS) trial. We grouped patients into high and low learners if their PASAT score change was above or below the median change in their screening PASAT quartile group. We used Wilcoxon test to compare baseline disease characteristics between high and low learners, and multiple regression models to assess the respective impact of learning ability, baseline normalised brain volume and treatment on brain volume loss and 6-month confirmed disability progression over 2 years. Results The mean PASAT score at screening was 45.38, increasing on average by 3.18 from day a '14 to day 0. High learners were younger (p=0.003), had lower Expanded Disability Status Scale score (p=0.031), higher brain volume (p<0.001) and lower T2 lesion volume (p=0.009) at baseline. Learning status was not significantly associated with disability progression (HR=0.953, p=0.779), when adjusting for baseline normalised brain volume, screening PASAT score and treatment arm. However, the effect of fingolimod on disability progression was more pronounced in high learners (HR=0.396, p<0.001) than in low learners (HR=0.798, p=0.351; p for interaction=0.05). Brain volume loss at month 24 tended to be higher in low learners (0.17%, p=0.058), after adjusting for the same covariates. Conclusions Short-term practice effects on PASAT are related to brain volume, disease severity and age and have clinically meaningful prognostic implications. High learners benefited more from fingolimod treatment