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

In vivo stem cell tracking using scintigraphy in a canine model of DMD

One of the main challenges in cell therapy for muscle diseases is to efficiently target the muscle. To address this issue and achieve better understanding of in vivo cell fate, we evaluated the relevance of a non-invasive cell tracking method in the Golden Retriever Muscular Dystrophy (GRMD) model, a well-recognised model of Duchenne Muscular Dystrophy (DMD). Mesoangioblasts were directly labelled with 111In-oxine, and injected through one of the femoral arteries. The scintigraphy images obtained provided the first quantitative mapping of the immediate biodistribution of mesoangioblasts in a large animal model of DMD. The results revealed that cells were trapped by the first capillary filters: the injected limb and the lung. During the days following injection, radioactivity was redistributed to the liver. In vitro studies, performed with the same cells prepared for injecting the animal, revealed prominent cell death and 111In release. In vivo, cell death resulted in 111In release into the vasculature that was taken up by the liver, resulting in a non-specific and non-cell-bound radioactive signal. Indirect labelling methods would be an attractive alternative to track cells on the mid- and long-term

Warm, but not hypoxic acclimation, prolongs ventricular diastole and decreases the protein level of Na+/Ca2+exchanger to enhance cardiac thermal tolerance in European sea bass

One of the physiological mechanisms that can limit the fish's ability to face hypoxia or elevated temperature, is maximal cardiac performance. Yet, few studies have measured how cardiac electrical activity and associated calcium cycling proteins change with acclimation to those environmental stressors. To examine this, we acclimated European sea bass for 6 weeks to three experimental conditions: a seasonal average temperature in normoxia (16 °C; 100% air sat.), an elevated temperature in normoxia (25 °C; 100% air sat.) and a seasonal average temperature in hypoxia (16 °C; 50% air sat.). Following each acclimation, the electrocardiogram was measured to assess how acclimation affected the different phases of cardiac cycle, the maximal heart rate (fHmax) and cardiac thermal performance during an acute increase of temperature. Whereas warm acclimation prolonged especially the diastolic phase of the ventricular contraction, reduced the fHmax and increased the cardiac arrhythmia temperature (TARR), hypoxic acclimation was without effect on these functional indices. We measured the level of two key proteins involved with cellular relaxation of cardiomyocytes, i.e. sarco(endo)plasmic reticulum Ca2+-ATPase (SERCA) and Na+/Ca2+ exchanger (NCX). Warm acclimation reduced protein level of both NCX and SERCA and hypoxic acclimation reduced SERCA protein levels without affecting NCX. The changes in ventricular NCX level correlated with the observed changes in diastole duration and fHmax as well as TARR. Our results shed new light on mechanisms of cardiac plasticity to environmental stressors and suggest that NCX might be involved with the observed functional changes, yet future studies should also measure its electrophysiological activity.</p

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

Leukemia Inhibitory Factor Is a Key Signal for Injury-Induced Neurogenesis in the Adult Mouse Olfactory Epithelium

The mammalian olfactory epithelium (OE) is composed of primary olfactory sensory neurons (OSNs) that are renewed throughout adulthood by local, restricted neuronal progenitor cells. The molecular signals that control this neurogenesis in vivo are unknown. Using olfactory bulb ablation (OBX) in adult mice to trigger synchronous mitotic stimulation of neuronal progenitors in the OE, we show the in vivo involvement of a cytokine in the cellular events leading to the regeneration of the OE. We find that, of many potential mitogenic signals, only leukemia inhibitory factor (LIF) is induced before the onset of neuronal progenitor proliferation. The rise in LIF mRNA expression peaks at 8 hr after OBX, and in situ RT-PCR and immunocytochemistry indicate that LIF is upregulated, in part, in the injured neurons themselves. This rise in LIF is necessary for injury-induced neurogenesis, as OBX in the LIF knock-out mouse fails to stimulate cell proliferation in the OE. Moreover, delivery of exogenous LIF to the intact adult OE using an adenoviral vector stimulates BrdU labeling in the apical OE. Taken together, these results suggest that injured OSNs release LIF as a stimulus to initiate their own replacement

A mesenchymal to epithelial switch in Fgf10 expression specifies an evolutionary-conserved population of ionocytes in salivary glands

Fibroblast growth factor 10 (FGF10) is well established as a mesenchyme-derived growth factor and a critical regulator of fetal organ development in mice and humans. Using a single-cell RNA sequencing (RNA-seq) atlas of salivary gland (SG) and a tamoxifen inducible Fgf10CreERT2:R26-tdTomato mouse, we show that FGF10pos cells are exclusively mesenchymal until postnatal day 5 (P5) but, after P7, there is a switch in expression and only epithelial FGF10pos cells are observed after P15. Further RNA-seq analysis of sorted mesenchymal and epithelial FGF10pos cells shows that the epithelial FGF10pos population express the hall- marks of ancient ionocyte signature Forkhead box i1 and 2 (Foxi1, Foxi2), Achaete-scute homolog 3 (Ascl3), and the cystic fibrosis transmembrane conductance regulator (Cftr). We propose that epithelial FGF10pos cells are specialized SG ionocytes located in ducts and important for the ionic modification of saliva. In addition, they maintain FGF10-dependent gland homeostasis via communication with FGFR2bpos ductal and myoepithelial cells

A Role for Immune Responses against Non-CS Components in the Cross-Species Protection Induced by Immunization with Irradiated Malaria Sporozoites

Immunization with irradiated Plasmodium sporozoites induces sterile immunity in rodents, monkeys and humans. The major surface component of the sporozoite the circumsporozoite protein (CS) long considered as the antigen predominantly responsible for this immunity, thus remains the leading candidate antigen for vaccines targeting the parasite's pre-erythrocytic (PE) stages. However, this role for CS was questioned when we recently showed that immunization with irradiated sporozoites (IrrSpz) of a P. berghei line whose endogenous CS was replaced by that of P. falciparum still conferred sterile protection against challenge with wild type P. berghei sporozoites. In order to investigate the involvement of CS in the cross-species protection recently observed between the two rodent parasites P. berghei and P. yoelii, we adopted our gene replacement approach for the P. yoelii CS and exploited the ability to conduct reciprocal challenges. Overall, we found that immunization led to sterile immunity irrespective of the origin of the CS in the immunizing or challenge sporozoites. However, for some combinations, immune responses to CS contributed to the acquisition of protective immunity and were dependent on the immunizing IrrSpz dose. Nonetheless, when data from all the cross-species immunization/challenges were considered, the immune responses directed against non-CS parasite antigens shared by the two parasite species played a major role in the sterile protection induced by immunization with IrrSpz. This opens the perspective to develop a single vaccine formulation that could protect against multiple parasite species

Gaia Universe Model Snapshot : A statistical analysis of the expected contents of the Gaia catalogue

Context. This study has been developed in the framework of the computational simulations executed for the preparation of the ESA Gaia astrometric mission. Aims. We focus on describing the objects and characteristics that Gaia will potentially observe without taking into consideration instrumental effects (detection efficiency, observing errors). Methods. The theoretical Universe Model prepared for the Gaia simulation has been statistically analyzed at a given time. Ingredients of the model are described, giving most attention to the stellar content, the double and multiple stars, and variability. Results. In this simulation the errors have not been included yet. Hence we estimate the number of objects and their theoretical photometric, astrometric and spectroscopic characteristics in the case that they are perfectly detected. We show that Gaia will be able to potentially observe 1.1 billion of stars (single or part of multiple star systems) of which about 2% are variable stars, 3% have one or two exoplanets. At the extragalactic level, observations will be potentially composed by several millions of galaxies, half million to 1 million of quasars and about 50,000 supernovas that will occur during the 5 years of mission. The simulated catalogue will be made publicly available by the DPAC on the Gaia portal of the ESA web site http://www.rssd.esa.int/gaia/.Comment: 21 pages, 21 figures, accepted for publication in Astronomy and Astrophysics, typos corrected in author name