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Dissertation
Generalized Involutive Bases and Their Induced Free Resolutions
(2022-05)
In this thesis, we generalize several types of involutive and marked bases for ideals in quotient rings of commutative polynomial rings. We apply these new types of bases to the analysis of infinite free resolutions and of Hilbert schemes defined over certain types of quotient rings. We are mostly concerned with Pommaret and Janet bases; the marked bases we consider are marked over monomial submodules that are quasi-stable, i.e., that possess finite Pommaret bases.
Involutive bases of the types we consider induce ...
Dissertation
Regulatory mechanisms of Protein kinase A - Isoform mediated fine-tuning
(2023)
cAMP-dependent protein kinase (PKA) is a crucial part in eukaryotic signal transduction and controls biological processes. With a multitude of substrates, a great variety of cellular functions are regulated by PKA. Regulation of metabolism, cell growth and -differentiation, conductivity of ion channels, movement of sperm cells, embryonic development, neuroplasticity as well as conversion of short- to long-term memory are just examples for the many tasks of the kinase. To achieve and coordinate these diverse functions, ...
Dissertation
Populationsgenetik und Phylogeographie des Großen Immergrüns (Vinca major L.; Apocynaceae) im autochthonen vs. allochthonen Verbreitungsgebiet
(2023-04-21)
Populationsgenetik und Phylogeographie des Großen Immergrüns (Vinca major L.; Apocynaceae) im autochthonen vs. allochthonen Verbreitungsgebiet
Das Große Immergrün (Vinca major L., Apocynaceae) stammt aus dem Mittelmeerraum und wurde durch den Menschen als Nutz-, Arznei- und Zierpflanze sowie wegen seiner mythologischen Bedeutung in zahlreiche zuvor unbesiedelte Gebiete verschleppt. In einigen Regionen des allochthonen Areals (Australien, Neuseeland, USA) gilt V. major als invasiv und wird massiv bekämpft. Ziel ...
Dissertation
Symmetrien von Differentialgleichungen via Vessiot-Theorie
(2021-04)
Die übliche Definition des Symmetriebegriffs einer Differentialgleichung lautet wie folgt: Symmetrien sind Transformationen, die Lösungen wieder in Lösungen überführen. Modelliert man Differentialgleichungen als Untermannigfaltigkeiten eines Jetbündels, so lassen sich zwei Arten von Symmetrien unterscheiden: innere und äußere. Der erste Fall entspricht einer Transformation, die ausschließlich auf der Differentialgleichung definiert ist. Im zweiten Fall ist die betrachtete Transformation auf dem gesamten umgebenden ...
Konferenzveröffentlichung
Propagation and branching strategies for job shop scheduling minimizing the weighted energy consumption
(2023)
We consider a job shop scheduling problem with time windows, flexible energy prices, and machines whose energy consumption depends on their operational state (offline, ramp-up, setup, processing, standby or ramp-down). The goal is to find a valid schedule that minimizes the overall energy cost. To solve this problem to optimality, we developed a branch-and-bound algorithm based on a time-indexed integer linear programming (ILP) formulation, which uses binary variables that describe blocks spanning multiple inactive ...
Konferenzveröffentlichung
Identifying critical demand periods in capacity planning for networks including storage
(2023)
We consider a capacity planning problem for networks including storage. Given a graph and a time series of demands and supplies, we seek for integer link and storage capacities that permit a single commodity flow with valid storage in- and outtakes over all time steps. This problem arises, for example, in power systems planning, where storage can be used to buffer peaks of varying supplies and demands. For typical time series spanning a full year at hourly resolution, this leads to huge optimization models. To reduce ...
Dissertation
Pathogenic Mutations in Catalytic Subunit Isoforms of the cAMP-Dependent Protein Kinase
(2023)
Protein kinase A (PKA) is an integral part in a myriad of cellular pathways and a main effector of the second messenger cAMP. Since its discovery in the late 1960s, PKA has become one of the best-studied eukaryotic protein kinases in terms of enzymatic and structural features. Pathological implications of PKA have just started to emerge. There are three main isoforms (α, β, γ) of the catalytic subunit of PKA (PKA-C) which constitute a holoenzyme (R2C2) by association with a regulatory subunit (PKA-R) dimer. While ...
Dissertation
Asymmetric magnetization reversal processes in exchange-biased microstructures
(2023)
Over the last decades, the exchange bias (EB) effect has captured the attention of the research community striving for high-density logic memory devices and sensitive sensor technologies based on bi-, multilayered, or patterned magnetic thin film systems. Macroscopically, the EB manifests in a horizontal shift of the ferromagnetic remagnetization loop and an enhancement of the coercivity, both connected to the induced unidirectional anisotropy (UDA) at the exchange-coupled ferromagnetic/antiferromagnetic interface. ...
Dissertation
Generation Human Body Motion by the Centralized Networks
(2023)
The main goal of the thesis is to describe and study reduced models for efficient simulations of human body motions (HBM). To this end, we propose new coupled oscillator models, which are networks of dynamically coupled elements. These networks consist of a few of centers and many satellites. The centers evolve in time as periodical oscillators with different frequencies. The satellite states are defined via center states by a radial basis function (RBF) networks. To simulate different motions we adjust the parameter ...
Dissertation
Ultraschnelle kohärente Kontrollmethoden für die nichtlineare Mikroskopie und Spektroskopie
(2023-11-28)
Ultrakurze Laserpulse im Nanojoule-Energiebereich auf der Femto- bis Pikosekunden-Zeitskala ermöglichen die Erzeugung immenser Feldstärken bei Fokussierung auf wenige Quadratmikrometer Fläche. In diesem Szenario wirken starke Kräfte auf die Elektronensysteme von Atomen und Molekülen im Fokus ein, so dass sich die linearen optischen Eigenschaften von Stoffen ändern können – nichtlineare Eigenschaften treten zutage. Mit einem Pulsformer kann auf die breiten Spektren ultrakurzer Laserpulse per spektraler Phasenmodulation ...