This thesis presents advances in the description of quantum magnets, primarily through the development of a new method called the pseudo-Majorana functional renormalization group (PMFRG). The PMFRG is capable of accurately describing strongly interacting quantum magnets in challenging scenarios where most other methods fail.

Fundamental to the formalism of the PMFRG is a resummation of Feynman diagrams, which allows direct treatment of the many-body problem in the thermodynamic limit of infinitely many particles. While exact resummation schemes are impossible, the PMFRG uses the framework of the renormalization group to perform a numerical summation of several classes of diagrams to infinite order. Notable examples of such diagrams are associated with common phenomena such as magnetic order, as well as more exotic quantum spin liquids, which are phases described by emergent gauge theories and fractionalization. To exploit this advantage, spin operators for which diagrammatic techniques are limited are mapped to auxiliary Majorana fermions. This mapping proves to be advantageous compared to the more commonly used complex fermions. After establishing its formalism, the PMFRG is applied to paradigmatic problems in the field of frustrated magnetism at finite temperature. The numerical results obtained with the PMFRG are shown to be quantitatively accurate, typically providing errors of less than 10% compared to exact solutions. In particular, the PMFRG remains applicable to more general scenarios of frustrated three-dimensional magnets where exact solutions are unavailable, and where most other methods are infeasible.

In addition, this thesis investigates emergent higher-rank gauge theories with immobile quasiparticle excitations known as fractons. The physics of several pinch point features associated with these gauge theories is then analyzed. Using the PMFRG, it is found that these phases are very fragile under the inclusion of quantum fluctuations. Finally, a new fracton spin model is constructed that exhibits an exactly soluble point with a spin liquid phase. The stability of this phase is then verified by numerically exact quantum Monte Carlo simulations of the spin model compared to the analytical solution of the emergent rank-2 lattice gauge theory, making it the first two-body spin model with an emergent fracton quantum spin liquid. The following chapters therefore present substantial progress in two important areas: numerical solutions of the quantum many-body problem and the study of emergent gauge theories in spin systems.

Die klassischen Prognosefaktoren wie FIGO-Stadium und makroskopische Tumorfreiheit konnten als die wichtigsten Prognosefaktoren für Langzeitüberleben mit Ovarialkarzinom bestätigt werden. Zu den positiven prognostischen Faktoren zählten auch das Ansprechen auf die platinbasierte Therapie, während Aszites und das Auftreten von Rezidiven prognostisch negativ waren. Bezüglich des Tumorbefallmusters war ein Befall des oberen Abdomens bei Langzeitüberlebenden auch nach Matching für die wichtigsten Prognosefaktoren seltener im Vergleich zur Kontrollgruppe. Polypharmazie war nicht mit dem Gesamtüberleben assoziiert, es bestand jedoch eine positive Korrelation mit dem progressionsfreien Überleben. Neben den klassischen klinischen Prognosefaktoren sind auch Lebensqualität und Tumor- bzw. Therapie-assoziierte Symptomen von Bedeutung. Sowohl Chemotherapie-induzierte Übelkeit und Erbrechen als auch Schmerzen waren mit einem schlechteren Gesamtüberleben assoziiert. Dies ist vor allem therapeutisch interessant und es sollte in zukünftigen Studien prospektiv evaluiert werden, ob eine suffiziente Therapie von Krebs- und Therapie-assoziierten Symptomen nicht nur die Lebensqualität, sondern auch das Überleben von Ovarialkarzinompatientinnen verbessern kann. Die Charakterisierung von Langzeitüberlebenden mit Ovarialkarzinom und die Identifikation von Prognosefaktoren sollten sowohl klinisch als auch auf molekularer Ebene weiterverfolgt werden, um die Erkenntnisse zukünftigen Patientinnen zugutekommen zu lassen, z.B. im Hinblick auf eine personalisierte Medizin. Langzeitüberleben bedeutet nicht automatisch geheilt oder gesund zu sein. Knapp die Hälfte der Langzeitüberlebenden hat (mindestens) ein Rezidiv entwickelt und ein Teil der Patientinnen befindet sich unter Krebstherapie. Auch leidet fast jede zweite Langzeitüberlebende mit Ovarialkarzinom noch an körperlichen bzw. psychischen Spätfolgen, wie z.B. Lymphödemen, Fatigue, Distress oder neurologischen Langzeitnebenwirkungen. Auch Zweitkarzinome sind eine nicht zu unterschätzende Spätfolge. Neben der Erkennung von potenziellen Rezidiven gehören daher auch die Diagnostik und Behandlung von Spätfolgen, aber auch die Prävention zu den Säulen der Nachsorge bzw. Survivorship Care. Die große Herausforderung ist die Koordination der einzelnen Disziplinen und Stakeholder. Ein individueller Survivorship Care Plan, der gemeinsam mit der Patientin erstellt werden sollte, kann die wichtigsten Behandlungsziele für die Patientin zusammenfassen und stellt eine Grundlage für eine transparente interdisziplinäre Versorgung der Langzeitüberlebenden dar. Ob eine multidimensionale spezialisierte Survivorship Sprechstunde die Lebensqualität und den Gesundheitszustand verbessern kann, wird derzeit in der Versorgungsforschungsstudie Survivorship Clinic untersucht (www.survivorship-clinic.de). Die Erkenntnisse aus den Studien über Langzeitüberleben mit Eierstockkrebs sollten genutzt werden, um auch die Versorgung der Patientinnen innerhalb der ersten fünf Jahre nach der Krebsdiagnose zu verbessern. Ziel ist es, durch eine holistische Versorgung bereits ab der Krebsdiagnose die Lebensqualität, den Gesundheitszustand und das Überleben nachhaltig zu verbessern. Langfristig angelegte Interventionsstudien mit Beginn zum Zeitpunkt der Diagnose wären hier wünschenswert, sind aber auch sehr kostenintensiv. Es gibt erste vielversprechende Studien, die neben der Krebstherapie bei Erstdiagnose auch den Einfluss von physischer Aktivität, Ernährung und Gesundheitskompetenz auf den Therapieerfolg und die Lebensqualität untersuchen. Hier seien die KORE-Studie und die BENITA-Studie als Beispiel für holistische Konzepte genannt. Solche Forschungsaktivitäten sollten langfristig fortgeführt und finanziert werden, um die Versorgung unserer Patientinnen nachhaltig zu verbessern.

Die vorliegende Habilitationsschrift befasst sich mit Behandlungsstrategien der periprothetischen Infektion des Hüftgelenks. Diese Infektionen sind mit langen Behandlungszeiten, hohen Kosten und Komplikationsraten verbunden. Ziel der Arbeit war die Evaluierung verschiedener diagnostischer und therapeutischer Konzepte.

Die Studienergebnisse zeigen, dass eine zweizeitige Hüftprothesenimplantation bei septischer Arthritis auch ohne Gelenkspacer vergleichbare klinische und radiologische Ergebnisse liefert. Die Analyse von intraoperativen Proben bei Wechseloperationen aufgrund vermeintlich aseptischer Hüftprothesenlockerung ergab eine unerwartet hohe Rate positiver Befunde, wobei die Abgrenzung zwischen Infektion und Kontamination schwierig ist. Eine weitere Untersuchung befasste sich mit dem zweizeitigen Hüftprothesenwechsel bei chronischen Infektionen mit ausgeprägten Knochen- und Weichteildefekten. Hierbei wurden fehlgeschlagene septische Revisionen, größere femorale Knochendefekte und verlängerte Intervallzeiten als Risikofaktoren für eine Reinfektion identifiziert. Die Anwendung einer erweiterten Trochanterosteotomie beim septischen Prothesenwechsel erzielte vergleichbare Ergebnisse, ging aber mit einer geringeren Anzahl an Débridements einher. Zudem wurde gezeigt, dass eine Infektion eines zementierten Implantates mit einem erhöhten Risiko für eine Reinfektion und erneute Revision assoziiert war.

Diese Arbeit verdeutlicht, dass eine differenzierte diagnostische und chirurgische Vorgehensweise dazu beitragen, die Ergebnisse zu optimieren. Dennoch bleibt die hohe Rate an Reinfektionen und diagnostischen Unsicherheiten eine Herausforderung, die weitere Forschung erfordert, um Muster zu erkennen, die den Behandlungserfolg verbessern.

Increasing reports of anthelmintic resistance of the liver fluke Fasciola hepatica pose a threat to sheep farming in many countries worldwide. Particularly resistance to triclabendazole, the only flukicide effective against the highly pathogenic juvenile flukes, is of major concern. However, data about the susceptibility of F. hepatica to flukicides in Germany were lacking. Therefore, a field study was conducted from 2020-2022 to evaluate the frequency of F. hepatica on German sheep farms and to test the efficacy of triclabendazole and albendazole by means of a Faecal Egg Count Reduction Test (FECRT) and a Coproantigen Reduction Test (CRT). In advance of the field study, a systemic comparison between three coproscopical methods was conducted in order to determine the most appropriate method for the FECRT. Sufficient fasciolicidal efficacy of albendazole was proven on 1/1 farm and triclabendazole was efficient on 10/11 farms. One one farm, complete failure of triclabendazole, even in double the recommended dose, was observed associated with massive animal losses due to acute fasciolosis. This is the first report of triclabendazole resistance in Germany. The results indicate, that flukicide resistance is not widespread in Germany so far, but the observations clearly illustrate the drastic consequences of triclabendazole resistance. Due to the lack of alternative drugs to eliminate juvenile flukes, triclabendazole resistance should be considered a serious therapy emergency in sheep and resistance might spread in the future.

Kardiale Pathologien sind häufige und häufig unentdeckte Ursachen eines ischämischen Schlaganfalls. Gleichzeitig treten nach einem Schlaganfall vermehrt kardiale Komplikationen auf, die einen entscheidenden Einfluss auf die kurz- und langfristige Prognose haben. Neben der Echokardiographie stehen weitere Methoden wie die kardiovaskuläre MRT zur morphologischen und funktionellen Beurteilung des Herzens in der Akutphase nach ischämischem Schlaganfall zur Verfügung. In einer prospektiven Beobachtungsstudie konnten wir zeigen, dass ein kombinierter Einsatz der kardiovaskulären MRT einschließlich MR-Angiographie des Aortenbogens sowie ein prolongiertes EKG-Monitoring die Detektionsrate präspezifizierter pathologischer Befunde im Vergleich zur Routinediagnostik erhöhen und die Rate der als kryptogen klassifizierten Schlaganfälle signifikant reduzieren konnte. In einer zweiten Arbeit wurde die Bedeutung des kardialen Biomarkers Troponin T für das Auftreten kardiovaskulärer Komplikationen im langfristigen Verlauf nach ischämischem Schlaganfall oder TIA untersucht. Hierbei war ein Troponinwert über dem Assay-spezifischen Referenzlimit bei Aufnahme mit einem bis zu zweifach erhöhten Risiko für ein schwerwiegendes kardiovaskuläres Ereignis während eines durchschnittlichen Nachverfolgungszeitraums von über drei Jahren assoziiert. Für bestimmte kardiale Pathologien stellt eine orale Antikoagulation (OAK) die leitliniengerechte Sekundärprävention nach Schlaganfall dar, wobei hier insbesondere das Vorhofflimmern zu nennen ist. Bis Ende 2010 standen hierfür nur Vitamin K-Antagonisten (VKA) zur Verfügung. In einer retrospektiven Analyse untersuchten wir, ob die Verfügbarkeit sog. Nicht-Vitamin K-abhängiger oraler Antikoagulanzien (NOAK) ab 2010/2011 einen Einfluss auf die Verschreibepraxis bei Patient*innen mit Vorhofflimmern und einer Indikation für eine OAK hatte. Während hier annähernd eine Verdopplung der OAK-Rate nachgewiesen werden konnte, blieb dennoch jede*r Zweite ohne adäquate Behandlung. Ischämische Schlaganfälle treten auch bei Patient*innen mit Vorhofflimmern unter bestehender Antikoagulation auf. In einer retrospektiven multizentrischen Analyse betrachteten wir die mutmaßliche Schlaganfallätiologie, Sekundärprävention und Behandlungsergebnisse in einem Kollektiv solcher Patient*innen. Hier zeigte sich, dass jede*r Vierte eine konkurrierende Schlaganfallursache (zusätzlich zum bekannten Vorhofflimmern) aufwies, jede*r Dritte unzureichend antikoaguliert war und nahezu jede*r Zweite einen kardio-embolischen Schlaganfall trotz bestehender (suffizienter) Antikoagulation erlitt. Nach drei Monaten hatte bereits mehr als jede*r Vierte ein schwerwiegendes Folgeereignis erlitten (erneuter Schlaganfall, intrazerebrale Blutung oder Tod), wobei einzig die Einnahme eines NOAK einen protektiven Einfluss aufwies. Abschließend untersuchten wir die Hypothese, dass die Einnahme eines NOAK bei Patient*innen mit bekanntem VHF einen positiven Einfluss auf den Schlaganfallschweregrad haben könnte. Patient*innen mit Einnahme eines NOAK erlitten hierbei signifikant seltener einen schweren Schlaganfall, vergleichbar mit Patient*innen unter wirksamer Einnahme eines VKA. Eine solche Assoziation zeigte sich auch für ein schlechtes funktionelles Behandlungsergebnis bei Entlassung und die Aufenthaltsdauer im Krankenhaus. Die in dieser Habilitationsschrift vorgestellten Arbeiten tragen zum besseren Verständnis der pathophysiologischen Zusammenhänge zwischen Herz und Hirn im Kontext des ischämischen Schlaganfalls bei. Eine erweiterte kardiale Diagnostik erscheint zumindest bei ausgewählten Patient*innen eine sinnvolle Ergänzung. Der kardiale Biomarker Troponin ist mit dem langfristigen Auftreten kardiovaskulärer Rezidiv- und Folgeereignisse assoziiert. Diese Erkenntnisse können Grundlage für weiterführende Studien einer individualisierteren Risikoprädiktion und Sekundärprophylaxe sein.

Die Anzahl der Implantationen inverser Schultertotalendoprothesen (iSTEP) steigt stetig und das Ziel dieser Arbeit ist es Erkenntnisse zur Optimierung der Ergebnisse dieser Operation bei Patienten mit Defektarthropathie zu teilen. Dabei ging es neben dem möglichst reinen Designvergleich auch um die kritische Auseinandersetzung mit objektivierbaren Messmethoden des Prothesendesigns. Des Weiteren wurde im Rahmen der vorhersehbaren Ergebnisoptimierung einer solchen Operation auch eine formal sehr risikobehaftete Population der Ältesten untersucht. Patienten über 85 Jahre, die eine primäre iSTEP erhielten, zeigten eine hervorragende Verbesserung der Schulterfunktion bei niedriger Komplikationsrate. Gute kurzfristige klinische Ergebnisse und eine hohe Patientenzufriedenheit sind zu erwarten und die iSTEP ist selbst bei diesen ältesten Patienten ein sicheres Verfahren mit niedriger Rate an lokalen und systemischen Komplikationen. Beim Vergleich lateralisierter und nicht lateralisierter Implantate für verschiedene Hamada-Stadien der Defekarthropathie war bewusst, dass es beim Vergleich von Prothesendesigns mehrere Störfaktoren gibt, und diese wurden so ausführlich wie möglich beseitigt. Es wurde sorgfältig eine Gruppe von Patienten mit vergleichbarem Status der Rotatorenmanschette, Rotatorenmanschettenrissmuster und Gelenkstatus ausgewählt. Berücksichtigung fand auch die Anatomie des Glenoids und des Scapulahalses und die Positionierung des Implantats, indem mehrere spezifische Parameter gemessen wurden, um bereits bestehende anatomische Unterschiede zwischen unseren Gruppen auszuschließen. Der einzige eindeutig signifikante Unterschied zwischen den Prothesengruppen war der Parameter der Lateralisierung, der einen echten Vergleich zwischen einer lateralisierten und einer nicht-lateralisierten iSTEP ermöglichte. Bei der Aussenrotation und dem Skapulanotching wurden Unterschiede zugunsten des lateralisierten Implantats festgestellt. Mit einem ähnlichen Studiendesign verglichen wir drei Implantate um die Variablen der Lateralisierung und Distalisierung, sowie auch deren Kombination zu untersuchen. In einer großen Stichprobe von 226 Patienten und einer homogenen Verteilung der drei Patientenkohorten mit jeweils gleicher Implantatkonfiguration und Diagnose sowie kontinuierlichem Nachuntersuchungsprotokoll wurde gezeigt, dass der Hals-Schaft-Winkel nicht der einzige wichtige Faktor ist. Verantwortlich für die bessere Funktion bei Patienten mit iSTEP bei Defektarthropathie ist vielmehr das kombinierte Ausmass der Humeruslateralisierung und -distalisierung. Darüber hinaus reduziert die Glenoidlateralisierung in Kombination mit einem Hals-Schaft-Winkel, der niedriger ist als beim ursprünglichen Grammont-Design, das skapuläre Notching, das durch einen suffizienten unteren Überhang der Glenosphäre weiter verringert wird.

The exploration of ocean worlds within our Solar System stands at the forefront of contemporary planetary investigation, offering profound insights into potential habitability beyond Earth. This thesis examines some of the geological characteristics of Europa, one of Jupiter's icy moons, with a particular focus on features of high astrobiological relevance. Using existing imaging and newly generated topographic data, the research provides fundamental insights into Europa's geological processes, preparing for the upcoming NASA’s Europa Clipper mission. Three key features - Ménec Fossae, Thrace Macula, and Libya Linea – all located in a transitional region of Europa's southern hemisphere, are comprehensively studied. My investigations on each of these features have been previously published - and in one case are in review - in international peer-reviewed publications, and constitute the core of this cumulative dissertation (Sections II, II, and IV, respectively). After an overview of the current state of research on ocean worlds, Europa, and its geology in Part I, in Part II Ménec Fossae's geological complexity is investigated, suggesting tectonic activity possibly linked to a shallow water pocket within Europa's ice shell. Detailed geomorphologic and topographic analyses reveal the presence of numerous geological features within Ménec Fossae, indicating a dynamic history shaped by tectonic forces. The conclusions drawn in Part II provide additional evidence for the widespread presence of shallow water pockets within Europa's ice shell. This understanding could facilitate the assessment of Europa's habitability by future space missions. Part III offers a novel perspective on the formation and evolution of Thrace Macula, a poorly understood chaos terrain. Through detailed analysis of topographic data and structural features, Part III proposes a new hypothesis suggesting that preexisting faults constrained its emplacement and distribution. Moreover, a sequence of geological events could be inferred: the formation of the neighboring band Agenor Linea occurred first, succeeded by that of Libya Linea and subsequently by the emplacement of Thrace Macula. Ultimately, strike-slip tectonic activity likely related to Libya Linea displaced a part of Thrace Macula. These findings suggest how forthcoming space missions could sample subsurface material from Thrace, which has only recently been emplaced on the surface along faults subsequent to its formation, offering access to the freshest - and most astrobiologically relevant - material in this area. Part IV focuses on the detailed characterization of Libya Linea, a prominent dilational band. By examining its elevation characteristics and structural features, Part IV identifies different stages of deformation, shedding new light on its geological history. Furthermore, small features possibly related to cryovolcanism or diapirism are identified within the vicinity of Libya Linea, adding additional complexity to its geological context. Part IV contributes significantly to the broader comprehension of Europa's geological history, particularly shedding light on the evolutionary processes of its bands. Through rigorous geomorphological-structural and topographic analyses, this thesis contributes to our understanding of Europa's geological dynamics and the astrobiological significance of its surface features. The insights gained from the study of Ménec Fossae, Thrace Macula, and Libya Linea provide a valuable foundation for future missions, particularly Europa Clipper, which will utilize the findings to assess Europa's potential habitability. The research presented here establishes a fundamental groundwork for understanding Europa's geological evolution and advancing our quest to uncover the potential for life beyond Earth.

The partial oxidation of methanol to methyl formate (MeFo) proceeds with high selectivity at high conversion on nanoporous gold (np-Au) catalysts. To obtain fundamental insights into the surface processes required for a rational improvement of this catalyst, a surface science approach investigating simplified model catalysts under well-defined single-collision conditions is used. Pulsed molecular beam (MB) experiments allow to study the transient and steady state kinetics under isothermal conditions and thereby for comparison to the applied systems. As np-Au catalysts contain, next to terraces, a high number of low-coordinated surface sites (LCS), the reactivity of flat Au(111) was compared to stepped Au(332) exhibiting (111)-terraces separated by monoatomic steps and thus, a notable number of LCS. These LCS enhance at high temperatures MeFo formation and lower overoxidation, as desired for an ideal partial oxidation catalyst. For low coverage conditions preferential adsorption of reactants at LCS enhances the selectivity for the coupling product, whereas conditions with higher surface coverage, e.g. at low temperatures, lower the MeFo selectivity, as adsorbates can act as obstacles for successful reactant encounters required for the coupling reaction. In addition to LCS, accumulated AuxOy-phases play a crucial role for understanding the observed chemistry. If formed at step sites density functional theory calculations from our collaborators reveal increased barriers for unwanted overoxidation explaining the experimentally observed differences in selectivity. Moreover, MeFo formation may require or benefit from AuxOy-phases, especially at step sites, as indicated by the experimental transient kinetics. As water is an oxidation product and a common (methanol) feed impurity, it may affect under applied multi collision conditions the methanol oxidation on np-Au catalysts. MB experiments on model catalysts conducted with and without added water demonstrated that in case of oxygen rich conditions water has a detrimental effect on MeFo formation rationalized by hydrogen-bonding with methanol as well as by reaction with adsorbed oxygen e.g. affecting the formation of AuxOy-phases and thus their beneficial effect at steps in suppressing overoxidation. Yet, under oxygen-poor, low coverage conditions, the negative effect of water decreases and almost disappears for Au(332) exhibiting a high number of LCS. This allows to propose a rationale for diverse findings for the impact of water on methanol oxidation in liquid and gas phases on np- Au, as these results provide insights into conditions critical for high selectivity in partial oxidation.

This cumulative dissertation explores the economic and social consequences of the 2003–2013 commodity price boom in Latin America through three essays, examining its effects on the productive structure and social spending in the region. The research employs a variety of empirical methods, contributing to the understanding of how commodity-driven economies navigate periods of high resource revenue.

The first essay investigates sector-specific Dutch Disease effects across 46 low- and middle-income countries from 2000 to 2018. Using system Generalized Method of Moments (GMM) panel data analysis, it finds that the impact of rising commodity prices on economic sectors is more complex than previously assumed. While manufacturing—a tradable sector—is significantly negatively affected, other tradable sectors show no clear contraction. Among non-tradable sectors, only construction and trade services benefit from commodity price booms. These findings challenge the traditional dichotomy of tradable and non-tradable sectors, suggesting that the heterogeneous sectoral effects require a more nuanced analytical framework to avoid overestimating the Dutch Disease's impact on tradable sectors.

The second essay shifts focus to regional trade dynamics and Dutch Disease in Latin American manufacturing exports. It posits that South-South trade within the region mitigates Dutch Disease effects compared to exports to extra-regional markets. This chapter identifies two key mechanisms: a higher share of technologically sophisticated products in regional trade, and trade barriers reducing external competition. A panel data analysis from 1996 to 2018 reveals that commodity price increases lead to smaller declines in manufacturing exports within the region (-0.31%) than in extra-regional trade (-0.48%). Low-tech exports are disproportionately affected, with pronounced declines in extra-regional trade (-0.95%) compared to regional trade (-0.58%). The results underscore the role of regional trade integration and technological upgrading in softening the adverse effects of resource dependency on manufacturing.

The third essay examines the relationship between the commodity price boom and public social spending in 16 Latin American countries between 1990 and 2019. Employing structural vector autoregressions and local projections, it finds highly heterogeneous country responses. For example, Argentina and Ecuador experienced sustained increases in health, education, and social protection spending, while Brazil and Mexico saw only temporary gains. Bolivia, Colombia, and Peru showed no significant responses, and countries without commodity booms displayed no link between rising prices and social spending. Attempts to explain these divergent outcomes reveal no consistent patterns related to political ideology, fiscal rules, or resource dependence. Instead, wealthier and more diversified economies were more likely to sustain increased social spending. These findings challenge the assumption that the commodity price boom was the primary driver of social policy expansion in Latin America, highlighting the importance of country-specific factors.

By disentangling the sectoral and social implications of the commodity price boom, this dissertation contributes to the broader discourse on resource-driven development. It emphasizes the role of economic diversification, regional trade integration, and adaptive social spending strategies to achieve sustainable development in resource-rich economies.

Da die essentielle Aminosäure Tryptophan in dem Epimerase-Anteil der UDP- GlcNAc-2-Epimerase/ManNAc-Kinase nur einmal vorkommt und Arbeiten an bakteriellen Glycosyltransferasen gezeigt haben, daß Tryptophan für die mit seiner hydrophoben, polaren Seitenkette für die Bindung von Zuckermolekülen oder UDP geeignet zu sein scheint, lag es nahe anzunehmen, daß W204 für den Reaktionsmechanismus der UDP-GlcNAc-2-Epimerase/ManNAc-Kinase von Bedeutung ist. Mittels Site-Directet-Mutagenesis wurde W204 jeweils gegen die Aminosäuren Phenylalanin, Isoleucin und Alanin ausgetauscht und die Enzymaktivität gemessen. Der Versuch, W204 gegen Histidin auszutauschen, schlug trotz vielfacher Versuche fehl, da sich das Codon an dieser Stelle, vermutlich aufgrund der zu niedrigen Schmelztemperatur des DNA-Stranges, nicht in das Genom der UDP-GlcNAc-2-Epimerase/ManNAc-Kinase einfügen ließ. Ersatz von Tryptophan durch Alanin schaltete die Enzymaktivität völlig aus. Mit Phenylalanin anstelle von Tryptophan war noch Aktivität nachweisbar, was sich wahrscheinlich durch die an Polarität und Größe dem Tryptophan nahe kommende Ähnlichkeit erklärt. Für Isoleucin ist es fraglich, ob die geringe Aktivität, die noch nachgewiesen wurde, reell ist, oder ob sie durch Hintergrundstrahlung oder ähnliche Störfaktoren in den Messungen zustande kam.

This dissertation comprises four empirical chapters which contribute to the fields of inequality research and labor economics.

The first chapter examines the interaction between socioeconomic status, place of residence and life expectancy, which so far remains poorly understood. I contribute to deepening this understanding by, firstly, using administrative data from the German Pension Insurance to provide novel estimates for remaining life expectancy at age 65 by lifetime earnings quintiles and geographic areas (NUTS2). I show evidence for substantial heterogeneity in the link between lifetime earnings and life expectancy across NUTS2 regions in Germany. Subsequently, I use these life expectancy estimates together with a rich set of place characteristics to conduct a correlational analysis investigating which place factors are associated with longevity. Specifically, I examine whether place matters differently for individuals’ life expectancy depending on their socioeconomic status and whether this interaction between place factors, socioeconomic status and life expectancy has changed over time. Place factors associated with longevity are better healthcare supply, lower air pollution levels, lower regional poverty levels and a higher prevalence of healthy behaviors. Strikingly, the correlations between place factors and life expectancy appear to be homogeneous rather than heterogeneous in magnitude and direction for individuals at the top and the bottom of the lifetime earnings distribution. Furthermore, I find suggestive evidence that the importance of place for the life expectancy of low income individuals may have decreased over time.

While the second chapter of this thesis also investigates lifetime earnings, here we refrain from using administrative data. Instead, we use data from the Socio-economic Panel (SOEP) together with a dynamic microsimulation approach to facilitate lifetime analysis for a more comprehensive sample (including women, self-employed individuals and civil servants). The aim of this chapter is to advance understanding of the persisting gender earnings gap in Germany. First, we briefly investigate gender inequality in wages and annual earnings in the cross-section, which is mainly driven by gender differences in hours worked and accumulated work experience. Subsequently, we focus on the simulation of complete earnings biographies from SOEP data, which in the next step facilitates the investigation of the gender gap in lifetime earnings. We find evidence for an average gender lifetime earnings gap of 51.5% for birth cohorts 1964-1972. We show that this unadjusted gender lifetime earnings gap increases strongly with the number of children, ranging from 17.3% for childless women to 68.0% for women with three or more children. However, using a counterfactual analysis we find that the adjusted gender lifetime earnings gap only differs slightly by women’s family background.

In the third chapter, we examine the effect of an individual’s involuntary job loss on their partner’s actual and desired labor supply response. Thus—while existing research has found little to no evidence for an added worker effect in Germany—we shed light on the question of whether a desired added worker effect exists. Using data from the SOEP, we study individuals’ changes in actual and desired working hours after their partners’ involuntary job loss in an event study design. Our results show that neither desired nor actual working hours change significantly. These findings are robust for several sub-groups and for different econometric specifications. Therefore, we provide first evidence that the absence of the added worker effect is in line with individuals’ stated labor supply preferences and is not the result of an inability to realize desired working hours.

In the fourth chapter, we construct a comprehensive wealth distribution for Germany in order to inform the national and international debate on the distribution of wealth including pension entitlements. We estimate the net present value of pension wealth in Germany in 2012 and 2017 using SOEP data. To ensure international comparability, we also implement state-of-the-art methods to deal with two well- documented shortcomings of survey data. First, to address the undercoverage of assets such as financial and business assets, we uprate the survey data to macroeconomic aggregates. Second, in order to address the underrepresentation of the rich, we top-correct the survey data using rich lists. We show that including pension wealth increases German households’ wealth-income ratio from 570% to 850% in 2017. Furthermore, we provide evidence that pension wealth has an equalizing role by showing that the wealth share of the bottom 50% increases from 2% to 9% once pension wealth is included, while the wealth share of the top 1% declines from 30% to 20%.

The magnesium phosphate mineral struvite (MgNH4PO4·6H2O) has gained scientific significance in the field of phosphorous and nitrogen recovery from wastewater. The recovery of these elements has become critical due to the limited availability of natural P resources like phosphorites and as a tool to reduce the environmental harm linked to mining such deposits. Furthermore, recovered struvite is employed as a slow-release fertiliser for agriculture. Fertilisers from wastewater-derived struvite are produced through intentional precipitation in wastewater treatment plants. However, it is fundamental to gain an in-depth understanding of the conditions necessary for the formation of struvite to maximise the efficiency of this process. This includes the formation conditions of struvite and the kinetics involved in its nucleation and growth. While the formation conditions of struvite-forming wastewater have been widely examined, a significant scientific knowledge gap still exists regarding the formation of struvite from pure salt solutions and the kinetic parameters of nucleation and growth. Aspects such as the nucleation and growth mechanisms of struvite and the role of temperature in the formation of struvite remain poorly understood. Better understanding these parameters is paramount to predicting struvite nucleation in complex solutions like the ones found in residual wastewater. As a result, my first aim for this study was to investigate the nucleation and growth kinetics of struvite from pure salt solutions at different temperatures. The use of struvite fertiliser is limited by the fact that struvite is unstable under atmospheric conditions. The precise conditions that trigger the breakdown of struvite are not fully understood, which limits its widespread use as a fertiliser. The secure transport and storage of struvite for its later industrial use requires fully comprehending the conditions in which it transforms into secondary phases. This constitutes the second objective of my thesis, where I addressed the stability of struvite by looking at its crystal structure and the transformation of struvite in air as a function of temperature. I used an experimental approach to address these knowledge gaps, including synthetic struvite solutions and crystals. To evaluate kinetic parameters governing the formation of struvite, I conducted nucleation and growth experiments at different solution concentrations and temperatures, employing in-situ spectroscopy and X-ray diffraction techniques. To provide a more fundamental understanding of the stability of struvite, I used single-crystal X-ray diffraction and evaluated a more accurate crystal structure of struvite by analysis at low temperatures (100 K), providing less temperature-induced influence on the atomic bonds. Furthermore, I evaluated the conditions and the mechanism of struvite decomposition into secondary phases through dry transformation experiments at different temperatures. I used powder XRD, Infrared and Raman spectroscopy, and scanning electron microscopy to follow the decomposition kinetics and characterise the resulting products to elucidate the mechanisms of struvite decomposition. The investigation of struvite nucleation and growth kinetics as a function of temperature revealed a reaction order (n) of ~ 0.4–0.8, indicating a diffusion-controlled nucleation mechanism and rate constants (k) of ~ 0.3–0.8 s-1. The activation energy of crystallisation was calculated as ~ 17 kJ/mol. No significant changes in n and k values across temperatures were observed. However, the induction period of struvite nucleation decreased up to 25 °C and increased beyond this temperature, supporting previous assumptions about the reverse temperature-dependence of struvite solubility. The improved crystal structure of struvite revealed that ammonia plays a key role in its stability. At low temperatures, NH3 is retained within the structure of struvite as ammonium, stabilised by three hydrogen bonds connected to phosphate anions and magnesium cations. This configuration is critical for the structural stability of struvite at low temperatures. In contrast, at room temperature, NH4+ forms fewer hydrogen bonds and exhibits rotational behaviour, which leads to a decrease in the stability of struvite. Finally, I evaluated kinetic parameters for the decomposition and transformation of struvite with temperature during the struvite transformation experiments. Struvite transformed into two different minerals: newberyite (MgHPO4·3H2O) and dittmarite (MgNH4PO4·H2O), and one amorphous product, depending on the reaction temperature. The transformation reactions comprise similar reaction orders n of ~ 0.5 and rate constants k of 0.5–8.1·10-4 s-1 for the reaction to newberyite, and 2.9·10-3 s-1 for the reaction to dittmarite, indicative of a diffusion-dominated mechanism that was interpreted as the transport of NH3 and water out of the struvite structure. Electron microscopy and Raman spectroscopy revealed that the following nucleation and growth of the new phases occur via a coupled dissolution-reprecipitation reaction. In summary, through my thesis, I could extend the knowledge of struvite nucleation and growth kinetics from aqueous solution and give new information on this mineral's decomposition and transformation pathways. This work probed the critical role played by temperature in the formation and decomposition of struvite. My findings contribute to improving struvite precipitation processes in wastewater treatment plants for P recovery. Furthermore, the new insights into the decomposition and transformation parameters of struvite in air have significant implications for struvite fertiliser storage and transportation, as understanding the transformation to secondary phases helps ensure the fertiliser properties and quality.

The ability of animals to navigate their environment, locate food sources, and find mating partners hinges on their capacity to process and integrate information provided by the visual system. At the heart of this complex task lies the intricate web of thousands of individual neurons, each playing a crucial role in the orchestration of sensory information. Understanding the rules and mechanisms guiding this neural computation is a profound pursuit central to the fields of neuroscience and ethology. My doctoral research advances our understanding of navigation by delving into neural circuitry and information processing mechanisms, particularly emphasizing polarized skylight detection in insects. Focused on Drosophila melanogaster, a powerful model organism, the study explores the intricate visual system comprised of optically isolated unit eyes called ommatidia. Approximately 800 of these units populate the adult retina, facilitating precise spatial sampling. Within the Drosophila retina, different ommatidial subtypes house specialized inner photoreceptors for color perception in the central retina or the detection of skylight polarization in the dorsal rim area (DRA). Visual information undergoes complex processing in the optic lobes before being relayed to higher brain structures, such as the anterior optic tubercle (AOTU) within the visual glomeruli. My thesis contributes to understanding the less well-known ventral polarization vision, exploring local circuitries in the optic lobes, and shedding light on the less-understood aspect of this visual modality. The literature study identifies functionally specialized non-DRA detectors by examining non-celestial polarization vision across diverse insect species, including dragonflies, butterflies, beetles, bugs, and flies. Although the ventral polarization vision in Drosophila melanogaster presents a fascinating modality, the unknown location of the specific circuitry stays hidden. Therefore, I turned my attention to the better-known specific circuitry of skylight polarization vision in the DRA and unveiled modality-specific connectivities of local medulla neurons in the DRA. Including Mt11-like medulla tangential cells that avoid the DRA region. Despite gathering comprehensive information from the entire medulla, these cells lack inputs related to polarized light from the DRA, indicating separate processing of distinct visual attributes within the central brain. Finally, I characterized the anatomical and physiological properties of MeTu-types, modality-specific to the DRA, called MeTu-DRA1 and MeTu-DRA2. Using the genetic toolkit of Drosophila melanogaster, the study showed for the first time that both populations are modality-specific postsynaptic to DRA.R7 photoreceptors only, project to the same subunit of the AOTU and show differences in their morphology as well as connectivity. Although the morphology showed significant differences, single-cell clones revealed a topographic projection of both MeTu-DRA sub-populations from the medulla to the AOTU. Based on these findings, we hypothesized that the anatomical and connectivity differences might result in different physiological response patterns of MeTu-DRA1 and MeTu-DRA2. In order to test this theory, I implemented calcium imaging (using GCaMP) under a 2-photon microscope. I recorded the physiological response properties of Dm-DRA1 (in the medulla) and MeTu-DRA1 and MeTu-DRA2 responses in the AOTU. Interestingly, I could show for the first time that MeTu-DRA1 shows a detailed representation of different ’Angle of Polarization’ (AoP) in the AOTU, and MeTu-DRA2 responses, however, split the AOTU in a dorsal or ventral half pattern. With EM reconstruction, we could identify a more detailed circuitry of the MeTu-DRAs and a new DRA-specific interhemispheric cell type called MeMe-DRAs. Additionally, I could show that only MeTu-DRA2 responds to unpolarized UV flashes presented contralaterally, which is most likely mediated by MeMe-DRAs and presents an early binocular integration of polarized skylight information. In conclusion, the discoveries made during my doctoral research significantly contribute to our comprehension of the functional characteristics and circuitry of MeTu-DRA neurons in . This comprehensive understanding enhances our knowledge of how binocular integration plays a crucial role in the neural mechanisms guiding polarization vision and navigation.

We use the results of Quigley and Shah to give a formula for the geometric fixed points of real topological cyclic homology of a bounded below ring spectrum with anti-involution. The anti-involution on a ring spectrum $A$ gives rise to a spectrum with canonical left and right $A$-module structures, whose tensor product over $A$ can be equipped with an action by the cyclic group of order 2. Our formula is then given by the homotopy equalizer of two maps from the homotopy fixed points to the Tate construction. Furthermore, we show that this homotopy equalizer is equivalent to the one given in the computation by Dotto, Moi and Patchkoria, thereby proving their result with different methods.

As an application of our result we calculate the real topological cyclic homology of group ring spectra for abelian groups and certain classes of dihedral groups. We do this for arbitrary ground ring spectra, whose underlying spectra are bounded below. This is accomplished via a decomposition formula for the dihedral bar construction of a group.

Entlang des Strukturwandels von Öffentlichkeit, bei dem digitale vernetzte Öffentlichkeiten die jüngste Ausprägung darstellen, geht nicht nur ein gesellschaftlicher Wandel einher, sondern auch erhebliche Veränderungen im Kommunikationsverhalten von Organisationen als Public Affairs-Akteur*innen sowie deren Praktiker*innen. Die Dissertation untersucht auf Basis des Strukturwandels von Öffentlichkeit, wie die Public Affairs-Praktiker*innen der DAX-40-Unternehmen mit dem Wandel von Öffentlichkeit und digitalen vernetzten Öffentlichkeiten umgehen. Dabei werden die Kommunikationsmittel und -formen analysiert, die zur Erreichung der Public Affairs-Ziele eingesetzt werden.

Bislang existieren nur wenige empirische Erkenntnisse zu diesem Forschungsfeld, weshalb die Arbeit darauf abzielt, diese Lücke zu schließen. In Zeiten des digitalen Wandels stehen Organisationen vor neuen Herausforderungen. Die strukturelle Organisation der Public Affairs-Arbeit muss angepasst, das (digitale) Kommunikationsrepertoire erweitert und die Verknüpfung zu anderen Unternehmensbereichen optimiert werden. Daher beleuchtet die Arbeit, wie Unternehmen mit den vielfältigen Herausforderungen der digitalen Public Affairs-Arbeit umgehen. Zentrale Forschungsfragen umfassen unter anderem den Umgang mit digitalen Kommunikationsformen, das Selbstverständnis der Praktiker*innen und die Nutzung sozialer Medien. Im Fokus der empirischen Untersuchung stehen 21 DAX-40-Unternehmen, deren Praktiker*innen im Rahmen von qualitativen Expert*innen-Interviews Erkenntnisse zum Forschungsinteresse liefern. Unterstützt durch eine Vorab-Systematisierung relevanter Spezifika der DAX-40-Unternehmen, wie deren Online-Auftritte, soll die Forschungsfrage der vorliegenden Arbeit beantwortet werden. Die Ergebnisse zeigen, dass in digitalen vernetzten Öffentlichkeiten dem Individuum, also den Public Affairs-Praktiker*innen eine herausragende und noch wissenschaftlich unzureichend anerkannte Rolle zukommt, da ein Großteil der Kommunikation hin zu politischen Entscheider*innen oder auch Monitoring und Recherche-Arbeiten über die eigenen Praktiker*innen-Profile stattfindet. Ebenfalls skizziert sich die digitale Public Affairs-Arbeit von Unternehmen als sehr vielschichtig, strategisch und individuell gestaltet. Über allem liegt die Skepsis eher in einem nicht-öffentlichen Rahmen der Public Affairs-Arbeit nachzugehen, anstatt diese öffentlich zu betreiben.

Durch die vorliegende Arbeit wird die Forschungsliteratur zu digitaler Public Affairs-Arbeit von Unternehmen und im speziellen von DAX-40-Unternehmen erweitert. Die Betrachtung aus kommunikationswissenschaftlicher Sicht schließt eine Lücke in Wissenschaft und Praxis und zeigt die vielfältigen Herausforderungen, denen Unternehmen im digitalen Wandel gegenüberstehen.

Canine digital squamous cell carcinomas (CDSCC) tend to behave more aggressively than other areas of the skin. Furthermore, CDSCC in dark-haired animals are more biologically aggressive than in light-haired animals. However, up to date there is no standardized histological evaluation and comparison of DSCC morphology between dark and light breeds. In addition, dark-haired dogs have a known predisposition to develop DSCC. Additionally, some studies have suggested that dogs with a copy number > 4 in the KITLG locus, which is associated with melanogenesis, have an increased susceptibility to the development of DSCC. However, if the KITLG copy number had an effect on the morphology and histopathological features of DSCC still remains largely unknown. Study 1 included the histological evaluation of DSCC from 94 dogs, divided into two groups, (1) dark-haired (n = 76) and (2) light-haired breeds (n = 18). Group 1 was further subdivided into three subgroups, (1a) various black-haired breeds (n = 11), (1b) black Schnauzers (n = 34) and (1c) black & tan breeds (n = 31). For an objective evaluation, two known grading schemes for squamous cell carcinomas were used comparatively. As a result, both histological grading systems exhibited significant differences between groups 1 and 2. Digital SCC of the light-haired dogs were consistently better differentiated than those of group 1. There were no significant differences between the different dark-haired breeds in any of the individual characteristics assessed (invasive front, degree of invasion, nuclear pleomorphism, tumor cell buds, smallest tumor nest size and amount of tumor stroma). For study 2, 70 blood samples were collected from dogs with DSCC (partially overlapping with study 1). This study was designed to test whether and to what extent the previously evaluated histologic grades correlated with the number of copies KITLG locus determined by ddPCR. For the second study, the grouping was established as follows; Group 0/unknown haircoat color (n = 11); Group 1.a/black non-Schnauzers (n = 15); group 1.b/black Schnauzers (n = 33); group 1.c/black & tan dogs (n = 7); group 2/light-haired animals (n = 4). The results showed a significant correlation between increased KITLG copy number and more malignant histologic grading. This suggests that KITLG may have a role in the development of DSCC by causing different, more aggressive morphologic features. The compilation of these two studies may help to better characterize and understand canine squamous cell carcinoma of the toe. By taking genetic predispositions into account, a better and individualized assessment of the risk of disease in black dogs and thus earlier treatment is possible.

This thesis investigates personality functioning and maladaptive traits as indicators and treatment targets in various, mostly clinical and adult populations. While personality functioning derives from object relations and mentalization theories, both theories of etiology and treatment within a psychodynamic paradigm, maladaptive traits derive from a lexical or multivariate paradigm within personality psychology. This thesis sought to answer questions on these concepts' assessment, etiological claims, and clinical utility. To these aims, five empirical studies are included. The first study investigated the psychodynamic theory that early childhood adversities and personality functioning interact in predicting adult psychopathology. Using a large representative sample, the study found that these factors explained up to 91% of the variance in symptoms of depression, anxiety, and somatization. In addition, previous analyses based on this data corroborate that personality functioning may be assessed reliably using a short questionnaire. The second study developed the PID5BF+ questionnaire to assess maladaptive traits as per DSM-5 and ICD-11. This measurement, validated on large clinical and non-clinical samples, successfully distinguishes between various psychopathologies, including differentiating internalizing disorders and borderline personality disorder. A slightly refined version was tested in 13 languages across 16,327 participants, proved reliable, and is now globally used in mental health studies. The third study investigated the lexical approach of maladaptive traits together with the etiologically informed approach of personality functioning, using data from mental health app users. It found that aspects of personality functioning, as outlined in object relations and mentalization theory, are central to psychopathology and explain large proportions of higher order variance in a hierarchical taxonomy of psychopathology. Specifically, interpersonal aspects of personality functioning were linked to externalizing disorders, while self-related aspects were associated with internalizing disorders. The study also demonstrated that personality functioning accounts for a significant portion of longitudinal variance in affective well-being and psychosocial functioning. Additionally, it highlighted that while personality functioning captures broad psychopathology aspects, maladaptive traits are more useful in capturing variance that is specific to particular disorders.

Study 4 explored if maladaptive traits are malleable through clinical psychological interventions, comparing a guided online intervention with face-to-face/blended psychotherapy in small clinical samples. While both treatments effectively reduced mental health symptoms, their impacts on maladaptive traits differed. The online intervention primarily influenced negative affectivity, consistent with its focus on targeting neuroticism. In contrast, the face-to-face therapy resulted in significant changes across all maladaptive trait domains and the overall personality dysfunction score. Notably, in the face-to-face setting, the reduction of personality dysfunction was a more robust predictor of post-treatment symptom reduction than in the online treatment. Study 5, a large randomized controlled trial, investigated the effects of a self-guided internet-based intervention, employing multiple imputation and random forest lee-bound methods to handle missing data. Precision of these methods depends on baseline variables that predict future outcomes and behaviors of the participants. Personality functioning and maladaptive traits were significant predictors for trial dropout, indicating that individuals with greater personality dysfunction tend to disengage more from self-guided digital mental health interventions, suggesting a need for more personalized support for this population in such interventions. Taken together, these studies establish that personality functioning is instrumental in capturing broad aspects of psychopathology, while maladaptive traits are more specific to individual psychopathologies. The findings suggest the potential for expanding the dual assessment approach of severity and style in the diagnostics of personality disorder according to ICD-11 to general psychopathology. Additionally, these studies show that personality dysfunction and maladaptive traits can change through clinical interventions and are useful in handling missing data in clinical trials. This thesis underscores the emerging relevance of these concepts, rooted in early psychological theories, for modern mental health research and practice.

Pectins are abundant polysaccharides in plant-derived biomass, with a plethora of possible applications such as usage as food preservative, formulation for cancer treatment and corrosion inhibitors for steels among many others. These acidic polysaccharides of high structural complexity have important biological functions in the plant cell wall. One domain of pectin, rhamnogalacturonan-II (RG-II) is the most complex oligosaccharide known to date. It is constructed from at least 13 different monosaccharides and at least 21 distinct glycosidic linkages. Despite its complexity, it is widely conserved in the plant kingdom. RG-II molecules form borate diesters with each other, an essential structure in the cell wall for plant growth. However, very little is known about the biosynthesis, the structure-function relationships and the three-dimensional structure of RG-II. Synthetic oligosaccharides that are well-defined and of high purity are very valuable tools to study RG-II. Here, a synthetic approach to a highly complex side chain A nonasaccharide equipped with an aminoalkyl linker for later immobilization on surfaces or fuctionalization with fluorescent dyes was developed. The main challenges were to design a retrosynthetic approach for the branched target nonasaccharide with a highly orthogonal protective group strategy, to find suitable glycosylation strategies to construct all nine glycosidic bonds, including four 1,2-cis-glycosidic bonds between monosaccharides, and the 1,2-cis-selective installation of an aminoalkyl linker at the reducing end. Using this strategy, small amounts of a protected version of the full side chain A analogue containing one backbone galacturonic acid were succesfully synthesized in 89 steps. Key transformation was a final [4+5]-glycosylation that requires further optimization. The results demonstrate that even the most complex oligosaccharides become synthetically accessible if modern synthetic glycochemistry methods are applied and further developed. Additionally, three linear side chain A fragments were synthesized. The obtained side chain A fragments are important tools for the investigation of RG-II biosynthesis. Furthermore, they may be useful to investigate structure-function relationships and the three-dimensional structure of the highly complex RG-II structure, which remain currently elusive. With the developed synthetic methods further RG-II fragments can be synthesized, expanding the molecular toolbox for studying RG-II biology.

The subterranean naked mole-rat (Heterocephalus glaber, NM-R) is a rodent that has attracted growing research interest from a biomedical and zoological perspective. NM-Rs exhibit unique physiological characteristics including eusociality, pain insensitivity, cancer resistance, an unusual immune system, a long lifespan, and the lower basal metabolic rate than expected for its body mass. In addition, NM-Rs are poikilothermic mammals. So far, the precise mechanisms of cold detection processes remain poorly understood. The transient receptor potential melastatin 8 (TRPM8) ion channel is the principal cold receptor in mammals, a better understanding of the role of TRPM8 is needed to improve our current knowledge of the thermosensory system in NM-R. We used RNAScope and immunofluorescence to better understand the expression and localization of TRPM8 in sensory and non-sensory tissues. TRPM8 is expressed in the NM-R DRGs but more TRPM8+ NF200+ neurons are found in NM-R compared to mice. Approximately 33.7% of TRPM8-positive neurons also express NF200, indicating a significant presence in myelinated sensory neurons, while 39.33% and 19.14% of these neurons co-express CGRP and TRPV1, respectively. Interestingly, TRPM8 was also observed in large-diameter neurons and was not limited to smaller neurons typically associated with cold sensing in mice. Furthermore, we identified TRPM8 expression in the near lamina I of the dorsal horn of the NM-R spinal cord, which is similar to mice. Notably, we observed abundant and specific Trpm8 mRNA expression in the neurons of grey matter within the NM-R spinal cord. A notable discovery was the identification of a unique extended N-terminal sequence in NM-R TRPM8 compared with TRPM8 sequences from more than 30 mammals. We confirmed a unique extended N-terminal variant of the TRPM8 ion channel in NM-Rs using RT-PCR and a custom Ex-trpm8 probe designed for the 415–854 bp region from the NM-R Trpm8 mRNA. To explore the functional implications of this extended N-terminal sequence, we performed calcium imaging assays using HEK293T cells expressing NM-R TRPM8. The results demonstrated that the extended sequence significantly diminishes the response of TRPM8 to cold, menthol, and icilin. When this sequence was deleted, TRPM8 function was restored to levels similar to the mouse TRPM8. Additionally, fusing this N-terminal extension to mouse TRPM8 reduced its responsiveness, suggesting that the extended sequence modulates cold sensitivity in NM-Rs. VII Further experiments using calcium imaging of cultured NM-R DRG neurons and skin-nerve preparations demonstrated that NM-Rs retain intact cold sensation, which is largely independent of TRPM8. Cold-sensitive neurons were more abundant in NM-Rs than in mice, particularly among larger neurons. Additionally, cold-sensitive fibers in NM-Rs exhibited faster conduction velocities compared to those in mice, suggesting the involvement of alternative pathways for cold detection and potential evolutionary adaptations for rapid cold sensing in subterranean environments. These findings suggest that NM-Rs may have evolved unique TRPM8 isoforms and alternative mechanisms for cold perception, which may reflect adaptations to their distinct ecological niche. These findings not only advance our understanding of cold detection in NM-Rs but also raise intriguing questions about the evolutionary divergence of TRPM8 function in this species.

Search trees on graphs (STGs) are a far-reaching generalization of binary search trees (BSTs), where the key space is a graph instead of a totally ordered set. Intuitively, instead of comparing keys, we compare vertices, which tells us their relative position in the graph.

STGs can alternatively be seen as (1) a data structure for vertex searching that can be built on top of certain graphs that support vertex comparisons (e.g., quadtrees) or (2)~as a hierarchical decomposition of the underlying graph. For the latter purpose, search trees have appeared in the literature under different names (e.g., elimination trees and spines), and there are strong connections to the ubiquitous notions of tree-depth and tree-width.

Many computational and combinatorial questions about BSTs naturally generalize to the STG setting. In this thesis, we concentrate on the following three.

Suppose we are given a query distribution and want to compute the search tree that minimizes the expected search time. This is the optimal static search tree problem. Computing optimal static BSTs is possible in quadratic time, but for STGs no polynomial-time algorithm is known, even when the underlying graph is a tree. We discuss multiple approximation algorithms for trees and graphs of bounded tree-width, as well as NP-hardness of the problem in the general case.

In contrast to static search trees, which cannot be modified after construction, dynamic search trees may be restructured after each search using the rotation operation. We generalize the well-known Splay algorithm from BSTs to STGs in the special case where the underlying graph is a tree. We also use that algorithm for a dynamic forest data structure, including an implementation and its experimental evaluation.

Finally, the rotation distance between two STGs is the minimum number of rotations needed to transform one into the other. We are interested in the maximum rotation distance for a given underlying graph, which is exactly the diameter of the so-called graph associahedron of the underlying graph. Somewhat surprisingly, there is a tight connection between this combinatorial problem and the static and dynamic search tree problems. We present several new results, including a simple algorithm to compute the diameter of a graph associahedron when the underlying graph is a tree of bounded path-width.