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 $q$.

Repositioning precision of coronary arteries measured on X-ray angiography and its implications for coronary MR angiography.

BACKGROUND: To test the hypothesis that intervals with superior beat-to-beat coronary artery repositioning precision exist in the cardiac cycle, to design a coronary MR angiography (MRA) methodology in response, and to ascertain its performance. METHODS: Coronary repositioning precision in consecutive heartbeats was measured on x-ray coronary angiograms of 17 patients and periods with the highest repositioning precision were identified. In response, the temporal order of coronary MRA pulse sequence elements required modification and the T2 -prep now follows (T2 -post) rather than precedes the imaging part of the sequence. The performance of T2 -post was quantitatively compared (signal-to-noise [SNR], contrast-to-noise [CNR], vessel sharpness) to that of T2 -prep in vivo. RESULTS: Coronary repositioning precision is <1 mm at peak systole and in mid diastole. When comparing systolic T2 -post to diastolic T2 -prep, CNR and vessel sharpness remained unchanged (both P = NS) but SNR for muscle and blood increased by 104% and 36% (both P < 0.05), respectively. CONCLUSION: Windows with improved coronary repositioning precision exist in the cardiac cycle: one in peak systole and one in mid diastole. Peak-systolic imaging necessitates a re-design of conventional coronary MRA pulse sequences and leads to image quality very similar to that of conventional mid-diastolic data acquisition but improved SNR. J. Magn. Reson. Imaging 2015;41:1251-1258. © 2014 Wiley Periodicals, Inc.

High-precision dating and origin of synsedimentary volcanism in the Late Carboniferous Salvan-Dorenaz basin (Aiguilles-Rouges Massif, Western Alps)

Late Variscan volcanic activity is documented in the Late Carboniferous Salvan-Dorenaz sedimentary basin and in the neighboring basement units of the Aiguilles-Rouges and Mont-Blanc crystalline massifs (Western Alps). Precise U/Pb isotopic dating, zircon morphology and geochemical analyses indicate that volcanism occurred during short-lived pulses and that coexisting crustal and mantle sources were involved in the production of melts. Volcanic and subvolcanic products were emplaced along major N-S to NNE-SSW transtensional fracture zones, similar to the ones that governed intense basement exhumation and that favored the formation and filling of the Late Carboniferous Salvan-Dorenaz continental basin. In the Aiguilles-Rouges massif, dacitic flows outcropping at the base of the Salvan-Dorenaz basin erupted at 308 +/- 3 Ma; they represent the surface equivalent of the nearby Vallorcine peraluminous granite and associated rhyolitic dykes (311 +/- 17 Ma). In the Mont Blanc massif, calc-alkaline rhyolitic dykes were emplaced simultaneously (307 +/- 2 Ma) at shallow crustal levels, but they derive from deeper magma sources denoting enhanced mantellic activity. Recently identified tuffs and volcaniclastic layers embedded at different levels of the Salvan-Dorenaz stratigraphic record testify a 295 +3/-4 Ma old episode of highly explosive volcanism from distant volcanic centers, possibly located in the Aar-Gotthard massifs (Central Alps). Their zircon typology is highly heterogeneous. documenting wall-rock contamination of the melts and/or admixture of crustal sediments, whereas consistent subpopulations point to high-temperature magmas of deep-seated origin and alkaline affinity. The dated volcanic layers from the Salvan-Dorenaz basin set the beginning of the detrital sedimentation at 308 +/- 3 Ma and constrain the deposition of 1.5-1.7 km thick of elastic sediments within a time span of 10-15 Ma. These results infer minimum, long-term subsidence rates during basin evolution in the order of >0.1 mm/a, while in the surrounding basement units estimated exhumation rates are in the range of 1 mm/a. All dated rocks contain inherited zircon populations about 350, 450 or 600 Ma old.

High-precision confocal reflection measurement for two dimensional refractive index mapping of optical fibers

We introduce a new fiber-optical approach for reflection based refractive index mapping. Our approach leads to improved stability and reliability over existing free-space confocal instruments and significantly cuts alignment efforts and reduces the number of components needed. Other than properly cleaved fiber end-faces, this setup requires no additional sample preparation. The instrument is calibrated by means of a set of samples with known refractive indices. The index steps of commercially available fibers are measured accurately down to < 10⁻³. The precision limit of the instrument is currently of the order of 10⁻⁴.

Permanent matching of coupled optical bottle resonators with better than 0.16 GHz precision

The fabrication precision is one of the most critical challenges to the creation of practical photonic circuits composed of coupled high Q-factor microresonators. While very accurate transient tuning of microresonators based on local heating has been reported, the record precision of permanent resonance positioning achieved by post-processing is still within 1 and 5 GHz. Here we demonstrate two coupled bottle microresonators fabricated at the fiber surface with resonances that are matched with a better than 0.16 GHz precision. This corresponds to a better than 0.17 Å precision in the effective fiber radius variation. The achieved fabrication precision is only limited by the resolution of our optical spectrum analyzer and can be potentially improved by an order of magnitude.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.

Third-order nonlinear spectra and optical limiting of lead oxifluoroborate glasses

We have determined two-photon absorption and nonlinear refraction spectra of the 50BO(1.5) - (50-x)PbF(2) - xPbO glasses (with x = 25, 35, 50 cationic %) at the range of the 470 and 1550 nm. The replacement of fluor atoms by oxygen leads to an increase in the third-order susceptibility, due to the formation of non-bridging oxygens (NBO). The nonlinear index of refraction is one order of magnitude higher than the one for fused silica, and it increases almost twice for the sample with x = 50. This sample has also shown promising features for all-optical switching as well as for optical limiting. (C) 2011 Optical Society of America

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Quantitative CT analysis of the glabellar and anterior nasal spine regions for the placement of implants for nasal prosthesis retention

Objectives: The aim of this study was to determine the precision of the measurements of 2 craniometric anatomic points-glabella and anterior nasal spine-in order to verify their possibility as potential locations for placing implants aimed at nasal prostheses retention. Methods: Twenty-six dry human skulls were scanned in a high-resolution spiral tomography with 1-mm axial slice thickness and 1-mm interval reconstruction using a bone tissue filter. Images obtained were stored and transferred to an independent workstation containing e-film imaging software. The measurements (in the glabella and anterior nasal fossa) were made independently by 2 observers twice for each measurement. Data were submitted to statistical analysis (parametric t test). Results: The results demonstrated no statistically significant difference between interobserver and intraobserver measurements (P > .05). The standard error was found to be between 0.49 mm and 0.84 mrn for measurements in bone protocol, indicating a high /eve/ of precision. Conclusions: The measurements obtained in anterior nasal spine and glabella were considered precise and reproducible. Mean values of such measurements pointed to the possibility of implant placement in these regions, particularly in the anterior nasal spine.

Practical Quality Control: Comparision of Methods on the Quantification of Stationary Phases in Paper and Thin-Layer Chromatographic Systems

Introduction: Paper and thin layer chromatography methods are frequently used in Classic Nuclear Medicine for the determination of radiochemical purity (RCP) on radiopharmaceutical preparations. An aliquot of the radiopharmaceutical to be tested is spotted at the origin of a chromatographic strip (stationary phase), which in turn is placed in a chromatographic chamber in order to separate and quantify radiochemical species present in the radiopharmaceutical preparation. There are several methods for the RCP measurement, based on the use of equipment as dose calibrators, well scintillation counters, radiochromatografic scanners and gamma cameras. The purpose of this study was to compare these quantification methods for the determination of RCP. Material and Methods: 99mTc-Tetrofosmin and 99mTc-HDP are the radiopharmaceuticals chosen to serve as the basis for this study. For the determination of RCP of 99mTc-Tetrofosmin we used ITLC-SG (2.5 x 10 cm) and 2-butanone (99mTc-tetrofosmin Rf = 0.55, 99mTcO4- Rf = 1.0, other labeled impurities 99mTc-RH RF = 0.0). For the determination of RCP of 99mTc-HDP, Whatman 31ET and acetone was used (99mTc-HDP Rf = 0.0, 99mTcO4- Rf = 1.0, other labeled impurities RF = 0.0). After the development of the solvent front, the strips were allowed to dry and then imaged on the gamma camera (256x256 matrix; zoom 2; LEHR parallel-hole collimator; 5-minute image) and on the radiochromatogram scanner. Then, strips were cut in Rf 0.8 in the case of 99mTc-tetrofosmin and Rf 0.5 in the case of 99mTc-HDP. The resultant pieces were smashed in an assay tube (to minimize the effect of counting geometry) and counted in the dose calibrator and in the well scintillation counter (during 1 minute). The RCP was calculated using the formula: % 99mTc-Complex = [(99mTc-Complex) / (Total amount of 99mTc-labeled species)] x 100. Statistical analysis was done using the test of hypotheses for the difference between means in independent samples. Results:The gamma camera based method demonstrated higher operator-dependency (especially concerning the drawing of the ROIs) and the measures obtained using the dose calibrator are very sensitive to the amount of activity spotted in the chromatographic strip, so the use of a minimum of 3.7 MBq activity is essential to minimize quantification errors. Radiochromatographic scanner and well scintillation counter showed concordant results and demonstrated the higher level of precision. Conclusions: Radiochromatographic scanners and well scintillation counters based methods demonstrate to be the most accurate and less operator-dependant methods.

Representation of motor habit in a sequence of repetitive reach and grasp movements performed by macaque monkeys: evidence for a contribution of the dorsolateral prefrontal cortex.

In the context of an autologous cell transplantation study, a unilateral biopsy of cortical tissue was surgically performed from the right dorsolateral prefrontal cortex (dlPFC) in two intact adult macaque monkeys (dlPFC lesioned group), together with the implantation of a chronic chamber providing access to the left motor cortex. Three other monkeys were subjected to the same chronic chamber implantation, but without dlPFC biopsy (control group). All monkeys were initially trained to perform sequential manual dexterity tasks, requiring precision grip. The motor performance and the prehension's sequence (temporal order to grasp pellets from different spatial locations) were analysed for each hand. Following the surgery, transient and moderate deficits of manual dexterity per se occurred in both groups, indicating that they were not due to the dlPFC lesion (most likely related to the recording chamber implantation and/or general anaesthesia/medication). In contrast, changes of motor habit were observed for the sequential order of grasping in the two monkeys with dlPFC lesion only. The changes were more prominent in the monkey subjected to the largest lesion, supporting the notion of a specific effect of the dlPFC lesion on the motor habit of the monkeys. These observations are reminiscent of previous studies using conditional tasks with delay that have proposed a specialization of the dlPFC for visuo-spatial working memory, except that this is in a different context of "free-will", non-conditional manual dexterity task, without a component of working memory.

MR spectroscopy of the human brain with enhanced signal intensity at ultrashort echo times on a clinical platform at 3T and 7T.

Recently, the spin-echo full-intensity acquired localized (SPECIAL) spectroscopy technique was proposed to unite the advantages of short TEs on the order of milliseconds (ms) with full sensitivity and applied to in vivo rat brain. In the present study, SPECIAL was adapted and optimized for use on a clinical platform at 3T and 7T by combining interleaved water suppression (WS) and outer volume saturation (OVS), optimized sequence timing, and improved shimming using FASTMAP. High-quality single voxel spectra of human brain were acquired at TEs below or equal to 6 ms on a clinical 3T and 7T system for six volunteers. Narrow linewidths (6.6 +/- 0.6 Hz at 3T and 12.1 +/- 1.0 Hz at 7T for water) and the high signal-to-noise ratio (SNR) of the artifact-free spectra enabled the quantification of a neurochemical profile consisting of 18 metabolites with Cramér-Rao lower bounds (CRLBs) below 20% at both field strengths. The enhanced sensitivity and increased spectral resolution at 7T compared to 3T allowed a two-fold reduction in scan time, an increased precision of quantification for 12 metabolites, and the additional quantification of lactate with CRLB below 20%. Improved sensitivity at 7T was also demonstrated by a 1.7-fold increase in average SNR (= peak height/root mean square [RMS]-of-noise) per unit-time.

Influence of configurational atomic order on the relative stability of bcc and close-packed structures in Cu-based alloys

We present a study of the influence of atomic order on the relative stability of the bcc and the 18R martensitic structures in a Cu2.96Al0.92Be0.12 crystal. Calorimetric measurements have shown that disorder increases the stability of the 18R phase, contrary to what happens in Cu-Zn-Al alloys for which it is the bcc phase that is stabilized by disordering the system. This different behavior has been explained in terms of a model recently reported. We have also proved that the entropy change at the martensitic transition is independent of the state of atomic order of the crystal, as predicted theoretically. Our results suggest that differences in the vibrational spectrum of the crystal due to different states of atomic order must be equal in the bcc and in the close-packed phases.

Signatures of CP violation in the presence of multiple b-pair production at hadron colliders

We calculate the production of two b-quark pairs in hadron collisions. Sources of multiple pairs are multiple interactions and higher order perturbative QCD mechanisms. We subsequently investigate the competing effects of multiple b-pair production on measurements of CP violation: (i) the increase in event rate with multiple b-pair cross sections which may reach values of the order of 1 b in the presence of multiple interactions and (ii) the dilution of b versus b tagging efficiency because of the presence of events with four B mesons. The impact of multiple B-meson production is small unless the cross section for producing a single pair exceeds 1 mb. We show that even for larger values of the cross section the competing effects (i) and (ii) roughly compensate so that there is no loss in the precision with which CP-violating CKM angles can be determined.