Ursula Streckeisen / Denis Hänzi / Andrea Hungerbühler: Fördern und Auslesen. Deutungsmuster von Lehrpersonen zu einem beruflichen Dilemma. Wiesbaden: VS Verlag für Sozialwissenschaften 2007 (340 S.) [Rezension]

Rezension von: Ursula Streckeisen / Denis Hänzi / Andrea Hungerbühler: Fördern und Auslesen. Deutungsmuster von Lehrpersonen zu einem beruflichen Dilemma. Wiesbaden: VS Verlag für Sozialwissenschaften 2007 (340 S.; ISBN 978-3-531-15346-9; 34,90 EUR)

Piecewise-Linear Farthest-Site Voronoi Diagrams

Voronoi diagrams induced by distance functions whose unit balls are convex polyhedra are piecewise-linear structures. Nevertheless, analyzing their combinatorial and algorithmic properties in dimensions three and higher is an intriguing problem. The situation turns easier when the farthest-site variants of such Voronoi diagrams are considered, where each site gets assigned the region of all points in space farthest from (rather than closest to) it. We give asymptotically tight upper and lower worst-case bounds on the combinatorial size of farthest-site Voronoi diagrams for convex polyhedral distance functions in general dimensions, and propose an optimal construction algorithm. Our approach is uniform in the sense that (1) it can be extended from point sites to sites that are convex polyhedra, (2) it covers the case where the distance function is additively and/or multiplicatively weighted, and (3) it allows an anisotropic scenario where each site gets allotted its particular convex distance polytope

Die Sozioanalyse literarischer Texte als Methode der qualitativen Sozialforschung oder: welche Wirklichkeit enthält Fiktion?

"With his 1,200+ page study of Robert Musil's novel "The Man Without Qualities", Norbert Christian Wolf has produced a book which many may assume is "unreadable" on account of its enormous size alone. As a work of literary studies, it certainly runs the risk of being largely ignored by the social sciences. From a methodological perspective, however, there are good reasons to engage with this book: not only does it contain a concise theoretical substantiation and methodological description of the socio-analysis of literary texts according to Pierre Bourdieu, it also demonstrates this method in detail on the corpus of the fictional characters in Musil's novel. In terms of literary studies, Wolf's book can therefore be viewed as a kind of encyclopedia for Musil's work; sociologically, it represents a nuanced socio-analysis of the "history of the calamities of the 20th century". Before looking at the methodological and methodical aspects of Wolf's study, this review essay presents some introductory thoughts on the use of literary works in the social sciences as well as a few cursory references to selected works which introduce or make use of this method themselves." (author's abstract

Grundlage einer soziologischen Theorie der Zeitlichkeit? Bourdieus theoretische Denkwerkzeuge als Erkenntnispotenzial für qualitativ-empirische Forschung

Dem Aspekt der Zeitlichkeit des Sozialen in BOURDIEUs Soziologie wird bislang nur gelegentlich systematisch Beachtung geschenkt. Als vergessene Geschichte und Vorwegnahme der Zukunft wohnt diese Zeitlichkeit insbesondere BOURDIEUs Habitus-Konzept inne und ist dadurch fest mit sozialen Praktiken handelnder Akteur*innen in der Gegenwart verknüpft. Aber auch alle anderen theoretischen Konzepte BOURDIEUs enthalten im Kern zeitliche Aspekte, sodass Temporalität als Ligatur betrachtet werden kann, die seine theoretischen Denkwerkzeuge miteinander verbindet und zugleich Grundlage einer soziologischen Theorie der Zeitlichkeit sein könnte. Ziel meines Beitrages ist es einerseits, Zeitlichkeitsaspekte in einigen zentralen theoretischen Konzepten BOURDIEUs herauszuarbeiten, um andererseits an ausgewähltem empirischen Material aus einer qualitativen Studie zum Zusammenhang von politischen Gelegenheitsstrukturen und Bildungsaufstiegen darzulegen, welche Art des Verstehens zur empirischen Erforschung impliziter Zeitbezüge des Sozialen dieser Ansatz anbietet.The aspect of temporality in BOURDIEU's sociology has rarely been systematically evaluated. As forgotten history and anticipation of the future, temporality is particularly inherent in BOURDIEU's habitus concept and is thus closely intertwined with the social practices of actors in the present. However, his other theoretical concepts also implicate fundamental temporal aspects at their core. Therefore, temporality can be considered a linkage that connects BOURDIEU's theoretical concepts and could also be understood as a foundation for a sociological theory of temporality. My aim in this contribution is to work out aspects of temporality in some of BOURDIEU' s central theoretical concepts. Using selected empirical data taken from a qualitative study on the context of political opportunity structures and educational climbing, I would like to demonstrate how this approach provides a specific way of understanding implicit time references in social situations

Unbounded Regions of High-Order Voronoi Diagrams of Lines and Segments in Higher Dimensions

We study the behavior at infinity of the farthest and the higher-order Voronoi diagram of n line segments or lines in a d-dimensional Euclidean space. The unbounded parts of these diagrams can be encoded by a Gaussian map on the sphere of directions S^(d-1). We show that the combinatorial complexity of the Gaussian map for the order-k Voronoi diagram of n line segments or lines is O(min{k,n-k} n^(d-1)), which is tight for n-k = O(1). All the d-dimensional cells of the farthest Voronoi diagram are unbounded, its (d-1)-skeleton is connected, and it does not have tunnels. A d-cell of the Voronoi diagram is called a tunnel if the set of its unbounded directions, represented as points on its Gaussian map, is not connected. In a three-dimensional space, the farthest Voronoi diagram of lines has exactly n^2-n three-dimensional cells, when n >= 2. The Gaussian map of the farthest Voronoi diagram of line segments or lines can be constructed in O(n^(d-1) alpha(n)) time, while if d=3, the time drops to worst-case optimal O(n^2)

Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital Rays

We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in Zd. The construction must be consistent (that is, satisfy the natural extension of the Euclidean axioms) while resembling them as much as possible. Previous work has shown asymptotically tight results in two dimensions with Θ(logN) error, where resemblance between segments is measured with the Hausdorff distance, and N is the L1 distance between the two points. This construction was considered tight because of a Ω(logN) lower bound that applies to any consistent construction in Z2. In this paper we observe that the lower bound does not directly extend to higher dimensions. We give an alternative argument showing that any consistent construction in d dimensions must have Ω(log1/(d−1)N) error. We tie the error of a consistent construction in high dimensions to the error of similar weak constructions in two dimensions (constructions for which some points need not satisfy all the axioms). This not only opens the possibility for having constructions with o(logN) error in high dimensions, but also opens up an interesting line of research in the tradeoff between the number of axiom violations and the error of the construction. A side result, that we find of independent interest, is the introduction of the bichromatic discrepancy: a natural extension of the concept of discrepancy of a set of points. In this paper, we define this concept and extend known results to the chromatic setting

Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital Rays

We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of the Euclidean axioms) while resembling them as much as possible. Previous work has shown asymptotically tight results in two dimensions with $\Theta(\log N)$ error, where resemblance between segments is measured with the Hausdorff distance, and $N$ is the $L_1$ distance between the two points. This construction was considered tight because of a $\Omega(\log N)$ lower bound that applies to any consistent construction in $\mathbb{Z}^2$. In this paper we observe that the lower bound does not directly extend to higher dimensions. We give an alternative argument showing that any consistent construction in $d$ dimensions must have $\Omega(\log^{1/(d-1)} N)$ error. We tie the error of a consistent construction in high dimensions to the error of similar {\em weak} constructions in two dimensions (constructions for which some points need not satisfy all the axioms). This not only opens the possibility for having constructions with $o(\log N)$ error in high dimensions, but also opens up an interesting line of research in the tradeoff between the number of axiom violations and the error of the construction. In order to show our lower bound, we also consider a colored variation of the concept of discrepancy of a set of points that we find of independent interest

Certified Approximation Algorithms for the Fermat Point and n-Ellipses

Given a set A of n points in ?^d with weight function w: A??_{> 0}, the Fermat distance function is ?(x): = ?_{a?A}w(a)?x-a?. A classic problem in facility location dating back to 1643, is to find the Fermat point x*, the point that minimizes the function ?. We consider the problem of computing a point x?* that is an ?-approximation of x* in the sense that ?x?*-x*? ?(x*) and d = 2. Finally, all our planar (d = 2) algorithms are implemented in order to experimentally evaluate them, using both synthetic as well as real world datasets. These experiments show the practicality of our techniques

The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination

We introduce the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays, and the distance function is the counterclockwise angular distance between a point and a ray-site. This novel Voronoi diagram is motivated by illumination and coverage problems, where a domain has to be covered by floodlights (wedges) of uniform angle, and the goal is to find the minimum angle necessary to cover the domain. We study the diagram in the plane, and we present structural properties, combinatorial complexity bounds, and a construction algorithm. If the rays are induced by a convex polygon, we show how to construct the ray Voronoi diagram within this polygon in linear time. Using this information, we can find in optimal linear time the Brocard angle, the minimum angle required to illuminate a convex polygon with floodlights of uniform angle. This last algorithm improves upon previous results, settling an interesting open problem