In this thesis, I establish new relations between quantum information measures in a two-dimensional CFT and geometric objects in a three-dimensional AdS space employing the AdS/CFT correspondence. I focus on two quantum information measures: the computational cost of quantum circuits in a CFT and Berry phases in two entangled CFTs. In particular, I show that these quantities are associated with geometric objects in the dual AdS space.

The platelet cytoskeleton ensures normal size and discoid shape under resting conditions and undergoes immediate reorganization in response to changes in the extracellular environment through integrin-based adhesion sites, resulting in actomyosin-mediated contractile forces. Mutations in the contractile protein non-muscle myosin heavy chain IIA display, among others, macrothrombocytopenia and a mild to moderate bleeding tendency in human patients. It is insufficiently understood which factors contribute to the hemostatic defect found in MYH9-related disease patients. Therefore, a better understanding of the underlying biophysical mechanisms in thrombus formation and stabilization is warranted. This thesis demonstrates that an amino acid exchange at the positions 702, 1424 and 1841 in the heavy chain of the contractile protein non-muscle myosin IIA, caused by heterozygous point mutations in the gene, resulted in macrothrombocytopenia and increased bleeding in mice, reflecting the clinical hallmark of the MYH9-related disease in human patients. Basic characterization of biological functions of Myh9 mutant platelets revealed overall normal surface glycoprotein expression and agonist-induced activation when compared to wildtype platelets. However, myosin light chain phosphorylation after thrombin-activation was reduced in mutant platelets, resulting in less contractile forces and a defect in clot retraction. Altered biophysical characteristics with lower adhesion and interaction forces of Myh9 mutant platelets led to reduced thrombus formation and stability. Platelets from patients with the respective mutations recapitulated the findings obtained with murine platelets, such as impaired thrombus formation and stiffness. Besides biological and biophysical characterization of mutant platelets from mice and men, treatment options were investigated to prevent increased bleeding caused by reduced platelet forces. The antifibrinolytic agent tranexamic acid was applied to stabilize less compact thrombi, which are presumably more vulnerable to fibrinolysis. The hemostatic function in Myh9 mutant mice was improved by interfering with the fibrinolytic system. These results show the beneficial effect of fibrin stabilization to reduce bleeding in MYH9-related disease.

The hunt for topological materials is one of the main topics of recent research in condensed matter physics. We analyze the 4-band Luttinger model, which considers the total angular momentum \(j = 3/2\) hole states of many semiconductors. Our analysis shows that this model hosts a wide array of topological phases and allows analytical calculations of the related topological surface states. The existence of these surface states is highly desired due to their strong protection against perturbations. In the first part of the thesis, we predict the existence of either one or two two-dimensional (2D) surface states of topological origin in the three-dimensional (3D) quadratic-node semimetal phase of the Luttinger model, called the Luttinger semimetal phase. We associate the origin of these states with the inverted order of s and p-orbital states in the band structure and approximate chiral symmetry around the node. Hence, our findings are essential for many materials, including HgTe, α-Sn, and iridate compounds. Such materials are often modified with strain engineering by growing the crystal on a substrate with a different lattice constant, which adds a deformation potential to the electrons. While tensile strain is often used to drive such materials into a gapped topological insulator regime, we apply compressive strain to induce a topological semimetal regime. Here, we differentiate between Dirac and Weyl semimetals based on inversion and time-reversal symmetry being simultaneously present or not. One major part of this thesis is the theoretical study of the evolution of the Luttinger semimetal surface states in these topological semimetal phases. The relative strength of the compressive strain and typical bulk inversion asymmetry (BIA) terms allow the definition of a symmetry hierarchy in the system. The cubic symmetric \(O_h\) Luttinger model is the highest symmetry low-energy parent model. Since the BIA terms in the Weyl semimetal phase are small in most materials, we find a narrow energy and momentum range around the Weyl points where the surface states form Fermi arcs between two Weyl nodes with opposite chirality. Consequently, we see 2D momentum planes between the Weyl points, which can be considered as effective 2D Chern insulators with chiral edge states connecting the valence and conduction band in the bulk gap. Exceeding the range of the BIA terms, the compressive strain becomes dominating, and the system behaves like a Dirac semimetal with two doubly degenerate linear Dirac nodes in the band structure. For energies larger than the compressive strain strength, the quadratic terms in the Luttinger model dominate and surface band structure is indistinguishable from an unperturbed Luttinger semimetal. To conclude this symmetry hierarchy, we analyze the limit of the Luttinger model when the remote \(j = 1/2\) electron states show a considerable hybridization with the \(j = 3/2\) hole states around the Fermi level. Here, the Luttinger model is not valid anymore and one needs to consider more complicated models, like the 6-band Kane Hamiltonian. In the second part of this thesis, we analyze theoretically two different setups for s-wave superconductivity proximitized \(j = 3/2\) particles in Luttinger materials under a magnetic field. First, we explore a one-dimensional wire setup, where the intrinsic BIA of inversion asymmetric crystals opens a topological gap in the bulk states. In contrast to wires, modeled by a quadratic dispersion with Rashba or Dresselhaus spin-orbit coupling, we find two topological phase transitions due to the different effects of magnetic fields to \(|j_z| = 3/2\) heavy-hole (HH) and \(|j_z| = 1/2\) light-hole (LH) states. Second, we discuss a two-dimensional Josephson junction setup, where we find Andreev-bound states inside the superconducting gap. Here, the intrinsic spin-orbit coupling of the Luttinger model is sufficient to open a topological gap even in the presence of inversion symmetry. This originates from the hybridization of the light and heavy-hole bands in combination with the superconducting pairing. Consequently, both setups can form Majorana-bound states at the boundaries of the system. The existence of these states are highly relevant in the scientific community due to their nonabelian braiding statistics and stability against decoherence, making them a prime candidate for the realization of topological quantum computation. Majorana-bound states form at zero energy and are protected by the topological gap. We predict that our findings of the topological superconductor phase of the Luttinger model are valid for both semimetal and metal phases. Hence, our study is additionally relevant for metallic systems, like p-doped GaAs. This opens a new avenue for the search for topological superconductivity.

The human body has very good self-healing capabilities for numerous different injuries to a variety of different tissues. This includes the main human mechanical framework, the skeleton. The skeleton is limited in its healing without additional aid by medicine mostly by the defect size. When the defect reaches a size above 2.5 cm the regeneration of the defect ends up faulty. Here is where implants, defect fillers and other support approaches developed in medicine can help the body to heal the big defect still successfully. Usually sturdy implants (auto-/allo-/xenogenic) are implanted in the defect to bridge the distance, but for auto- and allogenic implants a suitable donor site must be found and for all sources the implant needs to be shaped into the defect specific site to ensure a perfect fit, the best support and good healing. This shaping is very time consuming and prone to error, already in the planning phase. The use of a material that is moldable and sets in the desired shape shortly after applying negates these disadvantages. Cementitious materials offer exactly this property by being in a pasty stage after the powder and liquid components have been mixed and the subsequently hardening to a solid implant. These properties also enable the extrusion, and therefore may also enable the injection, of the cement via a syringe in a minimal invasive approach. To enable a good injection of the cement modifications are necessary. This work aimed to modify commonly used calcium phosphate-based cement systems based on α-TCP (apatitic) and β-TCP (brushitic). These have been modified with sodium phytate and phytic acid, respectively. Additionally, the α-TCP system has been modified with sodium pyrophosphate, in a second study, to create a storable aqueous paste that can be activated once needed with a highly concentrated sodium orthophosphate solution. The powder phase of the α-TCP cement system consisted of nine parts α-TCP and one part CDHA. These were prepared to have different particle sizes and therefore enable a better powder flowability through the bimodal size distribution. α-TCP had a main particle size of 20 μm and CDHA of 2.6 μm. The modification with sodium phytate led to an adsorption of phytate ions on the surface of the α-TCP particles, where they started to form complexes with the Ca2+ ions in the solution. This adsorption had two effects. The first was to make the calcium ions unavailable, preventing supersaturation and ultimately the precipitation of CDHA what would lead to the cement hardening. The second was the increase of the absolute value of the surface charge, zeta potential, of the powder in the cement paste. Here a decrease from +3 mV to -40 mV could be measured. A strong value for the zeta potential leads to a higher repulsion of similarly charged particles and therefore prevents powder agglomeration and clogging on the nozzle during injection. These two modifications (bimodal particles size distribution and phytic acid) lead to a significant increase in the paste injectability. The unmodified paste was injectable for 30 % only, where all modified pastes were practically fully injectable ~90 % (the residual paste remained in the nozzle, while the syringe plunger already reached the end of the syringe). A very similar observation could be made for the β-TCP system. This system was modified with phytic acid. The zeta potential was decreased even stronger from -10 ± 1.5 mV to -71.5 ± 12 mV. The adsorption of the phytate ions and subsequent formation of chelate complexes with the newly dissolved Ca2+ ions also showed a retarding effect in the cements setting reaction. Where the unmodified cement was not measurable in the rheometer, as the reaction was faster than the measurement setup (~1.5 min), the modified cements showed a transition through the gel point between 3-6 min. This means the pastes stayed between 2 and 4 times longer viscous than without the modification. Like with the first cement system also here the effects of the phytate addition showed its beneficial influence in the injectability measurement. The unmodified cement was not injectable at all, due to the same issue already encountered at the rheology measurements, but all modified pastes were fully injectable for at least 5 min (lowest phytate concentration) and at least 10 min (all other concentrations) after the mixing of powder and liquid. The main goal of the last modification with sodium pyrophosphate was to create a paste that was stable in aqueous environment without setting until the activation takes place, but it should still show good injectability as this was the desired way of application after activation. Like before also the zeta potential changed after the addition of pyrophosphate. It could be lowered from -22 ± 2mV down to -61 to -68 ± 4mV (depending on the pyrophosphate concentration). The pastes were stored in airtight containers at room temperature and checked for their phase composition over 14 days. The unmodified paste showed a beginning phase conversion to hydroxyapatite between 7 and 14 days. All other pastes were still stable and unreacted. The pastes were activated with a high concentrated (30 wt%) sodium orthophosphate solution. After the activation the pastes were checked for their injectability and showed an increase from -57 ± 11% for the unmodified paste to -89 ± 3% (practically fully injectable as described earlier) for the best modified paste (PP005). It can be concluded that the goal of enabling full injection of conventional calcium phosphate bone cement systems was reached. Additional work produced a storage stable paste that still ensures full injectability. Subsequent work already used the storable paste and modified it with hyaluronic acid to create an ink for 3D extrusion printing. The first two cement systems have also already been investigated in cell culture for their influence on osteoblasts and osteoclasts. The next steps would have to go more into the direction of translation. Figuring out what properties still need to be checked and where the modification needs adjustment to enable a clinical use of the presented systems.

In den letzten Jahrzehnten haben Inzidenz und Prävalenz von GEP NET deutlich zugenommen (Yao et al. 2008). Den SSTR kommt eine entscheidende Rolle bei zahlreichen etablierten Therapieverfahren zu. Allerdings stoßen die meisten Therapien bei G3 Tumoren oder bei langfristigem Einsatz an ihre Grenzen, was die Etablierung neuer, molekular zielgerichteter Therapien notwendig macht. Die Inhibition des Wnt-Signalweges stellt einen möglichen Ansatzpunkt für Therapien dar. Ziel dieser Arbeit war es die Wirkung der Wnt-Modulatoren Quercetin und Lithiumchlorid auf die Wnt-Aktivität sowie die Expression von Somatostatinrezeptoren und CXCR4 in den neuroendokrinen Tumorzelllinien QGP-1 und BON-1 zu untersuchen. Durch Real-Time PCR, Western Blots und Immunhistochemie wurden die Effekte auf RNA-, und Proteinebene sowie morphologisch analysiert und ausgewertet. An den verwendeten Zelllinien konnte gezeigt werden, dass Quercetin die Wnt-Signalgebung inhibierte, die SSTR-Expression steigerte und die CXCR4-Expression senkte. Lithiumchlorid bewirkte eine Wnt-Aktivierung und konnte über diesen Weg eine gesteigerte Expression von CXCR4 erzielen. Es konnte gezeigt werden, dass ein Zusammenhang zwischen der Aktivität des Wnt- Signalwegs und der Befähigung der GEP-NET Zelllinien zur SSTR- und CXCR4-Expression bestand. Die Wnt-Inhibierung kann über den Effekt der Steigerung von SSTR Teil neuer Therapiestrategien sein. So ist z.B. eine „add-on“ Therapie von Wnt-Inhibitoren wie Quercetin zusammen mit der PRRT denkbar.