Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure

Crystallographic reconstruction study of the effects of finish rolling temperature on the variant selection during bainite transformation in C-Mn high-strength steels

The effect of finish rolling temperature (FRT) on the austenite- () to-bainite () phase transformation is quantitatively investigated in high-strength C-Mn steels. In particular, the present study aims to clarify the respective contributions of the conditioning during the hot rolling and the variant selection (VS) during the phase transformation to the inherited texture. To this end, an alternative crystallographic reconstruction procedure, which can be directly applied to experimental electron backscatter diffraction (EBSD) mappings, is developed by combining the best features of the existing models: the orientation relationship (OR) refinement, the local pixel-by-pixel analysis and the nuclei identification and spreading strategy. The applicability of this method is demonstrated on both quenching and partitioning (Q&P) and as-quenched lath-martensite steels. The results obtained on the C-Mn steels confirm that the sample finish rolled at the lowest temperature (829{\deg}C) exhibits the sharpest transformation texture. It is shown that this sharp texture is exclusively due to a strong VS from parent brass {110}, S {213} and Goss {110} grains, whereas the VS from the copper {112} grains is insensitive to the FRT. In addition, a statistical VS analysis proves that the habit planes of the selected variants do not systematically correspond to the predicted active slip planes using the Taylor model. In contrast, a correlation between the Bain group to which the selected variants belong and the FRT is clearly revealed, regardless of the parent orientation. These results are discussed in terms of polygranular accommodation mechanisms, especially in view of the observed development in the hot-rolled samples of high-angle grain boundaries with misorientation axes between and

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Prototype Tests for the CELESTE Solar Array Gamma--Ray Telescope

The CELESTE experiment will be an Atmospheric Cherenkov detector designed to bridge the gap in energy sensitivity between current satellite and ground-based gamma-ray telescopes, 20 to 300 GeV. We present test results made at the former solar power plant, Themis, in the French Pyrenees. The tests confirm the viability of using a central tower heliostat array for Cherenkov wavefront sampling.Comment: LaTeX2e,30 pages including 14 figures, accepted for publication by Nuclear Instruments & Methods Section

High-Resolution Functional Mapping of the Venezuelan Equine Encephalitis Virus Genome by Insertional Mutagenesis and Massively Parallel Sequencing

We have developed a high-resolution genomic mapping technique that combines transposon-mediated insertional mutagenesis with either capillary electrophoresis or massively parallel sequencing to identify functionally important regions of the Venezuelan equine encephalitis virus (VEEV) genome. We initially used a capillary electrophoresis method to gain insight into the role of the VEEV nonstructural protein 3 (nsP3) in viral replication. We identified several regions in nsP3 that are intolerant to small (15 bp) insertions, and thus are presumably functionally important. We also identified nine separate regions in nsP3 that will tolerate small insertions at low temperatures (30°C), but not at higher temperatures (37°C, and 40°C). Because we found this method to be extremely effective at identifying temperature sensitive (ts) mutations, but limited by capillary electrophoresis capacity, we replaced the capillary electrophoresis with massively parallel sequencing and used the improved method to generate a functional map of the entire VEEV genome. We identified several hundred potential ts mutations throughout the genome and we validated several of the mutations in nsP2, nsP3, E3, E2, E1 and capsid using single-cycle growth curve experiments with virus generated through reverse genetics. We further demonstrated that two of the nsP3 ts mutants were attenuated for virulence in mice but could elicit protective immunity against challenge with wild-type VEEV. The recombinant ts mutants will be valuable tools for further studies of VEEV replication and virulence. Moreover, the method that we developed is applicable for generating such tools for any virus with a robust reverse genetics system

Evidence for Reduced Drug Susceptibility without Emergence of Major Protease Mutations following Protease Inhibitor Monotherapy Failure in the SARA Trial

Background Major protease mutations are rarely observed following failure with protease inhibitors (PI), and other viral determinants of failure to PI are poorly understood. We therefore characterized Gag-Protease phenotypic susceptibility in subtype A and D viruses circulating in East Africa following viral rebound on PIs. Methods Samples from baseline and treatment failure in patients enrolled in the second line LPV/r trial SARA underwent phenotypic susceptibility testing. Data were expressed as fold-change in susceptibility relative to a LPV-susceptible reference strain. Results We cloned 48 Gag-Protease containing sequences from seven individuals and performed drug resistance phenotyping from pre-PI and treatment failure timepoints in seven patients. For the six patients where major protease inhibitor resistance mutations did not emerge, mean fold-change EC50 to LPV was 4.07 fold (95% CI, 2.08–6.07) at the pre-PI timepoint. Following viral failure the mean fold-change in EC50 to LPV was 4.25 fold (95% CI, 1.39–7.11, p = 0.91). All viruses remained susceptible to DRV. In our assay system, the major PI resistance mutation I84V, which emerged in one individual, conferred a 10.5-fold reduction in LPV susceptibility. One of the six patients exhibited a significant reduction in susceptibility between pre-PI and failure timepoints (from 4.7 fold to 9.6 fold) in the absence of known major mutations in protease, but associated with changes in Gag: V7I, G49D, R69Q, A120D, Q127K, N375S and I462S. Phylogenetic analysis provided evidence of the emergence of genetically distinct viruses at the time of treatment failure, indicating ongoing viral evolution in Gag-protease under PI pressure. Conclusions Here we observe in one patient the development of significantly reduced susceptibility conferred by changes in Gag which may have contributed to treatment failure on a protease inhibitor containing regimen. Further phenotype-genotype studies are required to elucidate genetic determinants of protease inhibitor failure in those who fail without traditional resistance mutations whilst PI use is being scaled up globally