Fixed-parameter tractability of Directed Multicut with three terminal pairs parameterized by the size of the cutset: twin-width meets flow-augmentation

We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and $(s_3,t_3)$, and an integer $k$, asks to find a set of at most $k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths, all $s_2t_2$-paths, and all $s_3t_3$-paths. The parameterized complexity of this case has been open since Chitnis, Cygan, Hajiaghayi, and Marx proved fixed-parameter tractability of the 2-terminal-pairs case at SODA 2012, and Pilipczuk and Wahlstr\"{o}m proved the W[1]-hardness of the 4-terminal-pairs case at SODA 2016. On the technical side, we use two recent developments in parameterized algorithms. Using the technique of directed flow-augmentation [Kim, Kratsch, Pilipczuk, Wahlstr\"{o}m, STOC 2022] we cast the problem as a CSP problem with few variables and constraints over a large ordered domain.We observe that this problem can be in turn encoded as an FO model-checking task over a structure consisting of a few 0-1 matrices. We look at this problem through the lenses of twin-width, a recently introduced structural parameter [Bonnet, Kim, Thomass\'{e}, Watrigant, FOCS 2020]: By a recent characterization [Bonnet, Giocanti, Ossona de Mendes, Simon, Thomass\'{e}, Toru\'{n}czyk, STOC 2022] the said FO model-checking task can be done in FPT time if the said matrices have bounded grid rank. To complete the proof, we show an irrelevant vertex rule: If any of the matrices in the said encoding has a large grid minor, a vertex corresponding to the ``middle'' box in the grid minor can be proclaimed irrelevant -- not contained in the sought solution -- and thus reduced

Vier empirische Aufsätze zu sozio-ökonomischen Aspekten der kohlenstoffarmen Energie-Transformation

This thesis contains four empirical contributions which address socio-economic challenges of the Anthropocene and carbon dioxide emissions as well as critical issues of nuclear power which are of relevance for achieving the transformation towards decentralized, sustainable energy systems. We start analyzing the relationship between economic growth and carbon dioxide emissions, thereby challenging the hypothesized long-term sustainability of further economic acceleration. The empirical results indicate that continued economic growth does not pose a natural solution to reduce carbon dioxide emissions in the long-term as suggested by the Environmental Kuznets Curve (EKC) hypothesis. Next, we provide an assessment of the primary drivers of carbon dioxide emissions and identify the average growth in consumption of goods and services produced rather than population as a stronger determinant. We analyze these issues using datasets comprising countries grouped according to their level of economic development and apply dynamic nonstationary panel time series estimation techniques which account for heterogeneity among countries. We then turn towards democracy and security issues surrounding both the introduction and usage of nuclear energy. We are the first to empirically analyze the impacts of democratic development on the introduction of nuclear power. Using a multinomial logistic regression approach to predict category membership, we find that countries with lower democratic development are more likely to introduce nuclear power. Finally, we provide the first empirical analysis of the determinants of the accumulation of nuclear weapons in seven nuclear arms states. Using econometric techniques for inferring causality in time series data, we identify a significant causal relationship between a state’s nuclear warhead stockpiles and its nuclear energy consumption levels.Die vorliegende Dissertation enthält vier empirische Beiträge, welche sich mit sozioökonomischen Herausforderungen des Anthropozäns und Kohlendioxidemissionen sowie kritischen Fragen der Atomkraft befassen, die für den Übergang zu einem dezentralen, nachhaltigen Energiesystemen von Bedeutung sind. Die Arbeit beginnt mit der Analyse des Zusammenhangs zwischen Wirtschaftswachstum und Kohlendioxidemissionen und hinterfragt die Hypothese der langfristigen Nachhaltigkeit von kontinuierlichem Wirtschaftswachstum. Die empirischen Befunde implizieren, dass anhaltendes Wirtschaftswachstum keine nachhaltige Lösung darstellt, um den Kohlendioxidausstoß langfristig zu reduzieren, wie von der Umwelt-Kuznets-Kurve Hypothese vorgeschlagen. Als nächstes evaluieren wir die Determinanten von Kohlendioxidemissionen und identifizieren das durchschnittliche Wachstum des Konsums der produzierten Güter und Dienstleistungen anstelle von Bevölkerungswachstum als stärksten Bestimmungsfaktor. Zur Analyse dieser Fragestellungen benutzen wir Datensätze, in denen Länder entsprechend ihrem wirtschaftlichen Entwicklungsstand klassifiziert werden. Wir verwenden dynamische ökonometrische Schätzverfahren zur Analyse von nicht-stationären Panel-Zeitreihen Daten, welche die Heterogenität zwischen den Ländern berücksichtigen. Danach fokussieren wir demokratie- und sicherheitsrelevante Fragestellungen, welche sowohl die Einführung als auch die Nutzung von Atomkraft betreffen. Wir testen erstmalig empirisch den Zusammenhang zwischen dem Ausmaß an demokratischer Entwicklung und dem Einstieg in die Atomkraft analysieren. Die empirischen Ergebnisse einer multinomialen logistischen Regressionsanalyse zur Vorhersage von Gruppenzugehörigkeiten zeigen, dass Länder mit einem niedrigeren Ausmaß an demokratischer Entwicklung eher den Einstieg in die Atomkraft durchgeführt haben. Abschließend liefern wir die erste empirische Analyse von Bestimmungsfaktoren für die Anhäufung von Atomwaffen in sieben atomar bewaffneten Staaten. Anhand von ökonometrischen Verfahren zur kausalen Modellierung in Zeitreihendaten identifizieren wir eine signifikante kausale Beziehung zwischen der Anzahl an Atomsprengköpfen eines Staates und seines Atomenergieverbrauchs

Rotating Instability in an Annular Cascade: Detailed Analysis of the Instationary Flow Phenomena

Rotating instability (RI) occurs at off-design conditions in compressors, predominantly in configurations with large tip or hub clearance ratios of s* �> 3%. RI is the source of the blade tip vortex noise and a potential indicator for critical operating conditions like rotating stall and surge. The objective of this paper is to give more physical insight into the RI phenomenon using the analysis results of combined near-field measurements with high-speed particle image velocimetry (PIV) and unsteady pressure sensors. The investigation was pursued on an annular cascade with hub clearance. Both the unsteady flow field next to the leading edge as well as the associated rotating pressure waves were captured. A special analysis method illustrates the characteristic pressure wave amplitude distribution, denoted as “modal events” of the RI. Moreover, the slightly adapted method reveals the unsteady flow structures corresponding to the RI. Correlations between the flow profile, the dominant vortex structures, and the rotating pressure waves were found. Results provide evidence to a new hypothesis, implying that shear layer instabilities constitute the basic mechanism of the RI