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

Long-term impact of maternal high-fat diet on offspring cardiac health: role of micro-RNA biogenesis.

Heart failure is a worldwide leading cause of death. Diet and obesity are particularly of high concern in heart disease etiology. Gravely, altered nutrition during developmental windows of vulnerability can have long-term impact on heart health; however, the underlying mechanisms are poorly understood. In the understanding of the initiation of chronic diseases related to developmental exposure to environmental challenges, deregulations in epigenetic mechanisms including micro-RNAs have been proposed as key events. In this context, we aimed at delineating the role of micro-RNAs in the programming of cardiac alterations induced by early developmental exposure to nutritional imbalance. To reach our aim, we developed a human relevant model of developmental exposure to nutritional imbalance by maternally exposing rat to high-fat diet during gestation and lactation. In this model, offspring exposed to maternal high-fat diet developed cardiac hypertrophy and increased extracellular matrix depot compared to those exposed to chow diet. Microarray approach performed on cardiac tissue allowed the identification of a micro-RNA subset which was down-regulated in high-fat diet-exposed animals and which were predicted to regulate transforming growth factor-beta (TGFβ)-mediated remodeling. As indicated by in vitro approaches and gene expression measurement in the heart of our animals, decrease in DiGeorge critical region 8 (DGCR8) expression, involved in micro-RNA biogenesis, seems to be a critical point in the alterations of the micro-RNA profile and the TGFβ-mediated remodeling induced by maternal exposure to high-fat diet. Finally, increasing DGCR8 activity and/or expression through hemin treatment in vitro revealed its potential in the rescue of the pro-fibrotic phenotype in cardiomyocytes driven by DGCR8 decrease. These findings suggest that cardiac alterations induced by maternal exposure to high-fat diet is related to abnormalities in TGFβ pathway and associated with down-regulated micro-RNA processing. Our study highlighted DGCR8 as a potential therapeutic target for heart diseases related to early exposure to dietary challenge

Acyl-Imidazoles A Privileged Ester Surrogate for Enantioselective Synthesis

International audienceSince the first report by Evans in asymmetric Friedel‐Crafts reactions, the use of acyl‐imidazoles has blossomed as powerful ester/amide surrogates. The imidazole scaffold indeed displays stability and special activation features allowing both better reactivity and selectivity in traditional ester/amide functionalizations: α‐(enolate chemistry), β‐(conjugate additions), α,β‐(cycloadditions) or γ/δ‐(vinylogous). An overview of the contemporary and growing interest in acyl‐imidazoles in metal‐ and organo‐catalyzed transformations (bio‐hybrid catalytic systems will be fully described in a back‐to‐back Minireview) will be highlighted. Moreover, post‐functionalization expediencies are also going to be discussed in this Minireview

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

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

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