The distribution of k-tuples of reduced residues

En 1940, Paul Erdős énonça une conjecture sur la distribution des classes inversibles modulo un entier. La présente thèse étudie la distribution des k-uplets de classes inversibles propose une preuve de la conjecture d'Erdős étendue au cas des k-uplets.

Irrégularités dans la distribution des nombres premiers et des suites plus générales dans les progressions arithmétiques

Le sujet principal de cette thèse est la distribution des nombres premiers dans les progressions arithmétiques, c'est-à-dire des nombres premiers de la forme $qn+a$, avec $a$ et $q$ des entiers fixés et $n=1,2,3,\dots$ La thèse porte aussi sur la comparaison de différentes suites arithmétiques par rapport à leur comportement dans les progressions arithmétiques. Elle est divisée en quatre chapitres et contient trois articles. Le premier chapitre est une invitation à la théorie analytique des nombres, suivie d'une revue des outils qui seront utilisés plus tard. Cette introduction comporte aussi certains résultats de recherche, que nous avons cru bon d'inclure au fil du texte. Le deuxième chapitre contient l'article \emph{Inequities in the Shanks-Rényi prime number race: an asymptotic formula for the densities}, qui est le fruit de recherche conjointe avec le professeur Greg Martin. Le but de cet article est d'étudier un phénomène appelé le <>, qui s'observe dans les <>. Chebyshev a observé qu'il semble y avoir plus de premiers de la forme $4n+3$ que de la forme $4n+1$. De manière plus générale, Rubinstein et Sarnak ont montré l'existence d'une quantité $\delta(q;a,b)$, qui désigne la probabilité d'avoir plus de premiers de la forme $qn+a$ que de la forme $qn+b$. Dans cet article nous prouvons une formule asymptotique pour $\delta(q;a,b)$ qui peut être d'un ordre de précision arbitraire (en terme de puissance négative de $q$). Nous présentons aussi des résultats numériques qui supportent nos formules. Le troisième chapitre contient l'article \emph{Residue classes containing an unexpected number of primes}. Le but est de fixer un entier $a\neq 0$ et ensuite d'étudier la répartition des premiers de la forme $qn+a$, en moyenne sur $q$. Nous montrons que l'entier $a$ fixé au départ a une grande influence sur cette répartition, et qu'il existe en fait certaines progressions arithmétiques contenant moins de premiers que d'autres. Ce phénomène est plutôt surprenant, compte tenu du théorème des premiers dans les progressions arithmétiques qui stipule que les premiers sont équidistribués dans les classes d'équivalence $\bmod q$. Le quatrième chapitre contient l'article \emph{The influence of the first term of an arithmetic progression}. Dans cet article on s'intéresse à des irrégularités similaires à celles observées au troisième chapitre, mais pour des suites arithmétiques plus générales. En effet, nous étudions des suites telles que les entiers s'exprimant comme la somme de deux carrés, les valeurs d'une forme quadratique binaire, les $k$-tuplets de premiers et les entiers sans petit facteur premier. Nous démontrons que dans chacun de ces exemples, ainsi que dans une grande classe de suites arithmétiques, il existe des irrégularités dans les progressions arithmétiques $a\bmod q$, avec $a$ fixé et en moyenne sur $q$.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Remarks on the classification of a pair of commuting semilinear operators

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

Regulation of pyridoxal $5\prime$-phosphate biosynthesis in {\it Escherichia coli\/} K-12

Vitamin B$\sb6$ (or pyridoxal 5$\sp\prime$-phosphate, PLP) is an essential, ubiquitous coenzyme that affects many aspects of amino acid and cellular metabolism in all organisms. The goal of this thesis is to examine the regulation of PLP biosynthesis in Escherichia coli K-12. First, PdxH oxidase is a PLP biosynthetic enzyme, which uses molecular oxygen as an electron acceptor under aerobic assay conditions. To test if facultative anaerobic E. coli uses another enzyme to replace the function of PdxH oxidase anaerobically, suppressors of a pdxH null mutant were isolated anaerobically after 2-aminopurine or spontaneous mutagenesis. Only one specific bypass mutation in another PLP biosynthetic gene pdxJ was found, suggesting that PdxH oxidase is able to function anaerobically and PdxT utilizes D-1-deoxyxyulose as a substrate. Second, regulation of the serC (pdxF)-aroA operon, which is involved the biosynthesis of L-serine, PLP and aromatic compounds was examined. A serC (pdxF) single gene transcript and a serC (pdXf)-aroA cotranscript initiated at P$\sb{serC\ (pdxF)}$ upstream of serC (pdxF) were detected. The expression of the operon is activated by leucine responsive regulatory protein (LRP) and repressed by cAMP receptor protein-cAMP complex (CRP$\cdot$cAMP) at the transcriptional level. LRP activates the operon by directly binding to the upstream consensus box. Binding of CRP$\cdot$cAMP to the upstream CRP box diminishes the activation effect of LRP. However, deletion of the CRP box did not affect the repression of CRP$\cdot$cAMP, suggesting that CRP$\cdot$cAMP may repress the operon indirectly by stimulating the activity or level of an unidentified repressor. The overall effect of this regulation is to maximize the expression of the operon when the cells are growing in minimal-glucose medium. In addition, the binding and the transcription of P$\sb{serC\ (pdxF)}$ by RNA polymerase require a supercoiled circular DNA, indicating that DNA supercoiling affects the transcription of the operon. Third, regulation of another PLP biosynthetic gene gapB was also examined. gapB is activated by CRP$\cdot$cAMP and repressed by catabolic repressor activator protein (CRA). However, the activation of CRP$\cdot$cAMP is epistatic to the repression of CRA. Due to the CRA repression, gapB was expressed at a low level in all the media tested, suggesting that it may be the rate-limiting step of PLP biosynthesis. In summary, unlike genes in many biosynthetic pathways, PLP biosynthetic genes are regulated by global regulators that are important for carbon and amino acid metabolism, instead of the end product(s) of the pathway. ^

EV02: a Phase I trial to compare the safety and immunogenicity of HIV DNA-C prime-NYVAC-C boost to NYVAC-C alone.

The aim of this randomised controlled trial was to see if the addition of 4 mg/ml DNA-C priming given by the intramuscular route at weeks 0 and 4 to NYVAC-C at weeks 20 and 24, safely increased the proportion of participants with HIV-specific T-cell responses measured by the interferon (IFN)-gamma ELISpot assay at weeks 26 and/or 28 compared to NYVAC-C alone. Although 2 individuals discontinued after the first DNA-C due to adverse events (1 vaso-vagal; 1 transient, asymptomatic elevation in alanine transaminase), the vaccines were well tolerated. Three others failed to complete the regimen (1 changed her mind; 2 lost to follow-up). Of the 35 that completed the regimen 90% (18/20) in the DNA-C group had ELISpot responses compared to 33% (5/15) that received NYVAC-C alone (p=0.001). Responses were to envelope in the majority (21/23). Of the 9 individuals with responses to envelope and other peptides, 8 were in the DNA-C group. These promising results suggest that DNA-C was an effective priming agent, that merits further investigation.

Comparison of Immunogenicity in Rhesus Macaques of Transmitted-Founder, HIV-1 Group M Consensus, and Trivalent Mosaic Envelope Vaccines Formulated as a DNA Prime, NYVAC, and Envelope Protein Boost.

An effective human immunodeficiency virus type 1 (HIV-1) vaccine must induce protective antibody responses, as well as CD4(+) and CD8(+) T cell responses, that can be effective despite extraordinary diversity of HIV-1. The consensus and mosaic immunogens are complete but artificial proteins, computationally designed to elicit immune responses with improved cross-reactive breadth, to attempt to overcome the challenge of global HIV diversity. In this study, we have compared the immunogenicity of a transmitted-founder (T/F) B clade Env (B.1059), a global group M consensus Env (Con-S), and a global trivalent mosaic Env protein in rhesus macaques. These antigens were delivered using a DNA prime-recombinant NYVAC (rNYVAC) vector and Env protein boost vaccination strategy. While Con-S Env was a single sequence, mosaic immunogens were a set of three Envs optimized to include the most common forms of potential T cell epitopes. Both Con-S and mosaic sequences retained common amino acids encompassed by both antibody and T cell epitopes and were central to globally circulating strains. Mosaics and Con-S Envs expressed as full-length proteins bound well to a number of neutralizing antibodies with discontinuous epitopes. Also, both consensus and mosaic immunogens induced significantly higher gamma interferon (IFN-γ) enzyme-linked immunosorbent spot assay (ELISpot) responses than B.1059 immunogen. Immunization with these proteins, particularly Con-S, also induced significantly higher neutralizing antibodies to viruses than B.1059 Env, primarily to tier 1 viruses. Both Con-S and mosaics stimulated more potent CD8-T cell responses against heterologous Envs than did B.1059. Both antibody and cellular data from this study strengthen the concept of using in silico-designed centralized immunogens for global HIV-1 vaccine development strategies. IMPORTANCE: There is an increasing appreciation for the importance of vaccine-induced anti-Env antibody responses for preventing HIV-1 acquisition. This nonhuman primate study demonstrates that in silico-designed global HIV-1 immunogens, designed for a human clinical trial, are capable of eliciting not only T lymphocyte responses but also potent anti-Env antibody responses.

Head-to-Head Comparison of Poxvirus NYVAC and ALVAC Vectors Expressing Identical HIV-1 Clade C Immunogens in Prime-Boost Combination with Env Protein in Nonhuman Primates.

UNLABELLED: We compared the HIV-1-specific cellular and humoral immune responses elicited in rhesus macaques immunized with two poxvirus vectors (NYVAC and ALVAC) expressing the same HIV-1 antigens from clade C, Env gp140 as a trimeric cell-released protein and a Gag-Pol-Nef polyprotein as Gag-induced virus-like particles (VLPs) (referred to as NYVAC-C and ALVAC-C). The immunization protocol consisted of two doses of the corresponding poxvirus vector plus two doses of a combination of the poxvirus vector and a purified HIV-1 gp120 protein from clade C. This immunogenicity profile was also compared to that elicited by vaccine regimens consisting of two doses of the ALVAC vector expressing HIV-1 antigens from clades B/E (ALVAC-vCP1521) plus two doses of a combination of ALVAC-vCP1521 and HIV-1 gp120 protein from clades B/E (similar to the RV144 trial regimen) or clade C. The results showed that immunization of macaques with NYVAC-C stimulated at different times more potent HIV-1-specific CD4(+) T-cell responses and induced a trend toward higher-magnitude HIV-1-specific CD8(+) T-cell immune responses than did ALVAC-C. Furthermore, NYVAC-C induced a trend toward higher levels of binding IgG antibodies against clade C HIV-1 gp140, gp120, or murine leukemia virus (MuLV) gp70-scaffolded V1/V2 and toward best cross-clade-binding IgG responses against HIV-1 gp140 from clades A, B, and group M consensus, than did ALVAC-C. Of the linear binding IgG responses, most were directed against the V3 loop in all immunization groups. Additionally, NYVAC-C and ALVAC-C also induced similar levels of HIV-1-neutralizing antibodies and antibody-dependent cellular cytotoxicity (ADCC) responses. Interestingly, binding IgA antibody levels against HIV-1 gp120 or MuLV gp70-scaffolded V1/V2 were absent or very low in all immunization groups. Overall, these results provide a comprehensive survey of the immunogenicity of NYVAC versus ALVAC expressing HIV-1 antigens in nonhuman primates and indicate that NYVAC may represent an alternative candidate to ALVAC in the development of a future HIV-1 vaccine. IMPORTANCE: The finding of a safe and effective HIV/AIDS vaccine immunogen is one of the main research priorities. Here, we generated two poxvirus-based HIV vaccine candidates (NYVAC and ALVAC vectors) expressing the same clade C HIV-1 antigens in separate vectors, and we analyzed in nonhuman primates their immunogenicity profiles. The results showed that immunization with NYVAC-C induced a trend toward higher HIV-1-specific cellular and humoral immune responses than did ALVAC-C, indicating that this new NYVAC vector could be a novel optimized HIV/AIDS vaccine candidate for human clinical trials.

The remarkable solar twin HIP 56948: a prime target in the quest for other Earths

Context. The Sun shows abundance anomalies relative to most solar twins. If the abundance peculiarities are due to the formation of inner rocky planets, that would mean that only a small fraction of solar type stars may host terrestrial planets. Aims. In this work we study HIP 56948, the best solar twin known to date, to determine with an unparalleled precision how similar it is to the Sun in its physical properties, chemical composition and planet architecture. We explore whether the abundances anomalies may be due to pollution from stellar ejecta or to terrestrial planet formation. Methods. We perform a differential abundance analysis (both in LTE and NLTE) using high resolution (R similar to 100 000) high S/N (600-650) Keck HIRES spectra of the Sun (as reflected from the asteroid Ceres) and HIP 56948. We use precise radial velocity data from the McDonald and Keck observatories to search for planets around this star. Results. We achieve a precision of sigma less than or similar to 0.003 dex for several elements. Including errors in stellar parameters the total uncertainty is as low as sigma similar or equal to 0.005 dex (1%), which is unprecedented in elemental abundance studies. The similarities between HIP 56948 and the Sun are astonishing. HIP 56948 is only 17 +/- 7 K hotter than the Sun, and log g, [Fe/H] and microturbulence velocity are only +0.02 +/- 0.02 dex, +0.02 +/- 0.01 dex and +0.01 +/- 0.01 km s(-1) higher than solar, respectively. Our precise stellar parameters and a differential isochrone analysis shows that HIP 56948 has a mass of 1.02 +/- 0.02 M-circle dot and that it is similar to 1 Gyr younger than the Sun, as constrained by isochrones, chromospheric activity, Li and rotation. Both stars show a chemical abundance pattern that differs from most solar twins, but the refractory elements (those with condensation temperature T-cond greater than or similar to 1000 K) are slightly (similar to 0.01 dex) more depleted in the Sun than in HIP 56948. The trend with T-cond in differential abundances (twins -HIP 56948) can be reproduced very well by adding similar to 3 M-circle plus of a mix of Earth and meteoritic material, to the convection zone of HIP 56948. The element-to-element scatter of the Earth/meteoritic mix for the case of hypothetical rocky planets around HIP 56948 is only 0.0047 dex. From our radial velocity monitoring we find no indications of giant planets interior to or within the habitable zone of HIP 56948. Conclusions. We conclude that HIP 56948 is an excellent candidate to host a planetary system like our own, including the possible presence of inner terrestrial planets. Its striking similarity to the Sun and its mature age makes HIP 56948 a prime target in the quest for other Earths and SETI endeavors.

Solitaire™ with the Intention for Thrombectomy as Primary Endovascular Treatment for Acute Ischemic Stroke (SWIFT PRIME) trial: protocol for a randomized, controlled, multicenter study comparing the Solitaire revascularization device with IV tPA with IV tPA alone in acute ischemic stroke.

RATIONALE Early reperfusion in patients experiencing acute ischemic stroke is critical, especially for patients with large vessel occlusion who have poor prognosis without revascularization. Solitaire™ stent retriever devices have been shown to immediately restore vascular perfusion safely, rapidly, and effectively in acute ischemic stroke patients with large vessel occlusions. AIM The aim of the study was to demonstrate that, among patients with large vessel, anterior circulation occlusion who have received intravenous tissue plasminogen activator, treatment with Solitaire revascularization devices reduces degree of disability 3 months post stroke. DESIGN The study is a global multicenter, two-arm, prospective, randomized, open, blinded end-point trial comparing functional outcomes in acute ischemic stroke patients who are treated with either intravenous tissue plasminogen activator alone or intravenous tissue plasminogen activator in combination with the Solitaire device. Up to 833 patients will be enrolled. PROCEDURES Patients who have received intravenous tissue plasminogen activator are randomized to either continue with intravenous tissue plasminogen activator alone or additionally proceed to neurothrombectomy using the Solitaire device within six-hours of symptom onset. STUDY OUTCOMES The primary end-point is 90-day global disability, assessed with the modified Rankin Scale (mRS). Secondary outcomes include mortality at 90 days, functional independence (mRS ≤ 2) at 90 days, change in National Institutes of Health Stroke Scale at 27 h, reperfusion at 27 h, and thrombolysis in cerebral infarction 2b/3 flow at the end of the procedure. ANALYSIS Statistical analysis will be conducted using simultaneous success criteria on the overall distribution of modified Rankin Scale (Rankin shift) and proportions of subjects achieving functional independence (mRS 0-2).

2-methylthio-N$\sp6$-dimethylallyl modification of adenosine 37 of tRNAs in {\it Escherichia coli\/} K-12

The hypermodified, hydrophobic 2-methylthio-N$\sp6$-(dimethylallyl)-adenosine (ms${2{\cdot}6}\atop1$A) residue occurs $3\sp\prime$ to the anticodon in tRNA species that read codons beginning with U. The first step (i$\sp6$A37 formation) of this modification is catalyzed by dimethylallyl diphosphate:tRNA dimethyallyltransferase (EC 2.5.1.8), which is the product of the miaA gene. Subsequent steps were proposed to be catalyzed by MiaB and MiaC enzymes to complete the ms${2{\cdot}6}\atop1$A37 modification. The study of functions of the ms${2{\cdot}6}\atop1$A37 is very important because this modified base is one of the best candidates for a role in global control in response to environmental stress. This dissertation describes the further delineation of functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli K-12 cells. This work provides significant information on functions of tRNA modifications in E. coli cells to adapt to stressful environmental conditions. Three hypotheses were tested in this work.^ The first hypothesis tested was that non-optimal translation processes cause increased spontaneous mutagenesis by the induction of SOS response in starving cells. To test this hypothesis, I measured spontaneous mutation rates of wild type cells and various mutant strains which are defective in tRNA modification, SOS response, or oxidative damage repair. I found that the miaA mutation acts as a mutator that increased Lac$\sp+$ reversion rates and Trp$\sp+$ reversion frequencies of the wild-type cells in starving conditions. However, the lexA3(Ind)(which abolishes the induction of SOS response) mutation abolished the mutator phenotype of the miaA mutant. The recA430 mutation, not other identified SOS genes, decreased the Lac$\sp+$ reversion to a less extent than that of the lexA3(Ind) mutation. These results suggest that RecA together with another unidentified SOS gene product are responsible for the process.^ The second hypothesis tested was that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ molecules in form of a protein dimer. To test this hypothesis, three versions of the MiaA protein and seven species of tRNA substrates were purified. Binding studies by gel mobility shift assays, filter binding assays and gel filtration shift assays support the hypothesis that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ as a protein dimer but as a monomer to the anticodon stem-and-loop. These results were further supported by using steady state enzyme kinetic studies.^ The third hypothesis tested in this work was that the miaB gene in E. coli exists and is clonable. The miaB::Tn10dCm insertion mutation of Salmonella typhimurium was transduced to E. coli K-12 cells by using P$\sb1$ and P$\sb{22}$ bacteriophages. The insertion was confirmed by HPLC analyses of nucleotide profiles of miaB mutants of E. coli. The insertion mutation was cloned and DNA sequences adjacent to the transposon were sequenced. These DNA sequences were 86% identical to the f474 gene at 14.97 min chromosome of E. coli. The f474 gene was then cloned by PCR from the wild-type chromosome of E. coli. The recombinant plasmid complemented the mutant phenotype of the miaB mutant of E. coli. These results support the hypothesis that the miaB gene of E. coli exists and is clonable. In summary, functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli cells are further delineated in this work in perspectives of adaptation to stressful environmental conditions and protein:tRNA interaction. (Abstract shortened by UMI.) ^

IL-4 and -5 prime human mast cells for different profiles of IgE-dependent cytokine production

Mast cells (MC) are stem cell factor-dependent tissue-based hematopoietic cells with substantial functional heterogeneity. Cord blood-derived human MC (hMC) express functional receptors for IL-5, and IL-5 mediates stem cell factor-dependent comitogenesis of hMC in vitro. Although IL-5 is not required for normal hMC development, we considered that it might prime hMC for their high-affinity Fc receptor for IgE (FcɛRI)-dependent generation of cytokines, as previously demonstrated for IL-4. Compared with hMC maintained in stem cell factor alone, hMC primed with IL-5 expressed 2- to 4-fold higher steady-state levels of TNF-α, IL-5, IL-13, macrophage inflammatory protein 1α, and granulocyte-macrophage colony-stimulating factor transcripts 2 h after FcɛRI crosslinking and secreted 2- to 5-fold greater quantities of the corresponding cytokines, except IL-13, at 6 h. Unlike IL-4, IL-5 priming did not enhance FcɛRI-dependent histamine release. Thus, IL-5 augments cytokine production by hMC by a mechanism distinct from that of IL-4 and with a different resultant profile of cytokine production. These observations suggest a potentially autocrine effect of IL-5 on hMC for amplification of allergic immune responses, in addition to its recognized paracrine effects on eosinophils, and implicate both IL-4 and IL-5 in the modulation of the hMC phenotype.

Cameron’s big speech on Europe – No, Prime Minister! CEPS Essay (No. 3), 31 January 2013

British Prime Minister David Cameron has clearly made the political assessment that he must appease the eurosceptics in his party with a plan for renegotiation and then an in-out referendum on the UK’s membership of the European Union. In the second of a series of analyses on the UK’s relationship with Europe, Michael Emerson considers the seven hazards of Cameron’s approach.

Proceedings at the unveiling of the statute of John Sandfield Macdonald, first prime minister of Ontario in the Queen's park, Toronto, November 16th, 1909.

Mode of access: Internet.

The relationship between adipokines and the onset of type 2 diabetes in middle-aged men: The PRIME study

Aims: Epidemiological evidence suggests that adipokines may be associated with the onset of type 2 diabetes, but the evidence to date is limited and inconclusive. This study examined the association between adiponectin and leptin and the subsequent diagnosis of type 2 diabetes in a UK population based cohort of non-diabetic middle-aged men.
Methods: Baseline serum levels of leptin and adiponectin were measured in 1839 nondiabetic men aged 50–60 years who were participating in the prospective populationbased PRIME study. Over a mean follow-up of 14.7 years, new cases of type 2 diabetes were determined from self-reported clinical information with subsequent validation by general practitioners.
Results: 151 Participants developed type 2 diabetes during follow-up. In Cox regression models adjusted for age, men in the top third of the leptin distribution were at increased risk (hazard ratio (HR) 4.27, 95% CI 2.67–6.83) and men in the top third of the adiponectin
distribution at reduced risk (HR 0.24, 95% CI 0.14–0.42) relative to men in the bottom third. However, significance was lost for leptin after additional adjustment for BMI, waist to hip ratio, lifestyle factors and biological risk factors, including C-reactive protein (CRP). Further adjustment for HOMA-IR also resulted in loss of significance for adiponectin.
Conclusions: This study provides evidence that adipokines are associated with men’s future type 2 diabetes risk but not independently of other risk factors.