Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Good just isn't Good enough. Best System Probabilities and the Foundations of Statistical Mechanics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two strategies, viz. a globalist as suggested by Loewer, and a localist as advocated by Frigg and Hoefer. Both strategies fail because the system they are part of have rivals that are roughly equally good, while ontic probabilities should be part of a clearly winning system. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Schulpraktika in der Lehrerbildung. Theoretische Grundlagen, Konzeptionen, Prozesse und Effekte = Pedagogical field experiences in teacher education. Theoretical foundations, programmes, processes, and effects

Seit mehr als zwanzig Jahren werden in der tertiären Lehramtsausbildung Schulpraktika reformiert und neuerdings in ihrem zeitlichen Umfang relativ zur Studienzeit vergrößert. Zum Gegenstand reger Forschungsaktivitäten avancierten Schulpraktika jedoch erst im letzten Jahrzehnt. Hiermit werden ein Überblick über das Forschungsfeld (Grundlagen der schulpraktischen Komponenten der Lehrerbildung; Forschungsmethodik) vorgelegt und aktuelle Forschungsergebnisse zu zentralen Aspekten der Wirksamkeit von Praktika und Effekten von Mentoring präsentiert. In englischsprachigen bzw. deutschsprachigen Beiträgen wird der Forschungsstand in Deutschland, den Niederlanden, Österreich und der Schweiz sowie den USA aufgezeigt. Der Band richtet sich an Personen, die in der Lehrerbildung tätig sind, also an Dozent/inn/en in Hochschulen und Seminaren, an Lehrerbildungsforscher/innen sowie an Fachpersonen in der Bildungsadministration und interessierte Studierende.

The Underwater Photic Environment of Cape Maclear, Lake Malawi: Comparison Between Rock- and Sand-Bottom Habitats and Implications for Cichlid Fish Vision

Lake Malawi boasts the highest diversity of freshwater fishes in the world. Nearshore sites are categorized according to their bottom substrate, rock or sand, and these habitats host divergent assemblages of cichlid fishes. Sexual selection driven by mate choice in cichlids led to spectacular diversification in male nuptial coloration. This suggests that the spectral radiance contrast of fish, the main determinant of visibility under water, plays a crucial role in cichlid visual communication. This study provides the first detailed description of underwater irradiance, radiance and beam attenuation at selected sites representing two major habitats in Lake Malawi. These quantities are essential for estimating radiance contrast and, thus, the constraints imposed on fish body coloration. Irradiance spectra in the sand habitat were shifted to longer wavelengths compared with those in the rock habitat. Beam attenuation in the sand habitat was higher than in the rock habitat. The effects of water depth, bottom depth and proximity to the lake bottom on radiometric quantities are discussed. The radiance contrast of targets exhibiting diffused and spectrally uniform reflectance depended on habitat type in deep water but not in shallow water. In deep water, radiance contrast of such targets was maximal at long wavelengths in the sand habitat and at short wavelengths in the rock habitat. Thus, to achieve conspicuousness, color patterns of rock-and sand-dwelling cichlids would be restricted to short and long wavelengths, respectively. This study provides a useful platform for the examination of cichlid visual communication.