Genetic control of DNA synthesis Bacillus subtilis

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A mean value theorem for systems of integrals

More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a,b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a,b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary interval. The proof relies on a version of Caratheodory's convex hull theorem for a continuous curve, that we also prove in the paper. As applications, we give a representation of the covariance for two continuous functions of a random variable, and a most general version of Gruess' inequality.Comment: 7 page

Limit laws for distorted return time processes for infinite measure preserving transformations

We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition. We identify two critical cases for which we prove uniform distribution laws. For this we introduce the notion of uniformly returning sets and discuss some of their properties.Comment: 18 pages, 2 figure

A simple recipe to detect possible C-Odd effects in high energy pˉp\bar p p and pppp

We provide a theorem to suggest that $t=0$ data may already be sufficient to detect possible asymptotic C-odd (Odderon) contributions. This can be done by comparing $\bar p p$ and $pp$ $t=0$ observables such as total cross sections, forward angular distributions and ratios of real to imaginary forward amplitudes for which well defined model independent correlations {must} exist which could already show up at RHIC energy but definitely at LHC energies.Comment: 10 pages in TeX, no figur

Multiple scattering in wide-field optical coherence tomography

Optical Coherence Tomography (OCT), a well-established imaging method based on low-coherence interferometry, provides cross-sectional images of the internal structure of biological samples with a resolution in the micrometer range. OCT was successfully applied on various tissues such as for instance the retina, the skin or a tooth. In highly scattering tissues like the skin, probing depth is limited to approximately 2mm, mainly due to insufficient rejection of multiply scattered light. Presently, the contribution of multiple scattering in OCT is not fully understood. Therefore, there is a strong and urgent need to develop models allowing a reliable evaluation of the system's limitations as well as the improvement of the imaging capabilities. It is generally believed that a relevant model should account for loss of correlation between the reference and the sample field due to multiple scattering. We developed a new comprehensive model of OCT. Our preliminary study revealed that the reference and sample fields are actually fully correlated. This important result allowed us to model the OCT signal as a sum of stationary random phasors and treated it as a statistical signal. The mean of this signal can be calculated thanks to classical results of statistical optics and to a Monte Carlo simulation. Unlike other existing models, our model accounts for the source autocorrelation function. The model proved to be in excellent agreement with a whole range of experimental data gathered in a comprehensive study of cross-talk in wide-field OCT. Moreover, our results put in question the applicability of widely used models of OCT based on the "extended Huygens-Fresnel principle", which assume a partial correlation between interfering fields due to multiple scattering. The construction of conventional OCT images is based on lateral scanning of a beam focused within the sample. To increase image acquisition speed and eliminate the need for lateral scanning, wide-field OCT was recently developed. Our experimental and theoretical investigations of the potential and limitations of wide-field OCT revealed the crucial role played by the spatial coherence of the light source. Spatially coherent illumination generates considerable coherent optical cross-talk, which prevents shot-noise-limited detection and diffraction-limited imaging in scattering samples. The dependence on several parameters of the optical system and of the sample properties was investigated in a comprehensive study. Cross-talk increases with the wide-field diameter, numerical aperture, source coherence length, and sample optical density; and strongly depends on sample anisotropy. We showed that spatially incoherent illumination realized with a thermal light source permits cross-talk suppression in wide-field OCT, i.e. rejection of multiply scattered light to a level comparable to that of point scanning OCT. We performed a theoretical study which revealed that the power per spatial mode radiated by thermal light sources is too low to permit a high signal-to-noise ratio while maintaining a fast acquisition speed. Therefore, wide-field OCT realized with either spatially coherent or spatially incoherent illumination suffers from inherent fundamental limitation. This led us to investigate the possibility of exploiting a spatially incoherent light source brighter than a thermal light source. We came to the conclusion that such a "pseudothermal" light source can potentially lead to wide-field OCT systems devoid of cross-talk and an image acquisition speed higher than that of a point scanning OCT system. However, the attractive properties of pseudothermal light sources could be gained at the expense of the simplicity and the economical advantages offered by thermal light sources. Furthermore, fast acquisition speed also relies on a performing "smart pixel detector array". Presently, such detectors do not have sufficient sensitivity and their frequency readout is too low as shown in our feasibility study. We performed a theoretical investigation of the potential of thermal light sources in terms of axial resolution and power per mode. The former revealed that the maximum power per mode is radiated at a wavelength higher than the spectral peak of a blackbody radiator. This led to the important practical conclusion that, at 6000 K, the maximum power is collected in the therapeutic spectral window in OCT (600 - 1300 nm), while at 3000 K this peak is shifted out of the therapeutic window leading to significant power losses. More generally, our work provides a design tool for choosing the optimal thermal light source for a given therapeutic window in terms of signal-to-noise ratio. Currently available sources at 6000 K consist of high pressure gas arc lamps providing a spectrum endowed with spectral lines deleterious for OCT. By suppressing a portion of the spectrum devoid of spectral lines of a mercury arc lamp, we obtained amongst the highest axial resolution so far reported in OCT. Furthermore, the importance of the speckle statistics in OCT incited us to clarify the origin of a difference between two theoretical results reported in the literature. Indeed, two calculations of the amplitude distribution of speckles in OCT, each of them based on a different mathematical formulation, yield different results. We showed that a modification of an initial assumption in one of the formulation leads to equivalent results. In conclusion, this thesis provides a deeper understanding of the potential and limitations of widefield OCT, leading to important design rules. Moreover, it presents a new comprehensive model of OCT putting in question other widely used models

The interval ordering problem

For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by earlier intervals in the ordering). This problem is motivated by an application in molecular biology that concerns the determination of the structure of the backbone of a protein. We present polynomial-time algorithms for several natural special cases of the problem that cover the situation where the interval boundaries are agreeably ordered and the situation where the interval set is laminar. Also the bottleneck variant of the problem is shown to be solvable in polynomial time. Finally we prove that the general problem is NP-hard, and that the existence of a constant-factor-approximation algorithm is unlikely

Limits and artefacts of reflective imaging goniophotometers for complex solar façade systems

The design of systems for solar light collection, modulation and/or distribution requires a thorough knowledge of their optical properties. The angular distribution of the scattered incident light flux, described by the Bidirectional Scattering Distribution Function (BSDF), can be measured with a step-by-step scanning goniophotometer but requires considerable time, especially when aiming at high angular resolution over a wide range and numerous incidence angles like in typical solar applications. Considerably faster measurements can be achieved with a so-called imaging goniophotometer, which simultaneously measures light fluxes in all scattered directions by dispatching them over different portions of a two-dimensional sensor array. In this contribution, we revisit the widely accepted principle of a reflective imaging goniophotometer (RIG), which is based on a hemispherical (or ellipsoidal) mirror and a fisheye camera. Specifically developed ray-tracing tools allowed us to obtain accurate figures relative to the influence of key design parameters on angular resolution. Our calculations reveal that the measurement accuracy is too low for samples larger than a few tens of millimeters. Most importantly, we found significant limitations and artefacts in the angular-to-spatial mapping function inherent to the RIG principle, which generally severely bias BSDF measurements

Genometrics as an essential tool for the assembly of whole genome sequences: the example of the chromosome of Bifidobacterium longum NCC2705

BACKGROUND: Analysis of the first reported complete genome sequence of Bifidobacterium longum NCC2705, an actinobacterium colonizing the gastrointestinal tract, uncovered its proteomic relatedness to Streptomyces coelicolor and Mycobacterium tuberculosis. However, a rapid scrutiny by genometric methods revealed a genome organization totally different from all so far sequenced high-GC Gram-positive chromosomes. RESULTS: Generally, the cumulative GC- and ORF orientation skew curves of prokaryotic genomes consist of two linear segments of opposite slope: the minimum and the maximum of the curves correspond to the origin and the terminus of chromosome replication, respectively. However, analyses of the B. longum NCC2705 chromosome yielded six, instead of two, linear segments, while its dnaA locus, usually associated with the origin of replication, was not located at the minimum of the curves. Furthermore, the coorientation of gene transcription with replication was very low. Comparison with closely related actinobacteria strongly suggested that the chromosome of B. longum was misassembled, and the identification of two pairs of relatively long homologous DNA sequences offers the possibility for an alternative genome assembly proposed here below. By genometric criteria, this configuration displays all of the characters common to bacteria, in particular to related high-GC Gram-positives. In addition, it is compatible with the partially sequenced genome of DJO10A B. longum strain. Recently, a corrected sequence of B. longum NCC2705, with a configuration similar to the one proposed here below, has been deposited in GenBank, confirming our predictions. CONCLUSION: Genometric analyses, in conjunction with standard bioinformatic tools and knowledge of bacterial chromosome architecture, represent fast and straightforward methods for the evaluation of chromosome assembly

Lighting and Energy Performance of an Adaptive Shading and Daylighting System for Arid Climates

Finding the proper trade-off between blocking direct sunlight, ensuring sufficient indoor daylighting and view out is a particularly delicate task especially in arid climates, due to harsh environmental conditions. As a tentative answer to this challenge, an adaptive shading and daylighting system (Shape Variable Mashrabiya – SVM) has been developed by the authors, described in an earlier paper. In this paper, we analyze how the SVM may affect annual lighting and global primary energy performance of an office building in Abu Dhabi: the SVM was applied to east and west façades and compared to external Venetian blinds, reflective and selective glazing