Une introduction a la thkorie des figures: la géometrie de E.S. Fedorov

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Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Long-term response to second-line afatinib in patients with recurrent or metastatic head and neck squamous cell carcinoma (R/M HNSCC): Analysis of the LUX-Head & Neck 1 (LHN1) trial

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Comparative genomics of Dothideomycete fungi

Fungi are a diverse group of eukaryotic micro-organisms particularly suited for comparative genomics analyses. Fungi are important to industry, fundamental science and many of them are notorious pathogens of crops, thereby endangering global food supply. Dozens of fungi have been sequenced in the last decade and with the advances of the next generation sequencing, thousands of new genome sequences will become available in coming years. In this thesis I have used bioinformatics tools to study different biological and evolutionary processes in various genomes with a focus on the genomes of the Dothideomycetefungi Cladosporium fulvum, Dothistroma septosporumand Zymoseptoria tritici. Chapter 1introduces the scientific disciplines of mycology and bioinformatics from a historical perspective. It exemplifies a typical whole-genome sequence analysis of a fungal genome, and focusses in particular on structural gene annotation and detection of transposable elements. In addition it shortly reviews the microRNA pathway as known in animal and plants in the context of the putative existence of similar yet subtle different small RNA pathways in other branches of the eukaryotic tree of life. Chapter 2addresses the novel sequenced genomes of the closely related Dothideomyceteplant pathogenic fungi Cladosporium fulvumand Dothistroma septosporum. Remarkably, it revealed occurrence of a surprisingly high similarity at the protein level combined with striking differences at the DNA level, gene repertoire and gene expression. Most noticeably, the genome of C. fulvumappears to be at least twice as large, which is solely attributable to a much larger content in repetitive sequences. Chapter 3describes a novel alignment-based fungal gene prediction method (ABFGP) that is particularly suitable for plastic genomes like those of fungi. It shows excellent performance benchmarked on a dataset of 7,000 unigene-supported gene models from ten different fungi. Applicability of the method was shown by revisiting the annotations of C. fulvumand D. septosporumand of various other fungal genomes from the first-generation sequencing era. Thousands of gene models were revised in each of the gene catalogues, indeed revealing a correlation to the quality of the genome assembly, and to sequencing strategies used in the sequencing centres, highlighting different types of errors in different annotation pipelines. Chapter 4focusses on the unexpected high number of gene models that were identified by ABFGP that align nicely to informant genes, but only upon toleration of frame shifts and in-frame stop-codons. These discordances could represent sequence errors (SEs) and/or disruptive mutations (DMs) that caused these truncated and erroneous gene models. We revisited the same fungal gene catalogues as in chapter 3, confirmed SEs by resequencing and successively removed those, yielding a high-confidence and large dataset of nearly 1,000 pseudogenes caused by DMs. This dataset of fungal pseudogenes, containing genes listed as bona fide genes in current gene catalogues, does not correspond to various observations previously done on fungal pseudogenes. Moreover, the degree of pseudogenization showing up to a ten-fold variation for the lowest versus the highest affected species, is generally higher in species that reproduce asexually compared to those that in addition reproduce sexually. Chapter 5describes explorative genomics and comparative genomics analyses revealing the presence of introner-like elements (ILEs) in various Dothideomycetefungi including Zymoseptoria triticiin which they had not identified yet, although its genome sequence is already publicly available for several years. ILEs combine hallmark intron properties with the apparent capability of multiplying themselves as repetitive sequence. ILEs strongly associate with events of intron gain, thereby delivering in silico proof of their mobility. Phylogenetic analyses at the intra- and inter-species level showed that most ILEs are related and likely share common ancestry. Chapter 6provides additional evidence that ILE multiplication strongly dominates over other types of intron duplication in fungi. The observed high rate of ILE multiplication followed by rapid sequence degeneration led us to hypothesize that multiplication of ILEs has been the major cause and mechanism of intron gain in fungi, and we speculate that this could be generalized to all eukaryotes. Chapter 7describes a new strategy for miRNA hairpin prediction using statistical distributions of observed biological variation of properties (descriptors) of known miRNA hairpins. We show that the method outperforms miRNA prediction by previous, conventional methods that usually apply threshold filtering. Using this method, several novel candidate miRNAs were assigned in the genomes of Caenorhabditis elegansand two human viruses. Although this chapter is not applied on fungi, the study does provide a flexible method to find evidence for existence of a putative miRNA-like pathway in fungi. Chapter 8provides a general discussion on the advent of bioinformatics in mycological research and its implications. It highlights the necessity of a prioriplanning and integration of functional analysis and bioinformatics in order to achieve scientific excellence, and describes possible scenarios for the near future of fungal (comparative) genomics research. Moreover, it discusses the intrinsic error rate in large-scale, automatically inferred datasets and the implications of using and comparing those.</p

Une introduction a la thkorie des figures: la géometrie de E.S. Fedorov

Peer Reviewe