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This thesis is a summary of existing and upcoming publications, with a focus on high order methods in numerical relativity and general relativistic flows. The text is structed in five chapters. In the first three ones, the ADER-DG technique and its application to the Einstein-Euler equations is introduced. Novel formulations for both the Einstein equations in the 3+1 split as well as the general relativistic magnetohydrodynamics (GRMHD) had to be derived. The first order conformal and covariant Z4 formulation of Einstein equations (FO-CCZ4) is proposed and proven to be strongly hyperbolic. Together with the fluid equations of general relativistic magnetohydodynamics (GRMHD), a number of benchmark scenarios is presented to show both the correctness of the PDEs as well as the applicability of the numerical scheme.
As an application in astrophysics, a general-relativistic study of the treshold mass for a prompt-collapse of a binary neutron star merger with realistic nuclear equation of states has been carried out. A nonlinear universal relation between the treshold mass and the maximum compactness is found. Furthermore, by taking recent measurements of GW170817 into account, lower limits on the stellar radii for any mass can be given.
Furthermore, an (unpaired) work in quantum mechanical black hole engineering is presented. Higher dimensional extensions of generalized Heisenberg’s uncertainty principle (GUP) are studied. A number of new phenomenology is found, such as the existence of a conical singularity which mimics the effect of a gravitational monopole on short scale and that of a Schwarzschild black hole at a large scale, as well as oscillating Hawking temperatures which we call "lighthouse effect". All results are consistent with the self complete paradigm and a cold evaporation endpoint remnant.
Corneal topometric, aberrometric and biomechanical parameters in mucopolysaccharidosis patients
(2019)
Aims: To report corneal topometric and aberrometric values in mucopolysaccharidosis (MPS) and to investigate their correlation with biomechanical corneal parameters.
Methods: One randomly chosen eye of 20 MPS patients with no to moderate corneal clouding and one eye of 23 healthy controls with comparable age were prospectively included into this study. Corneal surface regularity was assessed by index of surface variance (ISV), -vertical asymmetry (IVA), -height asymmetry (IHA), -height decentration (IHD); keratoconus index (KI), central keratoconus index (CKI) and Zernike indices of anterior and posterior corneal surface using Scheimpflug imaging (Pentacam). Corneal resistance factor (CRF) and corneal hysteresis (CH) were assessed by Ocular Response Analyzer. Statistical analyses were performed using Mann-Whitney-Test and Spearman Correlation Coefficients.
Results: IVA, ISV, IHD, IHA, but not KI and CKI were significantly higher in MPS patients compared to age matched healthy controls. Spherical aberration and asphericity coefficients either at the anterior or at the posterior corneal surface differed significantly between both groups. The grade of the MPS-associated corneal opacity correlated significantly with ISV (rho = 0.52), IVA (rho = 0.54), IHA (rho = 0.57) and IHD (rho = 0.48). Density of the MPS-affected corneas correlated significantly with ISV (rho = 0.52), IVA (rho = 0.72), IHA (rho = 0.57), IHD (rho = 0.69), 3rd order horizontal trefoil aberration at the posterior (rho = 0.62) and anterior surface (rho = 0.48) as well as with CH (rho = 0.55) and CRF (rho = 0.57). Spherical aberration at the back surface correlated with CRF and CH in MPS and in healthy controls.
Conclusions: This is the first study analyzing shape of the corneal surface in MPS patients. Topometric indices of corneal asymmetry are significantly increased and correlate with MPS-related corneal opacity and density. Spherical aberration and asphericity coefficient at the front and at the back corneal surface differ significantly between MPS and healthy controls.
As central component of the peptide loading complex, the ABC transporter TAP is a key player in the adaptive immune response. By recognizing and translocating antigenic peptides derived from proteasomal degradation into the ER lumen it connects the processing of harmful intruders and the marking of an infected cell for elimination. This work focused mainly on the interaction between TAP and one of its viral inhibitors. Of the five known TAP inhibitors, ICP47 is the only one that is not anchored in the ER membrane and has a nonomolar affinity to TAP. These properties and its specific architecture make it an interesting protein engineering tool that can be used in a variety of ways to generate functionally arrested TAP complexes. Different lengths of ICP47 were chosen to map the optimal distance between the binding pocket and the N-terminal elbow helix of either TAP1 or TAP2. I demonstrated that the interaction of fused ICP47 with coreTAP inhibits antigen presentation via MHC I. Interestingly, the loss of MHC I surface expression only depended on the presence of the active domain and not on the length of the fused ICP47 fragments. Summarizing it can be said that TAP complexes containing an intact active domain of ICP47 successfully suppressed MHC I surface expression. Considering the MHC I surface expression in the use of free ICP47 fragments it was revealed that the active domain may not be sufficient. All free constructs, except the one that contains exclusively the active domain (1-35), were able to fully arrest peptide translocation, while the fragment 1-35 partially restored MHC I surface expression. This was the first evidence suggesting that more residues might be present in the ICP47 sequence that contribute to the interaction with TAP.
Further characterization of the ICP47-coreTAP fusion complexes comprised the determination of their thermostability and melting temperatures. The ICP47-coreTAP fusion complexes revealed a preferred orientation for ICP47. The ICP47(1-65) fragment led to a stable complex only if fused to TAP2, highlighting an interesting asymmetry at the TAP1/TAP2 interface, which suggests a shorter distance of the C-terminus of the stabilizing region to the elbow helix of TAP2 than of TAP1. The shorter fragments 1-35 and 1-50, and the ICP47 linker fragments, which inhibited, but did not trigger any thermostabilizing effects on TAP, revealed a second hint for the presence of other residues important for the ICP47/TAP interaction. To define the thermostability in more detail, the melting temperature of complexes with fused or freely bound ICP47 fragments was determined. Short fused fragments of ICP47 (residues 1-35 or 1-50) did not fully stabilize the TAP complex. Only ICP47 fragments longer than residues 1-50 raised the melting temperature to the full extent and led to a completely stabilized complex, suggesting that the critical melting temperature, which determines whether a complex is fully stabilized or not, is about 44-45°C. By comparing different ICP47 proteins from the herpesviral clade, I further noticed that the 21 residues following the active domain are highly conserved. The residues in this region were exchanged by glycines and alanines to study their impact on the thermostabilization of TAP. I demonstrated that several charged residues, an alanine rich, and a proline rich sequence were mainly responsible for the preservation of high melting temperatures. In summary, these findings reveal a dual inhibition mechanism of ICP47. While the active domain of ICP47 is wedged at the TAP1/2 interface and arrests the complex in an open-inward facing conformation, the highly conserved C-terminal region stabilizes the ICP47/TAP interaction and generates a thermostabilized TAP complex.
The second part of this thesis deals with two alternative expression and stabilization strategies for coreTAP, designed to provide a 1:1 ratio of TAP subunits during protein biosynthesis. Different glycine-serine (GS) linkers and a self cleaving 2A site were im- plemented into the TAP sequence and used for comparison with the classical coreTAP. Despite their functionality in antigen translocation, the utilization of GS linkers proved to be unsuitable due to low expression and scarce purification efficiency caused by the unfeasible orthogonal purification. In contrast, the use of a 2A site allowed orthogonal His10- and SBP-tag purification and yielded comparable amounts to the classical coreTAP. However, the ICP47/coreTAP interaction appeared to be hampered by the modified N-terminus of ICP47, due to the cleavage process.
The third and last part of this work deals with the Thermus thermophilus ABC trans- porter TmrAB, which was identified to be part of the same ABC subfamily as TAP. The structure of TmrAB is similar to that of coreTAP and includes a TMD and an NBD for each subunit. In comparison to TAP, TmrAB has a broader substrate range, but it can transport peptides, which are also transported by TAP. Since the natural substrate, and thus the actual function, of TmrAB has not yet been identified, it is counted among the multidrug resistance ABC transporters, from where it also takes its name. In this work, the question was investigated whether TmrAB can be utilized as a TAP substitute. To compare the function of TmrAB and TAP in a natural cell environment, the N-terminal domains of the TAP subunits called TMD0s were fused to the TmrAB subunits and subsequently expressed as different combinations. I found that especially the hybrid complexes containing a TMD0 of TAP2 were functional in terms of MHC I surface expression. Furthermore, TmrAB with TMD0 co-localized prevalently with the ER marker PDI while complexes without TMD0 did not co-localize. Interestingly, the analysis of the interaction with components of the PLC revealed that interaction with tapasin could only occur when a TMD0 was present. In turn, calreticulin, MHC I, and ERp57 were bound, regardless of the presence of a TMD0. It is remarkable that a bacterial protein, sharing only 27-30% sequence identity with human TAP is able to take over a key function of our adaptive immune system. Yet, TmrAB originates from a hyperthermophilic bacterium and may have assembly and folding difficulties that the human cell seeks to overcome by recruiting chaperones like calreticulin and ERp57. Although further experiments will be necessary to analyze the interaction of TmrAB with the PLC components in more detail, TmrAB appears to be homologous to coreTAP, not only in terms of sequence and structure, but also in terms of function.
We show that "quasi-dark" trading venues, i.e., markets with somewhat non-transparent trading mechanisms, are important parts of modern equity market structure alongside lit markets and dark pools. Using the European MiFID II regulation as a quasi-natural experiment, we find that dark pool bans lead to (i) volume spill-overs into quasi-dark trading mechanisms including periodic auctions and order internalization systems; (ii) little volume returning to transparent public markets; and consequently, (iii) a negligible impact on market liquidity and short-term price efficiency. These results show that quasi-dark markets serve as close substitutes for dark pools and consequently mitigate the effectiveness of dark pool regulation. Our findings highlight the need for a broader approach to transparency regulation in modern markets that takes into consideration the many alternative forms of quasi-dark trading.
We study the effects of market incompleteness on speculation, investor survival, and asset pricing moments, when investors disagree about the likelihood of jumps and have recursive preferences. We consider two models. In a model with jumps in aggregate consumption, incompleteness barely matters, since the consumption claim resembles an insurance product against jump risk and effectively reproduces approximate spanning. In a long-run risk model with jumps in the long-run growth rate, market incompleteness affects speculation, and investor survival. Jump and diffusive risks are more balanced regarding their importance and, therefore, the consumption claim cannot reproduce approximate spanning.
Die meisten Informationen, die uns über Frauen im Römischen Reich zur Verfügung stehen, wurden von Männern in literarischen Texten und Rechtsquellen aufgeschrieben. Ein Thema, mit dem das Leben von Frauen des Römischen Reichs näher beleuchtet werden kann, sind Rechtstexte, die sich mit Themen beschäftigen, in denen Frauen eine zentrale Rolle spielen.
Weite Teile der Bevölkerung des Römischen Reichs konnten im zweiten und dritten nach- christlichen Jahrhundert zwischen lokalen und römischen Rechtsangeboten wählen, um be- stimmte Probleme des Alltags zu lösen. Innerhalb des römischen Reichs entstanden zu dieser Zeit Rechtstexte unterschiedlicher Kulturen und verschiedene Rechtssysteme entwickelten unterschiedliche Lösungen für sich inhaltlich überschneidende Themenbereiche und Probleme.
In Rom verschriftlichten römische Juristen ihre Gedanken zu theoretischen Fallbeispielen und gewannen in großen Teilen des römischen Reichs Ansehen. Teile davon liegen uns heute als die im fünften und sechsten Jahrhundert zusammengetragenen Digesten vor. In der römischen Provinz Palaestina lebten jüdische Gelehrte, Rabbinen, die über Jahrhunderte mündlich weitergegebenes Wissen und entwickelte Rechtsbestimmungen aufschrieben, die als die Schriften der Mischna und Tosefta überliefert wurden.
In der Dissertation werden anhand der Lebensabschnitte einer Frau wie sie in der Mischna gezeichnet werden – die Kindheit und Jugend in der Familie des Vaters, das Leben als Ehefrau und das Leben als Witwe – untersucht, welche Handlungsspielräume sich für Frauen in den Texten ergeben und welche Erwartungen an Frauen gestellt werden. Die untersuchten Abschnitte der Mischna und Tosefta werden mit Texten aus den Digesten verglichen.
Obwohl die jüdischen und römischen Rechtstexte auf Traditionen beruhen, die unabhängig voneinander entstanden, beschäftigen sie sich mit den gleichen Themen, nämlich mit dem Erwachsenwerden von jungen Frauen, Fragen des Erbrechts, der Heirat und dem Ende von Ehen durch den Tod des Ehemannes oder eine Scheidung. Weiterhin wird deutlich, dass die Autoren der jüdischen Rechtstexte als Bewohner des Römischen Reichs sich mithilfe von Bestimmungen für das Verhalten verschiedener Mitglieder ihrer Gesellschaft zugleich als Teil der griechisch–römischen Welt sahen und sich von dieser durch eigene Traditionen abgrenzten. Aus der Sicht der Rabbinen konnte das Verhalten von Frauen ihre Gruppenzugehörigkeit nach außen sichtbar machen.