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JLUpub bietet Mitgliedern und Angehörigen der Universität die Möglichkeit neben wissenschaftlichen Dokumenten auch Forschungsdaten elektronisch zu veröffentlichen und dauerhaft zugänglich zu machen. Alle Veröffentlichungen erhalten einen Digital Object Identifier (DOI) und werden über nationale und internationale Bibliothekskataloge sowie Suchmaschinen nachgewiesen und auffindbar.
Neue Veröffentlichungen:
Der zweite Frühling - Renaissance und Mathematik
(2025-11-07) Kafitz, Willi
Renaissance steht für „Wiedergeburt“. Es ist einerseits eine Rückbesinnung auf geistige Errungenschaften der Antike, aber auch ein Aufbruch nach dem Mittelalter hin zur Neuzeit. Die griechische Philosophie inklusive der griechischen, arabischen und persischen Mathematik wurde wiederentdeckt. Dazu bedurfte es einen langen historischen Weg bis in das 2. nachchristliche Jahrtausend und günstigen Rahmenbedingungen auf dem west-östlichen, eurasischen Kontinent. Schließlich fallen in diese Epoche bedeutende Entwicklungen, die diese Zeit so bedeutsam für die Kunst- und Kulturgeschichte machen und den Weg zur Neuzeit ebneten. Dazu gehören die Gründung von unabhängigen Universitäten, die lateinische Sprache als Grundlage der europaweiten Gelehrtensprache, die Erfindung des Buchdrucks mit beweglichen Lettern mit einer entsprechenden Papierindustrie als Multiplikatoreffekt für die rasante Verbreitung neuer Ideen, die Zentralperspektive in der bildenden Kunst mit ihrer geometrischen Grundlage, die Verbreitung der indisch-arabischen Ziffern und der Null, die Urbanisierung mit ihrem Übergang von der Natural- zur Geldwirtschaft und ein neues Menschenbild, das von humanistischen Gelehrten in Anknüpfung an antike Vorbilder propagiert wurde.
Die Mathematik erlebte in dieser Epoche eine rasche Evolution. Auch hier war die griechische Mathematik Ausgangspunkt. Euklid lieferte auf Basis weniger Axiome und Definitionen die grundsätzliche und bis heute gültige Logik von Voraussetzung, Behauptung und Beweis. Archimedes vermittelte grundlegende mathematische Techniken, Apollonios von Perge zeigte mit seinen Kegelschnitten, dass der Kreis nicht das Maß aller Dinge ist und wies damit den Weg für ein neues heliozentrisches kopernikanisches Weltbild, in dem die Planeten auf Ellipsenbahnen die Sonne umkreisen. Die neuen Ziffern und die Null wurden zuerst von Leonardo di Pisa, genannt Fibonacci, propagiert. Sein Liber abaci schrieb Mathematikgeschichte. Johannes Regiomontanus hatte trotz seines frühen Todes als Mathematiker, Astronom und Mathematik-Verleger eine herausragende Bedeutung. Seine Werke begleiteten Entdecker wie Christoph Columbus zu neuen Kontinenten. Gerolamo Cardano befruchtete gleich mehrere mathematische Disziplinen; gemeinsam mit Michael Stifel begründete er eine neue Algebra, die über arabische Vorbilder hinausging. Luca Pacioli bündelte das mathematische Wissen seiner Zeit. Er war Lehrer und Freund von Leonardo da Vinci, der sein Buch über den Goldenen Schnitt illustrierte. Er gilt als wichtiger Förderer der doppelten Buchführung. Die Zentralperspektive in der Kunst geht auf Brunelleschi zurück, den Erbauer der mächtigen Kuppel des Doms zu Florenz, der Renaissance-Metropole in der Toscana. Nördlich der Alpen prägt Albrecht Dürer mit viel mathematischem Sachverstand diese neue Kunstrichtung.
Visualization of parasite–host interactions using atmospheric-pressure MALDI mass spectrometry imaging
(2025) Wiedemann, Katja Rebecca
Endoparasites completely rely on the host organism to survive, once they entered their host. Though, hosts do not capitulate but try to protect themselves against potential damage induced by the parasite. Taking these two effects together, leads to measurable changes in the composition and lateral distribution of metabolites in host tissue (upon infection). In order to find novel drug targets, further knowledge on such changes is crucial. Using mass spectrometry imaging to investigate host-parasite interactions in vivo in an untargeted fashion whilst maintaining the lateral information of metabolites is a powerful approach. Therefore, two distinct models were studied: Schistosoma-mansoni-egg-containing liver samples of hamsters infected with the blood flukes, and bovine skin tissue, showing cysts formed by the apicomplexan parasite Besnoitia besnoiti.
For both parasite-host systems, characteristic infection markers were found with significant changes in signal intensities.
Additionally, by benefiting from the fact that lateral information is kept during mass spectrometry imaging analysis, the lateral distribution of infection markers was revealed. For some of them, co-localized biological structures were observed in optical images of the analyzed tissues.
During schistosomiasis, Schistosoma mansoni eggs are deposited in the hamster liver, leading to granuloma formation around the eggs. The high lateral resolution of the AP-SMALDI5 AF ion source enabled the unambiguous visualization of both, eggs (100 µm to 200 µm in diameter) and local abundance changes of lipids in granulomatous tissue compared to healthy hepatic tissue. Guided by results obtained with liquid chromatography-tandem mass spectrometry, we observed a substructure in formed granulomas by applying mass spectrometry imaging. For example, ether-phosphatidyl-ethanolamines were mainly found in the outer part of the granulomas. In total, 372 substances were found to be significantly changed due to infection.
In the skin of Besnoitia besnoiti-infected cattle, MS images showed both, enrichment and depletion of several lipid species inside parasite-formed cysts. Due to the high lateral resolution at 2 µm pixel size, some of them were even found to be characteristic for the thin cyst walls. Applying multiple MSI methodologies, cysts were further characterized by on-tissue tandem mass spectrometry as well as 3-dimensional imaging. Overall, 552 ions were found to be altered due to infection.
Overall, gained insights into parasite-host interactions can now be used as starting points for further metabolism studies and also serve as potential drug targets.
For both parasite-host systems, characteristic infection markers were found with significant changes in signal intensities.
Additionally, by benefiting from the fact that lateral information is kept during mass spectrometry imaging analysis, the lateral distribution of infection markers was revealed. For some of them, co-localized biological structures were observed in optical images of the analyzed tissues.
During schistosomiasis, Schistosoma mansoni eggs are deposited in the hamster liver, leading to granuloma formation around the eggs. The high lateral resolution of the AP-SMALDI5 AF ion source enabled the unambiguous visualization of both, eggs (100 µm to 200 µm in diameter) and local abundance changes of lipids in granulomatous tissue compared to healthy hepatic tissue. Guided by results obtained with liquid chromatography-tandem mass spectrometry, we observed a substructure in formed granulomas by applying mass spectrometry imaging. For example, ether-phosphatidyl-ethanolamines were mainly found in the outer part of the granulomas. In total, 372 substances were found to be significantly changed due to infection.
In the skin of Besnoitia besnoiti-infected cattle, MS images showed both, enrichment and depletion of several lipid species inside parasite-formed cysts. Due to the high lateral resolution at 2 µm pixel size, some of them were even found to be characteristic for the thin cyst walls. Applying multiple MSI methodologies, cysts were further characterized by on-tissue tandem mass spectrometry as well as 3-dimensional imaging. Overall, 552 ions were found to be altered due to infection.
Overall, gained insights into parasite-host interactions can now be used as starting points for further metabolism studies and also serve as potential drug targets.
Dynamic critical behavior of hot and dense QCD matter from the real-time functional renormalization group
(2025) Roth, Johannes
In this work, we study dynamic critical behavior of hot and dense QCD matter near second-order phase transitions. We consider the chiral phase transition for two flavors of massless quarks, as well as the conjectured critical point at physical quark masses and finite baryon chemical potential. These are plausibly in the same dynamic universality classes as a four-component Heisenberg antiferromagnet and the liquid-gas critical point of a pure fluid, respectively, whose critical dynamics are described by Models G and H in the Halperin-Hohenberg classification.
Our central tool in this work is a real-time generalization of the functional renormalization group (FRG) based on the Schwinger-Keldysh contour. Starting with Model G, we develop a novel formulation of the real-time FRG which preserves all relevant symmetries of dynamical systems with reversible mode couplings. We show that associated Ward identities imply exact statements about the FRG flow, including the non-renormalization of the mode-coupling constant, and the independence of the static free energy on the dynamics. We show that the formalism reproduces the non-trivial value z=d/2 for the dynamic critical exponent in d spatial dimensions, and we compute a novel scaling function which describes the universal temperature and momentum dependence of the iso-vector and iso-axial-vector charge diffusion coefficient in the chiral limit.
As a next step, we adapt this novel FRG technique to Model H. We derive analytical expressions for dynamic critical exponents that describe the universal power-law divergence of the heat conductivity and the shear viscosity near the QCD critical point. As a central result, we find that the critical exponent of the shear viscosity as a function of d exhibits a maximum in the range 2 < d < 4 and approaches zero for d=2 spatial dimensions. We verify the robustness of this result by considering improved truncations of the static free energy. In parallel, we emphasize the structural similarities and differences with Model G by comparing the fixed-point structures of both models and discuss the presence/absence of weak and strong dynamic scaling relations.
While the leading universal scaling behavior can be described by Models G and H, non-universal corrections require a real-time description of the microscopic dynamics. In this regard, we consider a real-time formulation of the quark-meson model as a particular low-energy effective theory for QCD. As a first application, we study the influence of bosonic dissipation on the phase diagram and the excitation spectrum. We find that dissipation has a non-vanishing but quantitatively small effect on equilibrium observables. The influence on the excitation spectrum, on the other hand, can be drastic, as (over-)damping potentially turns weakly-damped quasiparticles into purely relaxational excitations.
Our central tool in this work is a real-time generalization of the functional renormalization group (FRG) based on the Schwinger-Keldysh contour. Starting with Model G, we develop a novel formulation of the real-time FRG which preserves all relevant symmetries of dynamical systems with reversible mode couplings. We show that associated Ward identities imply exact statements about the FRG flow, including the non-renormalization of the mode-coupling constant, and the independence of the static free energy on the dynamics. We show that the formalism reproduces the non-trivial value z=d/2 for the dynamic critical exponent in d spatial dimensions, and we compute a novel scaling function which describes the universal temperature and momentum dependence of the iso-vector and iso-axial-vector charge diffusion coefficient in the chiral limit.
As a next step, we adapt this novel FRG technique to Model H. We derive analytical expressions for dynamic critical exponents that describe the universal power-law divergence of the heat conductivity and the shear viscosity near the QCD critical point. As a central result, we find that the critical exponent of the shear viscosity as a function of d exhibits a maximum in the range 2 < d < 4 and approaches zero for d=2 spatial dimensions. We verify the robustness of this result by considering improved truncations of the static free energy. In parallel, we emphasize the structural similarities and differences with Model G by comparing the fixed-point structures of both models and discuss the presence/absence of weak and strong dynamic scaling relations.
While the leading universal scaling behavior can be described by Models G and H, non-universal corrections require a real-time description of the microscopic dynamics. In this regard, we consider a real-time formulation of the quark-meson model as a particular low-energy effective theory for QCD. As a first application, we study the influence of bosonic dissipation on the phase diagram and the excitation spectrum. We find that dissipation has a non-vanishing but quantitatively small effect on equilibrium observables. The influence on the excitation spectrum, on the other hand, can be drastic, as (over-)damping potentially turns weakly-damped quasiparticles into purely relaxational excitations.