A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization

In a recent issue of this journal, Mordukhovich et al.\ pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem one is given $k+1$ closed convex sets in \Real^d equipped with its Euclidean norm and asked to find the point in the last set such that the sum of the distances to the first $k$ sets is minimal. In later work the authors generalize the Heron problem even further, relax its convexity assumptions, study its theoretical properties, and pursue subgradient algorithms for solving the convex case. Here, we revisit the original problem solely from the numerical perspective. By exploiting the majorization-minimization (MM) principle of computational statistics and rudimentary techniques from differential calculus, we are able to construct a very fast algorithm for solving the Euclidean version of the generalized Heron problem.Comment: 21 pages, 3 figure

Controlling construction-induced vibrations in healthcare facilities

Controlling excessive floor vibrations is critical in modern healthcare facilities where high-resolution imaging and diagnostic equipment are often used. These types of equipment have stringent floor vibration criteria to ensure the accuracy of their results. Controlling floor vibrations is further complicated as existing healthcare facilities are being renovated and upgraded to meet current healthcare demands, while remaining in operation. This paper presents a case study of an existing hospital which is undergoing extensive renovations. This hospital houses a variety of diagnostic imaging equipment including Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) equipment, as well as mass spectrometers. To determine the extent of the vibration mitigation required such that the equipment can remain operational during construction, vibration tests simulating the future construction activities were conducted. The vibration tests consisted of striking the ground with an excavator, while accelerometers were placed at strategic locations throughout the hospital to capture the excitation

Controlling construction-induced vibrations in healthcare facilities

Controlling excessive floor vibrations is critical in modern healthcare facilities where high-resolution imaging and diagnostic equipment are often used. These types of equipment have stringent floor vibration criteria to ensure the accuracy of their results. Controlling floor vibrations is further complicated as existing healthcare facilities are being renovated and upgraded to meet current healthcare demands, while remaining in operation. This paper presents a case study of an existing hospital which is undergoing extensive renovations. This hospital houses a variety of diagnostic imaging equipment including Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) equipment, as well as mass spectrometers. To determine the extent of the vibration mitigation required such that the equipment can remain operational during construction, vibration tests simulating the future construction activities were conducted. The vibration tests consisted of striking the ground with an excavator, while accelerometers were placed at strategic locations throughout the hospital to capture the excitation

Before and After the Wall : A Social History of German Cinema

This thesis deals with the perception of the Cold War in selected German feature films. Sonnenallee (Leander Haussmann, 1999), Die Unberührbare (Oscar Roehler, 2000), Good Bye Lenin! (Wolfgang Becker, 2003), Herr Lehmann (Leander Haussmann, 2003) and Das Leben der Anderen (Florian Henckel von Donnersmarck, 2006) have been selected for a comparative analysis that focusses on narratives of the Cold-War era after reunification, and for an examination of how the social impact of German unification has been addressed in these films. In terms of methodology, the thesis uses Pierre Sorlin's social history of cinema and Pierre Nora's concept of lieu de mémoire to describe the social imagination and nostalgic representation of memories. There is a research gap in previous studies concerning how the Cold War has become a topic in recent German feature film production, and this study aims to complement those earlier works.