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Structure theory and algorithms for highly regular colored graphs
Get PDFHighly regular finite graphs are mesmerizing combinatorial objects. Their core characteristics exhibit how the structure of local subgraphs relates to the global structure of the whole graph. They have applications in various mathematical fields such as statistics, coding theory, and the general study of symmetries.
We call a graph highly regular if it is k-ultrahomogeneous or ℓ-tuple regular for suitable k, ℓ ∈ N: a graph is k-ultrahomogeneous if every isomorphism between two induced subgraphs of order at most k extends to an automorphism of the entire graph. Further, it is ultrahomogeneous if it is simultaneously k-ultrahomogeneous for all k ∈ N. In contrast, a graph is ℓ-tuple regular if the number of common neighbors of a vertex set S of order at most ℓ only depends on the isomorphism type of the subgraph induced by S. These graph properties have been studied extensively in the past. Especially, 1-ultrahomogeneity and 2-tuple regularity are better known as vertex-transitivity and strong regularity, respectively.
The focus of this thesis lies in the investigation of highly regular colored graphs. These naturally appear in the context of symmetries and graph isomorphism algorithms. For example, the well-studied Weisfeiler-Leman algorithms form a family of incomplete approaches to the graph isomorphism problem. They store combinatorial information on the local structure of a graph by coloring it. In particular, the ℓ-tuple regular colored graphs are closely related to the ℓ-dimensional Weisfeiler-Leman algorithm. The amount of information needed to distinguish a graph from non-isomorphic ones is measured by the Weisfeiler-Leman dimension. Altogether, colored graphs are a natural choice to examine for high
regularity.
In this thesis, we classify the ℓ-tuple regular vertex-colored undirected finite graphs and the k-ultrahomogeneous vertex-colored undirected finite graphs for ℓ ≥ 5 and k ≥ 4. In particular, this includes the classification of ultrahomogeneous vertex-colored undirected finite graphs. Beyond that, we exhaustively enumerate all k-ultrahomogeneous and ℓ-tuple regular arc-colored directed finite graphs of order at most 34.
In recent years, the Weisfeiler-Leman dimension has become a standard measure of descriptive complexity of a graph. We establish a lower bound of 0.0105027 · n − o(n) and an upper bound of 0.15 · n + o(n) for the Weisfeiler-Leman dimension of n-vertex graphs. We reduce the claim for the upper bound to 2-tuple regular colored graphs. Given the complexity of their structure, we develop new techniques to facilitate their analysis. This includes conditions under which a vertex color class can be restored, up to isomorphism, if it is removed. Within our proof, we also derive an upper bound of 0.05 · n + o(n) on the Weisfeiler-Leman dimension of colored graphs whose color classes all have size at most 7
Characterization of hepatitis B virus genotypes in different stages of infection regarding their molecular virology in vitro and in vivo
Get PDFHepatitis B virus (HBV) infection is a major driver of liver disease, leading to hepatocellular carcinoma (HCC) and cirrhosis. Chronic HBV infection progresses through four distinct phases, with correct phase classification being critical for clinical decision-making. The presence of diverse HBV genotypes (Gt) and naturally occurring mutations influences disease progression, treatment responses, and viral protein expression. Notably, genotype G (GtG) has been associated with increased fibrosis risk in co-infected patients, necessitating further investigation into its molecular and clinical impact.
This study analyzed chronic HBV infection phases using a genotype-stratified approach, with a focus on the benign phase 3 (HBeAg-negative infection) and the prevalence of GtG co-infections. While standard PCR genotyping failed to detect GtG in the German Albatros trial, targeted PCR identified a 4-8% prevalence in patients initially classified as infected with GtA or GtE. In vitro, co-expression of GtG/A and GtG/E enhanced G-specific core protein synthesis, reducing the core protein expression of the second genotype. Viral replication remained unaffected, but HBsAg expression and release were diminished for GtG/E.
Patient-derived HBeAg-negative isolates (GtA, B, and D) exhibited reduced viral replication, intracellular and extracellular HBsAg levels, and endoplasmic reticulum retention of surface proteins compared to wildtype genomes. Reversion of the precore mutation (G1896A) increased intracellular HBsAg levels but did not enhance release. Additionally, patient isolates induced cytoprotective gene expression and displayed altered proliferative signaling, independent of HBeAg presence or specific mutations. No genotype-dependent differences in HBsAg composition or particle density were observed across infection phases.
In conclusion, GtG co-infections predominantly occurred alongside GtA and E, with standard PCR methods failing to detect them adequately. GtG may exert a regulatory role through core protein interactions, potentially influencing disease severity. The implementation of GtG-specific screening could enhance clinical care for affected patients. HBeAg-negative isolates exhibited an antiproliferative phenotype, suggesting a selective advantage in later infection stages that may reduce disease progression and HCC risk
Perspectives for Applications of Quantum Imaging
Get PDFQuantum imaging is a multifaceted field of research that promises highly efficient imaging in extreme spectral ranges as well as ultralow‐light microscopy. Since the first proof‐of‐concept experiments over 30 years ago, the field has evolved from highly fascinating academic research to the verge of demonstrating practical technological enhancements in imaging and microscopy. Here, the aim is to give researchers from outside the quantum optical community, in particular those applying imaging technology, an overview of several promising quantum imaging approaches and evaluate both the quantum benefit and the prospects for practical usage in the near future. Several use case scenarios are discussed and a careful analysis of related technology requirements and necessary developments toward practical and commercial application is provided
Engaging Paradoxical Tensions in Cross-Sectoral Collaborative Business Model Development for Sustainability: A Case Study in the Urban Energy Transition
Get PDFThis article presents an in-depth case study on cross-sectoral collaborative business model development (CBMD) that is pressured to produce systemic sustainability transformations. Drawing on paradox theory, we identify three paradoxical tensions—value, creativity, and consumer tensions. While engaging these tensions offers synergy and creativity potential, engagement barriers limit stakeholders’ ability to harness this potential. Stakeholder networks can access synergy potential by engaging meso-level tensions through increased trust and collaboration. Yet, macro-level engagement barriers posed by governments and society lead to a reliance on incumbent patterns and reduce creativity. This research advocates for reconsidering CBMD processes and regulatory frameworks to enable engagement with these paradoxical tensions. Our implications offer insights for industries transitioning from centralized models to more individualized, decentralized approaches. The findings underscore the necessity of promoting reciprocal interactions and engagement across different levels and the early integration and strategic orchestration of stakeholders to cultivate trust and align objectives
Bamboo–PCM: Comparative Analysis of Phase Change Material-Impregnated Dendrocalamus giganteus Culm Behavior Exposed to Thermal Variation in Wind Tunnel Assay
Get PDFThe construction industry’s pursuit of eco-friendly materials has sparked interest in bamboo, a renewable resource with exceptional physical and mechanical properties. This study analyzed the integration of Dendrocalamus giganteus bamboo with phase change materials (PCMs) to enhance thermal energy storage in building applications, aiming to improve temperature regulation and reduce energy consumption for climate control. The study compared the performance of bamboo impregnated with an industrial PCM or coconut oil, used in conjunction with a polyurethane resin (PU) coating treatment, assessing their thermal regulation performance against traditional building materials such as ceramic tiles, fiber cement, and metal sheets. From an anatomical perspective, the pores within bamboo culms offered ample space for PCM storage, resulting in a substantial heat storage capacity. Thermal behavior tests conducted in a wind tunnel revealed that the impregnated bamboo samples effectively mitigate temperature fluctuations by aligning them with the PCM’s phase change temperature. Additionally, it was observed that air flow velocity had an impact on this phenomenon. The study concluded that bamboo culms impregnated with PCM hold promise for temperature regulation in construction applications, with variations in airflow exerting an impact on the outcomes obtained
Characterization of a mock up nuclear waste package using energy resolved MeV neutron analysis
Get PDFReliable radiographic methods for characterizing nuclear waste packages non-destructively (without the need to open containers) have the potential to significantly contribute to safe handling and future disposal options, particularly for legacy waste of unknown content. Due to required shielding of waste containers and the need to characterize materials consisting of light elements, X-ray methods are not suitable. Here, energy-resolved MeV neutron radiography is demonstrated as a first-of-its-kind application for non-destructive and remote examination of mock up nuclear waste packages from a safe position using time-of-flight techniques enabled by a novel event-mode imaging detector system. Energy-resolved neutron transmission spectra were measured spatially, permitting the detection of analogue materials to actual nuclear waste such as water, melamine, and ion exchange resin within a 2.54 cm wall thickness steel pipe. The results demonstrate the capability to locate the materials through this wall thickness by radiography and tomographic reconstruction, revealing detailed 3D distributions and structural anomalies. The method effectively detects residual water in ion exchange resin, highlighting its sensitivity to moisture content, a crucial parameter for nuclear waste characterization. Monte Carlo simulations are in agreement with the experimental findings, providing a pathway to simulate waste forms more difficult to tackle experimentally. This work paves the way to apply sub-nanosecond intense MeV neutron sources, such as laser-driven neutron sources under development, to nuclear waste characterization
Utilization of RFLP in V-Model methodology for the interdisciplinary development of Digital Twins
Get PDFDigital Twins have numerous potentials like performance analysis, condition monitoring or process optimization. As the development of Digital Twins is a highly interdisciplinary task, it poses challenges and is therefore rarely utilized. This contribution considers the interdisciplinary development of Digital Twins as an interplay between sensors, models and IT infrastructure. It builds on previous publications that deal with the domains of models, sensors and IT infrastructures in the context of Digital Twins as well as domain-specific development procedures. For this purpose, the V‑model of VDI 2206 is used and modified for the context of the Digital Twin. In order to integrate the findings of the preliminary work into the V‑model at a more concrete level, they are sorted into an RFLP framework, which in turn is integrated into the V‑model. The resulting development approach covers the entire development process at a transferable, abstract level, while at the same time providing concrete steps at a directly applicable level. The results are illustrated using an exemplary application of an industrial gearbox
Thermoelectric properties and transport mechanisms of sustainable TiS₂-based materials
Get PDFThermoelectrics can directly convert a temperature difference or heat flow into electricity and vice versa, on the basis of the Peltier and Seebeck effect, thereby showing great potential in alleviating energy stress, mitigating environmental impact and building a sustainable society. Thermoelectric materials have been primarily used in niche applications such as spacecrafts or specialized industrial processes. However, with ongoing research and development, advanced materials and design strategies enable the production of more-efficient, cost-effective and eco-friendly thermoelectric devices. Advancing sustainable thermoelectric materials is crucial for expanding their applications beyond niche uses such as spacecraft to more everyday scenarios like portable and medical cooling applications, wearables, outdoor PowerPot, etc. In recent years, a member of the transition-metal dichalcogenides (TMDCs) family, TiS₂, has been reported to be great potential thermoelectric material for medium temperature applications. In addition to its large Seebeck coefficient (close to –300 μVK⁻¹) at room temperature, TiS₂ also offers significant sustainability advantages. It is known for being environmentally friendly, cost-effective, composed of non-critical elements, and lightweight.
With this motivation, the main work of my PhD thesis is to fabricate sustainable TiS₂-based thermoelectric materials with good thermoelectric properties via different strategies. The first strategy is based on the relatively wide van der Waals gaps of layered TiS₂ material, which can accept a variety of species as intercalants. In this work, iron intercalated TiS₂ (FeₓTiS₂) compounds with x varying from 0 to 0.05 were prepared using a solid-liquid-vapor reaction and spark plasma sintering. The intercalated iron cations are served as the electron donor, leading to a substantial decrease in electrical resistivity. In the meantime, structural disorder caused by iron intercalation significantly contributes to the reduction of lattice thermal conductivity in the direction parallel to the pressing direction. However, its contribution is limited in the direction perpendicular to the pressing direction. The second approach is to minimize its lattice thermal conductivity in the perpendicular direction by designing entropy-engineered transition metal sulfides (Ti/Nb/Ta/Zr)S₂ to introduce strong in-plane point defects. The composition with TiS₂ as the primary phase, supplemented by minor doping of Zr, Nb, and Ta, holds promise for reducing lattice thermal conductivity while preserving its high power factor. The third work continues with the entropy engineering strategy but introduces more elements on both Ti and S sites. In this work, multi-element doped TiS₂ materials, with Y and Nb, La and Ta on Ti sites, and Se on S sites, were investigated to further explore the potential for reducing the lattice thermal conductivity in the perpendicular direction. The lattice thermal conductivity was observed to decrease progressively with the increased diversity of elements in multi-element doped TiS₂. Importantly, the multi-element doping strategy enables the reduction of lattice thermal conductivity independently, without significantly compromising its large power factor.
In summary, my PhD work focuses on designing sustainable TiS₂-based thermoelectric materials. The findings indicate that intercalation effectively reduces lattice thermal conductivity in the parallel direction, thereby notably enhancing the figure of merit in this direction. Conversely, for the perpendicular direction, entropy engineering emerges as a promising strategy for minimizing lattice thermal conductivity while maintaining the integrity of the electrical transport framework
Refining the mechanism of CO₂ and H₂ activation over gold-ceria catalysts by IR modulation excitation spectroscopy
Get PDFThe activation and utilization of the greenhouse gas CO₂ is of great interest for the energy transition as a fossil-free carbon source for mitigating climate change. CO₂ hydrogenation via the reverse water–gas shift reaction (RWGSR) converts CO₂ to CO, a crucial component of syngas, enabling further transformation by means of the Fischer–Tropsch process. In this study, we unravel the detailed mechanism of the RWGSR on low-loaded Au/CeO₂ catalysts using IR modulation excitation spectroscopy (MES), by periodically modulating the concentration of the reactants, followed by phase-sensitive detection (PSD). Applying such a MES-PSD approach to Au/CeO₂ catalysts during RWGSR gives direct spectroscopic evidence for the active role of gold hydride, bidentate carbonate and hydroxyl species in the reaction mechanism, while disproving the participation of other species such as formate. Our results highlight the potential of modulation excitation spectroscopy combined with phase-sensitive detection to provide new mechanistic insight into catalytic reactions not accessible by steady-state techniques, including a profound understanding of the sequence of reaction steps
Harnessing click detectors for the genuine characterization of light states
Get PDFThe key requirement for harnessing the quantum properties of light is the capability to detect and count individual photons. Of particular interest are photon-number-resolving detectors, which allow one to determine whether a state of light is classical or genuinely quantum. Existing schemes for addressing this challenge rely on a proportional conversion of photons to electrons. As such, they are capable of correctly characterizing small photon fluxes, yet are limited by uncertainties in the conversion rate. In this work, we employ a divide-and-conquer approach to infallibly discerning non-classicality of states of light. This is achieved by transforming the incident fields into uniform spatial distributions that readily lend themselves for characterization by standard on-off detectors. Since the exact statistics of the light stream in multiplexed on-off detectors are click statistics, our technique is freely scalable to accommodate–in principle–arbitrarily large photon fluxes. Our experiments pave the way towards genuine integrated photon-number-resolving detection for advanced on-chip photonic quantum networks