On Pairwise Graph Connectivity

A graph on at least k+1 vertices is said to have global connectivity k if any two of its vertices are connected by k independent paths. The local connectivity of two vertices is the number of independent paths between those specific vertices. This dissertation is concerned with pairwise connectivity notions, meaning that the focus is on local connectivity relations that are required for a number of or all pairs of vertices. We give a detailed overview about how uniformly k-connected and uniformly k-edge-connected graphs are related and provide a complete constructive characterization of uniformly 3-connected graphs, complementing classical characterizations by Tutte. Besides a tight bound on the number of vertices of degree three in uniformly 3-connected graphs, we give results on how the crossing number and treewidth behaves under the constructions at hand. The second central concern is to introduce and study cut sequences of graphs. Such a sequence is the multiset of edge weights of a corresponding Gomory-Hu tree. The main result in that context is a constructive scheme that allows to generate graphs with prescribed cut sequence if that sequence satisfies a shifted variant of the classical Erdős-Gallai inequalities. A complete characterization of realizable cut sequences remains open. The third central goal is to investigate the spectral properties of matrices whose entries represent a graph's local connectivities. We explore how the spectral parameters of these matrices are related to the structure of the corresponding graphs, prove bounds on eigenvalues and related energies, which are sums of absolute values of all eigenvalues, and determine the attaining graphs. Furthermore, we show how these results translate to ultrametric distance matrices and touch on a Laplace analogue for connectivity matrices and a related isoperimetric inequality

Device-independent entanglement quantification and related applications

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.Comment: 4 pages + appendix, resubmitted versio

Assessment of Physical Activity Patterns in Adolescent Patients With Anorexia Nervosa and Their Effect on Weight Gain

(1) Background: Altered physical activity (PA) affects weight recovery in anorexia nervosa (AN) patients. The study aimed to objectively characterize PA patterns and their effect on weight trajectory in adolescent AN patients. (2) Methods: PA was assessed in 47 patients on admission to inpatient treatment, in n = 25 of these patients again 4 weeks after discharge (follow-up, FU), as well as in 20 adolescent healthy controls using the Sense Wear™ armband. The following PA categories were defined by metabolic equivalent (MET) ranges: sedentary behavior (SB), light (LPA), moderate (MPA), vigorous (VPA), and high-level PA (HLPA= MPA + VPA). (3) Results: LPA on admission was significantly higher in AN patients than in controls (103 vs. 55 min/d, p < 0.001), and LPA in AN decreased over time to 90 min/d (p = 0.006). Patients with higher admission LPA (n = 12) still had elevated LPA at FU (p = 0.003). High admission LPA was associated with a higher inpatient BMI percentage gain (ΔBMI%; 18.2% ± 10.0% vs. 12.0% ± 9.7%, p = 0.037) but with a loss of ΔBMI% at FU (-2.3% ± 3.6% vs. 0.8% ± 3.6%, p = 0.045). HLPA at baseline was associated with a lower inpatient ΔBMI% (p = 0.045). (4) Conclusion: Elevated LPA in AN patients decreased after inpatient treatment, and PA patterns had an impact on weight trajectory

Explaining non-compliance dynamics in the EU

1\. Introduction 6 2\. Non-Compliance and Policy-Variation 7 3\. Policy- Explanations 12 4\. Rule-specific Explanations 18 5\. Conclusions 27 Literature 29 Appendix: Operationalization of Power and Capacity 33The European Union’s infringement procedure is highly legalized. Nevertheless, as in other international institutions, non-compliance occurs on a regular basis and its transformation into compliance varies across EU infringement stages and over time. State of the art compliance literature focuses mainly on country-specific explanations, such as power, capacity, and legitimacy. In particular power-capacity models explain a good part of whether non-compliance occurs and how quickly it can be resolved. Yet, these approaches leave substantial parts of the empirical variation that we observe unexplained. This paper argues that policy and, in particular, rule-specific variables – although often neglected – are important for explaining non-compliance. Based on a quantitative analysis, we show that policy matters not only for the frequency with which EU law is violated, but also the persistence of non- compliance over time and over the different stages of the infringement procedure

Evaluation der intensitätsmodulierten Bestrahlungstechnik für die stereotaktische Strahlentherapie im kraniellen Bereich

Die fraktionierte stereotaktisch geführte Radiotherapie stellt eine Möglichkeit der Behandlung intrakranieller Tumoren dar, bei denen eine chirurgische Resektion nicht oder nicht vollständig möglich ist. Ziel dieser Arbeit war der Vergleich der Dosisverteilung von Bestrahlungsplänen, die mittels fluenzmodulierter (IMRT) und 3D konformaler stereotaktisch geführter Bestrahlungstechnik (conformal beam) für Hypophysenadenome und petroclivale Meningeome erstellt wurden. Auf Basis des CT-Datensatzes eines Alderson-Phantoms erfolgten zunächst die systematische Untersuchung der IMRT Eingabeparameter und die Definition von Dosis-Volumen-Constraints für beide Tumorentitäten. Im Anschluss wurden die gewonnenen Erkenntnisse bei der fluenzmodulierten Bestrahlungsplanung von 10 realen Patienten, 5 je Tumorentität, angewendet. Zusätzlich wurde für jeden dieser Patienten ein 3D konformaler Bestrahlungsplan erstellt. Die Evaluation der Bestrahlungspläne erfolgte durch verschiedene quantitativer Parameter unter Einbeziehung der subjektiven Beurteilung der Dosisverteilung. Bei beiden Tumorentitäten lieferte in je 4 von 5 Fällen die IMRT einen Vorteil gegenüber der conformal beam Bestrahlung, der vor allem auf der besseren Erfassung, Dosishomogenität und höheren Median-Dosis im bestrahlten Zielvolumen (PTV) beruhte. Komplex geformte Zielvolumina profitierten dabei besonders von der Fluenzmodulation. Dem stand jedoch in einigen Fälle eine stärke Belastung der Risikoorgane (OAR) mit einer höheren Dosis und die generell höhere Anzahl notwendiger Monitoreinheiten gegenüber. Zuletzt wurde auf Basis von MatLAB eine Software entwickelt, welche die Verifikation von stereotaktisch geführten IMRT-Bestrahlungen und die Analyse von Winston-Lutz-Tests ermöglicht