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

Evidence of a Cloud-Cloud Collision from Overshooting Gas in the Galactic Center

The Milky Way is a barred spiral galaxy with bar lanes that bring gas toward the Galactic center. Gas flowing along these bar lanes often overshoots, and instead of accreting onto the Central Molecular Zone (CMZ), it collides with the bar lane on the opposite side of the Galaxy. We observed G5, a cloud that we believe is the site of one such collision, near the Galactic center at (l, b) = (+5.4, −0.4) with the Atacama Large Millimeter/submillimeter Array/Atacama Compact Array. We took measurements of the spectral lines 12CO J = 2 → 1, 13CO J = 2 → 1, C18O J = 2 → 1, H2CO J = 303 → 202, H2CO J = 322 → 221, CH3OH J = 422 → 312, OCS J = 18 → 17, and SiO J = 5 → 4. We observed a velocity bridge between two clouds at ∼50 and ∼150 km s−1 in our position–velocity diagram, which is direct evidence of a cloud–cloud collision. We measured an average gas temperature of ∼60 K in G5 using H2CO integrated-intensity line ratios. We observed that the 12C/13C ratio in G5 is consistent with optically thin, or at most marginally optically thick 12CO. We measured 1.5 ́ 1019 cm-2 (K km s-1)-1 for the local XCO, 10–20× less than the average Galactic value. G5 is strong direct observational evidence of gas overshooting the CMZ and colliding with a bar lane on the opposite side of the Galactic center

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

Smooth kinematic and metallicity gradients reveal that the Milky Way's nuclear star cluster and disc might be part of the same structure

Context. The innermost regions of most galaxies are characterised by the presence of extremely dense nuclear star clusters. Nevertheless, these clusters are not the only stellar component present in galactic nuclei, where larger stellar structures known as nuclear stellar discs, have also been found. Understanding the relation between nuclear star clusters and nuclear stellar discs is challenging due to the large distance towards other galaxies which limits their analysis to integrated light. The Milky Way’s centre, at only ~8 kpc, hosts a nuclear star cluster and a nuclear stellar disc, constituting a unique template to understand their relation and formation scenario. Aims. We aim to study the kinematics and stellar metallicity of stars from the Milky Way’s nuclear star cluster and disc to shed light on the relation between these two Galactic centre components. Methods. We used publicly available photometric, proper motions, and spectroscopic catalogues to analyse a region of ~2.8′ × 4.9′ centred on the Milky Way’s nuclear star cluster. We built colour magnitude diagrams, and applied colour cuts to analyse the kinematic and metallicity distributions of Milky Way’s nuclear star cluster and disc stars with different extinction, along the line of sight. Results. We detect kinematic and metallicity gradients for the analysed stars along the line of sight towards the Milky Way’s nuclear star cluster, suggesting a smooth transition between the nuclear stellar disc and cluster.We also find a bi-modal metallicity distribution for all the analysed colour bins, which is compatible with previous work on the bulk population of the nuclear stellar disc and cluster. Our results suggest that these two Galactic centre components might be part of the same structure with the Milky Way’s nuclear stellar disc being the grown edge of the nuclear star cluster

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

ALMA Uncovers Highly Filamentary Structure toward the Sgr E Region

We report on the discovery of linear filaments observed in the CO(1-0) emission for a ∼2′ field of view toward the Sgr E star-forming region, centered at (l, b) = (358.°720, 0.°011). The Sgr E region is thought to be at the turbulent intersection of the “far dust lane” associated with the Galactic bar and the Central Molecular Zone (CMZ). This region is subject to strong accelerations, which are generally thought to inhibit star formation, yet Sgr E contains a large number of H ii regions. We present 12CO(1-0), 13CO(1-0), and C18O(1-0) spectral line observations from the Atacama Large Millimeter/submillimeter Array and provide measurements of the physical and kinematic properties for two of the brightest filaments. These filaments have widths (FWHMs) of ∼0.1 pc and are oriented nearly parallel to the Galactic plane, with angles from the Galactic plane of ∼2°. The filaments are elongated, with lower-limit aspect ratios of ∼5:1. For both filaments, we detect two distinct velocity components that are separated by about 15 km s−1. In the C18O spectral line data, with ∼0.09 pc spatial resolution, we find that these velocity components have relatively narrow (∼1-2 km s−1) FWHM line widths when compared to other sources toward the Galactic center. The properties of these filaments suggest that the gas in the Sgr E complex is being “stretched,” as it is rapidly accelerated by the gravitational field of the Galactic bar while falling toward the CMZ, a result that could provide insights into the extreme environment surrounding this region and the large-scale processes that fuel this environment