Hyperbolic Geometry With and Without Models

We explore the development of hyperbolic geometry in the 18th and early 19th following the works of Legendre, Lambert, Saccheri, Bolyai, Lobachevsky, and Gauss. In their attempts to prove Euclid\u27s parallel postulate, they developed hyperbolic geometry without a model. It was not until later in the 19th century, when Felix Klein provided a method (which was influenced by projective geometry) for viewing the hyperbolic plane as a disk in the Euclidean plane, appropriately named the Klein disk model . Later other models for viewing the hyperbolic plane as a subset of the Euclidean plane were created, namely the Poincaré disk model, Poincaré spherical model, and Poincaré upper halfplane model. In proving various theorems of hyperbolic geometry, the thesis focuses on the Klein disk model because this model allows us to view hyperbolic lines as Euclidean chords. We then establish the isomorphisms between the various models of hyperbolic geometry. And in the end, we consider a fifth model, the Minkowsky space-time model from the Special Theory of Relativity (STR), and its connection/isomorphism to the Klein disk and the Poincaré disk models of hyperbolic geometry

Versuche über die Entstehungsbedingungen peritonealer Adhäsionen nach Laparotomien

https://www.ester.ee/record=b4002474*es

Meletemata nonnulla de herba cannabis indicae et de lactucario : dissertatio inauguralis pharmacologica

http://tartu.ester.ee/record=b1918271~S1*es

Light-regulated adsorption and desorption of Chlamydomonas cells at surfaces

Microbial colonization of surfaces represents the first step towards biofilm formation, which is a recurring phenomenon in nature with beneficial and detrimental implications in technological and medical settings. Consequently, there is a current interest in elucidating the fundamental aspects of the initial stages of biofilm formation of microorganisms on solid surfaces. While most of the research is oriented to understand bacterial surface colonization, such observations at a fundamental level using photosynthetic microalgae are thus far elusive. Recent single-cell studies showed that the flagellar adhesion of Chlamydomonas is switched on in blue light and switched off under red light [Kreis et al., Nature Physics, 2018, 14, 45-49]. Here, we study this light-switchable surface association of C. reinhardtii on the population level and measure the kinetics of adsorption and desorption of suspensions of motile cells on glass surfaces using bright field optical microscopy. We observe that both processes exhibit a response lag relative to the time at which the blue- and red-light conditions are set and model this feature using time-delayed Langmuir-type kinetics. We find that cell adsorption occurs significantly faster than desorption, which we attribute to the protein-mediated molecular adhesion mechanism of the cells. Adsorption experiments using phototactically blind Chlamydomonas mutants demonstrate that phototaxis does not affect the cell adsorption kinetics. Hence, this method can be used as an assay for characterizing the dynamics of the surface colonization of microbial species exhibiting light-regulated surface adhesion.Comment: 10, pages, 6 figure

Lysine acetylation regulates moonlighting activity of the E2 subunit of the chloroplast pyruvate dehydrogenase complex in Chlamydomonas

The dihydrolipoamide acetyltransferase subunit DLA2 of the chloroplast pyruvate dehydrogenase complex (cpPDC) in the green alga Chlamydomonas reinhardtii has previously been shown to possess moonlighting activity in chloroplast gene expression. Under mixotrophic growth conditions, DLA2 forms part of a ribonucleoprotein particle (RNP) with the psbA mRNA that encodes the D1 protein of the photosystem II (PSII) reaction center. Here, we report on the characterization of the molecular switch that regulates shuttling of DLA2 between its functions in carbon metabolism and D1 synthesis. Determination of RNA‐binding affinities by microscale thermophoresis demonstrated that the E3‐binding domain (E3BD) of DLA2 mediates psbA‐specific RNA recognition. Analyses of cpPDC formation and activity, as well as RNP complex formation, showed that acetylation of a single lysine residue (K197) in E3BD induces the release of DLA2 from the cpPDC, and its functional shift towards RNA binding. Moreover, Förster resonance energy transfer microscopy revealed that psbA mRNA/DLA2 complexes localize around the chloroplast's pyrenoid. Pulse labeling and D1 re‐accumulation after induced PSII degradation strongly suggest that DLA2 is important for D1 synthesis during de novo PSII biogenesis.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

The <em>Bacillus</em> BioBrick Box:Generation and evaluation of essential genetic building blocks for standardized work with Bacillus subtilis

Background: Standardized and well-characterized genetic building blocks are a prerequisite for the convenient and reproducible assembly of novel genetic modules and devices. While numerous standardized parts exist for Escherichia coli, such tools are still missing for the Gram-positive model organism Bacillus subtilis. The goal of this study was to develop and thoroughly evaluate such a genetic toolbox. Results: We developed five BioBrick-compatible integrative B. subtilis vectors by deleting unnecessary parts and removing forbidden restriction sites to allow cloning in BioBrick (RFC10) standard. Three empty backbone vectors with compatible resistance markers and integration sites were generated, allowing the stable chromosomal integration and combination of up to three different devices in one strain. In addition, two integrative reporter vectors, based on the lacZ and luxABCDE cassettes, were BioBrick-adjusted, to enable beta-galactosidase and luciferase reporter assays, respectively. Four constitutive and two inducible promoters were thoroughly characterized by quantitative, time-resolved measurements. Together, these promoters cover a range of more than three orders of magnitude in promoter strength, thereby allowing a fine-tuned adjustment of cellular protein amounts. Finally, the Bacillus BioBrick Box also provides five widely used epitope tags (FLAG, His(10), cMyc, HA, StrepII), which can be translationally fused N- or C-terminally to any protein of choice. Conclusion: Our genetic toolbox contains three compatible empty integration vectors, two reporter vectors and a set of six promoters, two of them inducible. Furthermore, five different epitope tags offer convenient protein handling and detection. All parts adhere to the BioBrick standard and hence enable standardized work with B. subtilis. We believe that our well-documented and carefully evaluated Bacillus BioBrick Box represents a very useful genetic tool kit, not only for the iGEM competition but any other BioBrick-based project in B. subtilis

Altered N-glycan composition impacts flagella-mediated adhesion in Chlamydomonas reinhardtii

For the unicellular alga Chlamydomonas reinhardtii, the presence of N-glycosylated proteins on the surface of two flagella is crucial for both cell-cell interaction during mating and flagellar surface adhesion. However, it is not known whether only the presence or also the composition of N-glycans attached to respective proteins is important for these processes. To this end, we tested several C. reinhardtii insertional mutants and a CRISPR/Cas9 knockout mutant of xylosyltransferase 1A, all possessing altered N-glycan compositions. Taking advantage of atomic force microscopy and micropipette force measurements, our data revealed that reduction in N-glycan complexity impedes the adhesion force required for binding the flagella to surfaces. This results in impaired polystyrene bead binding and transport but not gliding of cells on solid surfaces. Notably, assembly, intraflagellar transport, and protein import into flagella are not affected by altered N-glycosylation. Thus, we conclude that proper N-glycosylation of flagellar proteins is crucial for adhering C. reinhardtii cells onto surfaces, indicating that N-glycans mediate surface adhesion via direct surface contact

Zum Verhältnis von Gehalt und Gestalt in klassischen chinesischen Gedichten

There is more to the prosodic and tonal features in Tang-dynasty poems than their mere use in the formal classification of individual texts as either new-style regulated verse (lüshi, jueju) or old-style verse such as the music bureau poem (yuefu). The prosodic and tonal patterns of a poem can also be related to its contents and its expressive qualities. Therefore, the close analysis and highlighting of such acoustic effects can support textual interpretation. The present paper scrutinizes a small sample of seven poems on the topic of Mount Wu (“Wushan gao”), comprising five yuefu and two jueju poems. It points out the deliberate use of tonal and formal peculiarities also in irregular poems. The significant tonal elements include such diverse features as the structuring function of prosodic patterns in longer poems, word repetition or a “missing” verse. Moreover, for instance, clusters of uneven tones are analyzed as expressing strong emotions. Creative elements such as these should be taken into consideration in reading, analyzing and translating classical Chinese poetry

Hyperbolic Geometry With and Without Models

We explore the development of hyperbolic geometry in the 18th and early 19th following the works of Legendre, Lambert, Saccheri, Bolyai, Lobachevsky, and Gauss. In their attempts to prove Euclid\u27s parallel postulate, they developed hyperbolic geometry without a model. It was not until later in the 19th century, when Felix Klein provided a method (which was influenced by projective geometry) for viewing the hyperbolic plane as a disk in the Euclidean plane, appropriately named the Klein disk model . Later other models for viewing the hyperbolic plane as a subset of the Euclidean plane were created, namely the Poincaré disk model, Poincaré spherical model, and Poincaré upper halfplane model. In proving various theorems of hyperbolic geometry, the thesis focuses on the Klein disk model because this model allows us to view hyperbolic lines as Euclidean chords. We then establish the isomorphisms between the various models of hyperbolic geometry. And in the end, we consider a fifth model, the Minkowsky space-time model from the Special Theory of Relativity (STR), and its connection/isomorphism to the Klein disk and the Poincaré disk models of hyperbolic geometry