A universal differentiability set in Banach spaces with separable dual

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fr\'echet differentiable somewhere in S.Comment: 41 pages, 1 figur

Universal Fréchet sets in Banach spaces

We define a universal Fréchet set S of a Banach space Y as a subset containing a point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a sufficient condition for S to be a universal Fréchet set and use this to construct new examples of such sets. The strongest such result says that in a non-zero Banach space Y with separable dual one can find a universal Fréchet set S ⊆ Y that is closed, bounded and has Hausdorff dimension one

Highly chemoselective formation of aldehyde enamines under very mild reaction conditions

Abstract: Although ketone enamines are widely used in organic synthesis, aldehyde enamines are rarely employed due to the limitations of their preparation using known methods (need for acid or base, excess of amine, and/or elevated temperature). We have successfully developed rapid and particularly mild condensation conditions (1 h, 0 °C, 1.2 equiv of amine) leading to di- and trisubstituted enamines with excellent conversion (84−100%). Remarkably high chemoselectivity was observed with complete discrimination between aldehyde and ketone, among other functional groups positively tested

Safety and efficacy of belimumab after B cell depletion therapy in systemic LUPUS erythematosus (BEAT-LUPUS) trial: statistical analysis plan.

BACKGROUND: There is limited evidence that rituximab, a B cell depletion therapy, is an effective treatment for systemic lupus erythematosus (SLE). Data on the mechanisms of B cell depletion in SLE indicate that the combination of rituximab and belimumab may be more effective than rituximab alone. The safety and efficacy of belimumab after B cell depletion therapy in systemic LUPUS erythematosus (BEAT-LUPUS) trial aims to determine whether belimumab is superior to placebo, when given 4-8 weeks after treatment with rituximab. This article describes the statistical analysis plan for this trial as an update to the published protocol. It is written prior to the end of patient follow-up, while the outcome of the trial is still unknown. DESIGN AND METHODS: BEAT-LUPUS is a randomised, double-blind, phase II trial of 52 weeks of belimumab versus placebo, initiated 4-8 weeks after rituximab treatment. The primary outcome is anti-dsDNA antibodies at 52 weeks post randomisation. Secondary outcomes include lupus flares and damage, adverse events, doses of concomitant medications, quality of life, and clinical biomarkers. We describe the trial's clinical context, outcome measures, sample size calculation, and statistical modelling strategy, and the supportive analyses planned to evaluate for mediation of the treatment effect through changes in concomitant medication doses and bias from missing data. DISCUSSION: The analysis will provide detailed information on the safety and effectiveness of belimumab. It will be implemented from July 2020 when patient follow-up and data collection is complete. TRIAL REGISTRATION: ISRCTN: 47873003 . Registered on 28 November 2016. EudracT: 2015-005543-14 . Registered on 19 November 2018

Multi-component Decomposition of Cosmic Infrared Background Fluctuations

The near-infrared background between 0.5 and 2 μm contains a wealth of information related to radiative processes in the universe. Infrared background anisotropies encode the redshift-weighted total emission over cosmic history, including any spatially diffuse and extended contributions. The anisotropy power spectrum is dominated by undetected galaxies at small angular scales and a diffuse background of Galactic emission at large angular scales. In addition to these known sources, the infrared background also arises from intrahalo light (IHL) at z < 3 associated with tidally stripped stars during galaxy mergers. Moreover, it contains information on the very first galaxies from the epoch of reionization (EoR). The EoR signal has a spectral energy distribution (SED) that goes to zero near optical wavelengths due to Lyman absorption, while other signals have spectra that vary smoothly with frequency. Due to differences in SEDs and spatial clustering, these components may be separated in a multi-wavelength-fluctuation experiment. To study the extent to which EoR fluctuations can be separated in the presence of IHL, and extragalactic and Galactic foregrounds, we develop a maximum likelihood technique that incorporates a full covariance matrix among all the frequencies at different angular scales. We apply this technique to simulated deep imaging data over a 2 × 45 deg^2 sky area from 0.75 to 5 μm in 9 bands and find that such a "frequency tomography" can successfully reconstruct both the amplitude and spectral shape for representative EoR, IHL, and the foreground signals

Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)

The Subaru Prime Focus Spectrograph (PFS) is a massively-multiplexed fiber-fed optical and near-infrared 3-arm spectrograph (N_fiber=2400, 380<lambda<1260nm, 1.3 degree diameter FoV), offering unique opportunities in survey astronomy. Here we summarize the science case feasible for a survey of Subaru 300 nights. We describe plans to constrain the nature of dark energy via a survey of emission line galaxies spanning a comoving volume of 9.3 (Gpc/h)^3 in the redshift range 0.8<z<2.4. In each of 6 redshift bins, the cosmological distances will be measured to 3% precision via BAO, and redshift-space distortions will be used to constrain structure growth to 6% precision. In the GA program, radial velocities and chemical abundances of stars in the Milky Way and M31 will be used to infer the past assembly histories of spiral galaxies and the structure of their dark matter halos. Data will be secured for 10^6 stars in the Galactic thick-disk, halo and tidal streams as faint as V~22, including stars with V < 20 to complement the goals of the Gaia mission. A medium-resolution mode with R = 5000 to be implemented in the red arm will allow the measurement of multiple alpha-element abundances and more precise velocities for Galactic stars, elucidating the detailed chemo-dynamical structure and evolution of each of the main stellar components of the Milky Way Galaxy and of its dwarf spheroidal galaxies. For the extragalactic program, our simulations suggest the wide avelength range will be powerful in probing the galaxy population and its clustering over a wide redshift range. We propose to conduct a color-selected survey of 1<z<2 galaxies and AGN over 16 deg^2 to J~23.4, yielding a fair sample of galaxies with stellar masses above ~10^{10}Ms at z~2. A two-tiered survey of higher redshift LBGs and LAEs will quantify the properties of early systems close to the reionization epoch.Comment: This document describes the scientific program and requirements for the Subaru Prime Focus Spectrograph (PFS) project. Made significant revision based on studies for the Preliminary Design Review (PRD) held in Feb 2013. The higher-resolution paper file is available from http://member.ipmu.jp/masahiro.takada/pfs_astroph_rv.pd

Science Impacts of the SPHEREx All-Sky Optical to Near-Infrared Spectral Survey II: Report of a Community Workshop on the Scientific Synergies Between the SPHEREx Survey and Other Astronomy Observatories

SPHEREx is a proposed NASA MIDEX mission selected for Phase A study. SPHEREx would carry out the first all-sky spectral survey in the near infrared. At the end of its two-year mission, SPHEREx would obtain 0.75-to-5μm spectra of every 6.2 arcsec pixel on the sky, with spectral resolution R>35 and a 5-σ sensitivity AB>19 per spectral/spatial resolution element. More details concerning SPHEREx are available at http://spherex.caltech.edu. The SPHEREx team has proposed three specific science investigations to be carried out with this unique data set: cosmic inflation, interstellar and circumstellar ices, and the extra-galactic background light. Though these three themes are undoubtedly compelling, they are far from exhausting the scientific output of SPHEREx. Indeed, SPHEREx would create a unique all-sky spectral database including spectra of very large numbers of astronomical and solar system targets, including both extended and diffuse sources. These spectra would enable a wide variety of investigations, and the SPHEREx team is dedicated to making the data available to the community to enable these investigations, which we refer to as Legacy Science. To that end, we have sponsored two workshops for the general scientific community to identify the most interesting Legacy Science themes and to ensure that the SPHEREx data products are responsive to their needs. In February of 2016, some 50 scientists from all fields met in Pasadena to develop these themes and to understand their implications for the SPHEREx mission. The 2016 workshop highlighted many synergies between SPHEREx and other contemporaneous astronomical missions, facilities, and databases. Consequently, in January 2018 we convened a second workshop at the Center for Astrophysics in Cambridge to focus specifically on these synergies. This white paper reports on the results of the 2018 SPHEREx workshop