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

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

On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG

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

Subdominant/Cryptic CD8 T Cell Epitopes Contribute to Resistance against Experimental Infection with a Human Protozoan Parasite

During adaptive immune response, pathogen-specific CD8+ T cells recognize preferentially a small number of epitopes, a phenomenon known as immunodominance. Its biological implications during natural or vaccine-induced immune responses are still unclear. Earlier, we have shown that during experimental infection, the human intracellular pathogen Trypanosoma cruzi restricts the repertoire of CD8+ T cells generating strong immunodominance. We hypothesized that this phenomenon could be a mechanism used by the parasite to reduce the breath and magnitude of the immune response, favoring parasitism, and thus that artificially broadening the T cell repertoire could favor the host. Here, we confirmed our previous observation by showing that CD8+ T cells of H-2a infected mice recognized a single epitope of an immunodominant antigen of the trans-sialidase super-family. In sharp contrast, CD8+ T cells from mice immunized with recombinant genetic vaccines (plasmid DNA and adenovirus) expressing this same T. cruzi antigen recognized, in addition to the immunodominant epitope, two other subdominant epitopes. This unexpected observation allowed us to test the protective role of the immune response to subdominant epitopes. This was accomplished by genetic vaccination of mice with mutated genes that did not express a functional immunodominant epitope. We found that these mice developed immune responses directed solely to the subdominant/cryptic CD8 T cell epitopes and a significant degree of protective immunity against infection mediated by CD8+ T cells. We concluded that artificially broadening the T cell repertoire contributes to host resistance against infection, a finding that has implications for the host-parasite relationship and vaccine development

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

Inhibitory Effect of TNF-α on Malaria Pre-Erythrocytic Stage Development: Influence of Host Hepatocyte/Parasite Combinations

BACKGROUND: The liver stages of malaria parasites are inhibited by cytokines such as interferon-gamma or Interleukin (IL)-6. Binding of these cytokines to their receptors at the surface of the infected hepatocytes leads to the production of nitric oxide (NO) and radical oxygen intermediates (ROI), which kill hepatic parasites. However, conflicting results were obtained with TNF-alpha possibly because of differences in the models used. We have reassessed the role of TNF-alpha in the different cellular systems used to study the Plasmodium pre-erythrocytic stages. METHODS AND FINDINGS: Human or mouse TNF-alpha were tested against human and rodent malaria parasites grown in vitro in human or rodent primary hepatocytes, or in hepatoma cell lines. Our data demonstrated that TNF-alpha treatment prevents the development of malaria pre-erythrocytic stages. This inhibitory effect however varies with the infecting parasite species and with the nature and origin of the cytokine and hepatocytes. Inhibition was only observed for all parasite species tested when hepatocytes were pre-incubated 24 or 48 hrs before infection and activity was directed only against early hepatic parasite. We further showed that TNF-alpha inhibition was mediated by a soluble factor present in the supernatant of TNF-alpha stimulated hepatocytes but it was not related to NO or ROI. Treatment TNF-alpha prevents the development of human and rodent malaria pre-erythrocytic stages through the activity of a mediator that remains to be identified. CONCLUSIONS: Treatment TNF-alpha prevents the development of human and rodent malaria pre-erythrocytic stages through the activity of a mediator that remains to be identified. However, the nature of the cytokine-host cell-parasite combination must be carefully considered for extrapolation to the human infection

The Lockman Hole project: LOFAR observations and spectral index properties of low-frequency radio sources

The Lockman Hole is a well-studied extragalactic field with extensive multi-band ancillary data covering a wide range in frequency, essential for characterizing the physical and evolutionary properties of the various source populations detected in deep radio fields (mainly star-forming galaxies and AGNs). In this paper, we present new 150-MHz observations carried out with the LOw-Frequency ARray (LOFAR), allowing us to explore a new spectral window for the faint radio source population. This 150-MHz image covers an area of 34.7 square degrees with a resolution of 18.6 × 14.7 arcsec and reaches an rms of 160 μJy beam$^-1$ at the centre of the field. As expected for a low-frequency selected sample, the vast majority of sources exhibit steep spectra, with a median spectral index of $\alpha _{150}^{1400}=-0.78\pm 0.015$. The median spectral index becomes slightly flatter (increasing from $\alpha _{150}^{1400}=-0.75)$ with decreasing flux density down to S_1_5_0 ∼10 mJy before flattening out and remaining constant below this flux level. For a bright subset of the 150-MHz selected sample, we can trace the spectral properties down to lower frequencies using 60-MHz LOFAR observations, finding tentative evidence for sources to become flatter in spectrum between 60 and 150 MHz. Using the deep, multi-frequency data available in the Lockman Hole, we identify a sample of 100 ultra-steep-spectrum sources and 13 peaked-spectrum sources. We estimate that up to 21 per cent of these could have z > 4 and are candidate high-z radio galaxies, but further follow-up observations are required to confirm the physical nature of these objects

The evolution of the star formation activity per halo mass up to redshift ~ 1.6 as seen by Herschel

Star formation in massive galaxies is quenched at some point during hierarchical mass assembly. To understand where and when the quenching processes takes place, we study the evolution of the total star formation rate per unit total halo mass (\Sigma(SFR/M)) in three different mass scales: low mass halos (field galaxies), groups, and clusters, up to a redshift ~1.6. We use deep far-infrared PACS data at 100 and 160 um to accurately estimate the total star formation rate of the Luminous Infrared Galaxy population of 9 clusters with mass ~10^{15} M_{\odot}, and 9 groups/poor clusters with mass ~ 5 x 10^{13} M_{\odot}. Estimates of the field \Sigma(SFR/M) are derived from the literature, by dividing the star formation rate density by the mean comoving matter density of the universe. The field \Sigma(SFR/M) increases with redshift up to z~1 and it is constant thereafter. The evolution of the \Sigma(SFR/M)-z relation in galaxy systems is much faster than in the field. Up to redshift z~0.2, the field has a higher \Sigma(SFR/M) than galaxy groups and galaxy clusters. At higher redshifts, galaxy groups and the field have similar \Sigma(SFR/M), while massive clusters have significantly lower \Sigma(SFR/M) than both groups and the field. There is a hint of a reversal of the SFR activity vs. environment at z~1.6, where the group \Sigma(SFR/M) lies above the field \Sigma(SFR/M)-z relation. We discuss possible interpretations of our results in terms of the processes of downsizing, and star-formation quenching.Comment: 8 pages, 3 figures, accepted for publication on A&