Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

DNA-Based Asymmetric Inverse Electron-Demand Hetero-Diels-Alder

International audienceWhile artificial cyclases hold great promise in chemical synthesis, this work presents the first example of a DNA-catalyzed inverse electron-demand hetero-Diels-Alder (IEDHDA) between dihydrofuran and various α,β-unsaturated acyl imidazoles. The resulting fused bicyclic O,O-acetals containing three contiguous stereogenic centers are obtained in high yields (up to 99 %) and excellent diastereo- (up to >99:1 dr) and enantioselectivities (up to 95 % ee) using a low catalyst loading. Most importantly, these results show that the concept of DNA-based asymmetric catalysis can be expanded to new synthetic transformations offering an efficient, sustainable, and highly selective tool for the construction of chiral building blocks

The universal distribution of halo interlopers in projected phase space. Bias in galaxy cluster concentration and velocity anisotropy?

When clusters of galaxies are viewed in projection, one cannot avoid picking up foreground/background interlopers (FBIs), that lie within the virial cone (VC), but outside the virial sphere. Structural & kinematic deprojection equations are not known for an expanding Universe, where the Hubble flow (HF) stretches the line-of-sight (LOS) distribution of velocities. We analyze 93 mock relaxed clusters, built from a cosmological simulation. The stacked mock cluster is well fit by an m=5 Einasto DM density profile (but only out to 1.5 virial radii [r_v]), with velocity anisotropy (VA) close to the Mamon-Lokas model with VA radius equal to that of density slope -2. The surface density of FBIs is nearly flat out to r_v, while their LOS velocity distribution shows a dominant gaussian cluster-outskirts component and a flat field component. This distribution of FBIs in projected phase space is nearly universal in mass. A local k=2.7 sigma velocity cut returns the LOS velocity dispersion profile (LOSVDP) expected from the NFW density and VA profiles measured in 3D. The HF causes a shallower outer LOSVDP that cannot be well matched by the Einasto model for any k. After this velocity cut, FBIs still account for 23% of DM particles within the VC (close to the observed fraction of cluster galaxies lying off the Red Sequence). The best-fit projected NFW/Einasto models underestimate the 3D concentration by 6+/-6% (16+/-7%) after (before) the velocity cut, unless a constant background is included in the fit. Assuming the correct mass profile, the VA profile is well recovered from the measured LOSVDP, with a slight bias towards more radial orbits in the outer regions. These small biases are overshadowed by large cluster-cluster variations caused by cosmic variance. An appendix provides an analytical approximation to the surface density, projected mass and tangential shear profiles of the Einasto model.Comment: Version published in A&A, 23 pages, 22 figure

The Spitzer Extragalactic Representative Volume Survey (SERVS): The Environments of High-z SDSS Quasi-Stellar-Objects

This paper presents a study of the environments of SDSS Quasi-Stellar-Objects (QSOs) in the Spitzer Extragalactic Representative Volume Survey (SERVS). We concentrate on the high-redshift QSOs as these have not been studied in large numbers with data of this depth before. We use the IRAC 3.6-4.5{\mu}m colour of objects and ancillary r-band data to filter out as much foreground contamination as possible. This technique allows us to find a significant (> 4-{\sigma}) over-density of galaxies around QSOs in a redshift bin centred on z ~ 2.0 and a (> 2-{\sigma}) over-density of galaxies around QSOs in a redshift bin centred on z ~ 3.3. We compare our findings to the predictions of a semi-analytic galaxy formation model, based on the {\Lambda}CDM millennium simulation, and find for both redshift bins that the model predictions match well the source-density we have measured from the SERVS data.Comment: 13 pages, 12 figures, Accepted by Ap

Protective CD8+ T lymphocytes in Primates Immunized with Malaria Sporozoites

Live attenuated malaria vaccines are more potent than the recombinant protein, bacterial or viral platform vaccines that have been tested, and an attenuated sporozoite vaccine against falciparum malaria is being developed for humans. In mice, attenuated malaria sporozoite vaccines induce CD8+ T cells that kill parasites developing in the liver. We were curious to know if CD8+ T cells were also important in protecting primates against malaria. We immunized 9 rhesus monkeys with radiation attenuated Plasmodium knowlesi sporozoites, and found that 5 did not develop blood stage infections after challenge with live sporozoites. We then injected 4 of these protected monkeys with cM-T807, a monoclonal antibody to the CD8 molecule which depletes T cells. The fifth monkey received equivalent doses of normal IgG. In 3 of the 4 monkeys receiving cM-T807 circulating CD8+ T cells were profoundly depleted. When re-challenged with live sporozoites all 3 of these depleted animals developed blood stage malaria. The fourth monkey receiving cM-T807 retained many circulating CD8+ T cells. This monkey, and the vaccinated monkey receiving normal IgG, did not develop blood stage malaria at re-challenge with live sporozoites. Animals were treated with antimalarial drugs and rested for 4 months. During this interval CD8+ T cells re-appeared in the circulation of the depleted monkeys. When all vaccinated animals received a third challenge with live sporozoites, all 5 monkeys were once again protected and did not develop blood stage malaria infections. These data indicate that CD8+ T cells are important effector cells protecting monkeys against malaria sporozoite infection. We believe that malaria vaccines which induce effector CD8+ T cells in humans will have the best chance of protecting against malaria

Suppressed radio emission in supercluster galaxies: enhanced ram pressure in merging clusters?

The environmental influence on the 1.4 GHz continuum radio emission of galaxies is analyzed in a 600 deg2 region of the local Universe containing the Shapley Supercluster (SSC). Galaxies in the FLASH and 6dFGS redshift surveys are cross-identified with NVSS radio sources, selected in a subsample doubly complete in volume and luminosity. Environmental effects are studied through a smoothed density field (normalized with random catalogs with the same survey edges and redshift selection function) and the distance to the nearest cluster (R/r200, where r200 is the virial radius, whose relation to the aperture velocity dispersion is quantified). The fraction of high radio loudness (R_K=L_radio/L_K) galaxies in the 10 Mpc Abell 3558 cluster complex at the core of the SSC (SSC-CR) is half as large than elsewhere. In the SSC-CR, R_K is anti-correlated with the density of the large-scale environment and correlated with R/r200: central brightest cluster galaxies (BCGs) in the SSC-CR are 10x less radio-loud than BCGs elsewhere, with signs of suppressed radio loudness in the SSC-CR also present beyond the BCGs, out to at least 0.3 r200. This correlation is nearly as strong as the tight correlation of L_K with R/r200 (K-luminosity segregation), inside the SSC-CR. The suppression of radio loudness in SSC-CR BCGs can be attributed to cluster-cluster mergers that destroy the cool core and thus the supply of gas to the central AGN. We analytically demonstrate that the low radio loudness of non-BCG galaxies within SSC-CR clusters cannot be explained by direct major galaxy mergers or rapid galaxy flyby collisions, but by the loss of gas supply through the enhanced ram pressure felt when these galaxies cross the shock front between the 2 merging clusters and are later subjected to the stronger wind from the 2nd cluster.Comment: Version consolidated with Erratum A&A 499, 4

NEOWISE Observations of Near-Earth Objects: Preliminary Results

With the NEOWISE portion of the \emph{Wide-field Infrared Survey Explorer} (WISE) project, we have carried out a highly uniform survey of the near-Earth object (NEO) population at thermal infrared wavelengths ranging from 3 to 22 $\mu$m, allowing us to refine estimates of their numbers, sizes, and albedos. The NEOWISE survey detected NEOs the same way whether they were previously known or not, subject to the availability of ground-based follow-up observations, resulting in the discovery of more than 130 new NEOs. The survey's uniformity in sensitivity, observing cadence, and image quality have permitted extrapolation of the 428 near-Earth asteroids (NEAs) detected by NEOWISE during the fully cryogenic portion of the WISE mission to the larger population. We find that there are 981$\pm$19 NEAs larger than 1 km and 20,500$\pm$3000 NEAs larger than 100 m. We show that the Spaceguard goal of detecting 90% of all 1 km NEAs has been met, and that the cumulative size distribution is best represented by a broken power law with a slope of 1.32$\pm$0.14 below 1.5 km. This power law slope produces $\sim13,200\pm$1,900 NEAs with $D>$140 m. Although previous studies predict another break in the cumulative size distribution below $D\sim$50-100 m, resulting in an increase in the number of NEOs in this size range and smaller, we did not detect enough objects to comment on this increase. The overall number for the NEA population between 100-1000 m are lower than previous estimates. The numbers of near-Earth comets will be the subject of future work.Comment: Accepted to Ap

The velocity modulation of galaxy properties in and near clusters: quantifying the decrease in star formation in backsplash galaxies

The efficiency of recent star formation (SF) in galaxies increases with increasing projected distance from the centre of a cluster out to several times its virial radius (R_v). Using a complete sample of galaxies in 268 clusters from the SDSS DR4, we investigate how, at a given projected radius from the cluster centre, M* and SF properties of a galaxy depend on its absolute line-of-sight velocity in the cluster rest frame, |v_LOS|. We find that for R<0.5 R_v, the fraction of high mass non-BCG galaxies increases towards the centre for low |v_LOS|. At a given projected radius, the fraction of Galaxies with Ongoing or Recent (<1-3 Gyr) Efficient Star Formation (GORES, with EW(H_delta)>2 ang & D_4000>1.5) is slightly but significantly lower for low |v_LOS| galaxies than for their high velocity counterparts. We study these observational trends with the help of a dark matter (DM) cosmological simulation. We find that the backsplash particles account for at least one-third (half) of all particles at projected radii slightly greater than the virial radius and |v_LOS|<sigma_v. The deprojection of the GORES fraction leads to a saturated linear increase with radius. We fit simple models of the fraction of GORES as a function of class only or class and distance to the cluster centre (as in our deprojected fraction). In our best-fitting model GORES account for 13% of galaxies within the virial sphere, 11% of the virial population, 34% of the distant (for projected radii R<2 R_v) infall population and 19% of the backsplash galaxies. Given the 1-3 Gyr lookback time of our GORES indicators, these results suggest that SF in a galaxy is almost completely quenched in a single passage through the cluster.Comment: 22 pages, 17 figures, MNRAS, 416, 2882, Labels for Figure 14 revise

The Spitzer Extragalactic Representative Volume Survey (SERVS): Survey Definition and Goals

We present the Spitzer Extragalactic Representative Volume Survey (SERVS), an 18 deg^2 medium-deep survey at 3.6 and 4.5 μm with the postcryogenic Spitzer Space Telescope to ≈2 μJy (AB = 23.1) depth of five highly observed astronomical fields (ELAIS-N1, ELAIS-S1, Lockman Hole, Chandra Deep Field South, and XMM-LSS). SERVS is designed to enable the study of galaxy evolution as a function of environment from z ∼ 5 to the present day and is the first extragalactic survey that is both large enough and deep enough to put rare objects such as luminous quasars and galaxy clusters at z ≳ 1 into their cosmological context. SERVS is designed to overlap with several key surveys at optical, near- through far-infrared, submillimeter, and radio wavelengths to provide an unprecedented view of the formation and evolution of massive galaxies. In this article, we discuss the SERVS survey design, the data processing flow from image reduction and mosaicking to catalogs, and coverage of ancillary data from other surveys in the SERVS fields. We also highlight a variety of early science results from the survey