The flow of two falling balls mixes rapidly

In this paper we study the system of two falling balls in continuous time. We modell the system by a suspension flow over a two dimensional, hyperbolic base map. By detailed analysis of the geometry of the system we identify special periodic points and show that the ratio of certain periods in continuous time is Diophantine for almost every value of the mass parameter in an interval. Using results of Melbourne (\cite{M}) and our previous achievements \cite{BBNV} we conclude that for these values of the parameter the flow mixes faster than any polynomial. Even though the calculations are presented for the specific physical system, the method is quite general and can be applied to other suspension flows, too

The Graph of Our Mind

Graph theory in the last two decades penetrated sociology, molecular biology, genetics, chemistry, computer engineering, and numerous other fields of science. One of the more recent areas of its applications is the study of the connections of the human brain. By the development of diffusion magnetic resonance imaging (diffusion MRI), it is possible today to map the connections between the 1-1.5 cm$^2$ regions of the gray matter of the human brain. These connections can be viewed as a graph: the vertices are the anatomically identified regions of the gray matter, and two vertices are connected by an edge if the diffusion MRI-based workflow finds neuronal fiber tracts between these areas. This way we can compute 1015-vertex graphs with tens of thousands of edges. In a previous work, we have analyzed the male and female braingraphs graph-theoretically, and we have found statistically significant differences in numerous parameters between the sexes: the female braingraphs are better expanders, have more edges, larger bipartition widths, and larger vertex cover than the braingraphs of the male subjects. Our previous study has applied the data of 96 subjects; here we present a much larger study of 426 subjects. Our data source is an NIH-founded project, the "Human Connectome Project (HCP)" public data release. As a service to the community, we have also made all of the braingraphs computed by us from the HCP data publicly available at the \url{http://braingraph.org} for independent validation and further investigations.Comment: arXiv admin note: substantial text overlap with arXiv:1512.01156, arXiv:1501.0072

The Advantage is at the Ladies: Brain Size Bias-Compensated Graph-Theoretical Parameters are Also Better in Women's Connectomes

In our previous study we have shown that the female connectomes have significantly better, deep graph-theoretical parameters, related to superior "connectivity", than the connectome of the males. Since the average female brain is smaller than the average male brain, one cannot rule out that the significant advantages are due to the size- and not to the sex-differences in the data. To filter out the possible brain-volume related artifacts, we have chosen 36 small male and 36 large female brains such that all the brains in the female set are larger than all the brains in the male set. For the sets, we have computed the corresponding braingraphs and computed numerous graph-theoretical parameters. We have found that (i) the small male brains lack the better connectivity advantages shown in our previous study for female brains in general; (ii) in numerous parameters, the connectomes computed from the large-brain females, still have the significant, deep connectivity advantages, demonstrated in our previous study.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0072

Limited Information Shared Control and its Applications to Large Vehicle Manipulators

Diese Dissertation beschäftigt sich mit der kooperativen Regelung einer mobilen Arbeitsmaschine, welche aus einem Nutzfahrzeug und einem oder mehreren hydraulischen Manipulatoren besteht. Solche Maschinen werden für Aufgaben in der Straßenunterhaltungsaufgaben eingesetzt. Die Arbeitsumgebung des Manipulators ist unstrukturiert, was die Bestimmung einer Referenztrajektorie erschwert oder unmöglich macht. Deshalb wird in dieser Arbeit ein Ansatz vorgeschlagen, welcher nur das Fahrzeug automatisiert, während der menschliche Bediener ein Teil des Systems bleibt und den Manipulator steuert. Eine solche Teilautomatisierung des Gesamtsystems führt zu einer speziellen Klasse von Mensch-Maschine-Interaktionen, welche in der Literatur noch nicht untersucht wurde: Eine kooperative Regelung zwischen zwei Teilsystemen, bei der die Automatisierung keine Informationen von dem vom Menschen gesteuerten Teilsystem hat. Deswegen wird in dieser Arbeit ein systematischer Ansatz der kooperativen Regelung mit begrenzter Information vorgestellt, der den menschlichen Bediener unterstützen kann, ohne die Referenzen oder die Systemzustände des Manipulators zu messen. Außerdem wird ein systematisches Entwurfskonzept für die kooperative Regelung mit begrenzter Information vorgestellt. Für diese Entwurfsmethode werden zwei neue Unterklassen der sogenannten Potenzialspiele eingeführt, die eine systematische Berechnung der Parameter der entwickelten kooperativen Regelung ohne manuelle Abstimmung ermöglichen. Schließlich wird das entwickelte Konzept der kooperativen Regelung am Beispiel einer großen mobilen Arbeitsmaschine angewandt, um seine Vorteile zu ermitteln und zu bewerten. Nach der Analyse in Simulationen wird die praktische Anwendbarkeit der Methode in drei Experimenten mit menschlichen Probanden an einem Simulator untersucht. Die Ergebnisse zeigen die Überlegenheit des entwickelten kooperativen Regelungskonzepts gegenüber der manuellen Steuerung und der nicht-kooperativen Steuerung hinsichtlich sowohl der objektiven Performanz als auch der subjektiven Bewertung der Probanden. Somit zeigt diese Dissertation, dass die kooperative Regelung mobiler Arbeitsmaschinen mit den entwickelten theoretischen Konzepten sowohl hilfreich als auch praktisch anwendbar ist

Two Essays on Contemporary Music

Bálint András Varga (1941–2019) was an advocate for and a keen critic of contemporary music, first on radio, and later as an acquisitions editor for both Editio Hungarica and Universal-Edition. He interviewed many musical figures and planned to interview visual artists before he died. His interlocutors were impressed with Varga’s insightful questions and frequently answered them much more comprehensively than they would ones from standard journalists. These two essays were intended to be published in Varga’s third book, From Boulanger to Stockhausen: Interviews and a Memoir. The first, “What to Listen for in Music,” refers to Aaron Copland’s book of the same name, furnishing some insight into the criteria Varga used when listening and judging a new work. The second, “Dogma,” recounts the twentieth-century smothering of individuality and creative imagination by a damp blanket of conformism and authoritarian dictates