We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hyperbolic space. Thus the main theorem states necessary and sufficient conditions for the existence and uniqueness of such polyhedra with prescribed combinatorial type and dihedral angles. More generally, we consider weighted Delaunay triangulations in piecewise flat surfaces, allowing cone singularities with prescribed cone angles in the vertices. The material presented here extends work by Rivin on Delaunay triangulations and ideal polyhedra.
The research for this article was conducted almost entirely while I enjoyed the hospitality of the , where I participated in the Research in Pairs Program together with Jean-Marc Schlenker, who was working on his closely related paper @cite_12 . I am grateful for the excellent working conditions I experienced in Oberwolfach and for the extremely inspiring and fruitful discussions with Jean-Marc, who was closely involved in the work presented here.
@cite_12
2122575992 2114030807 2113208984 1489181569
This book arises from a series of workshops on collaborative learning, that gathered together 20 scholars from the disciplines of psychology, education and computer science. The series was part of a research program entitled 'Learning in Humans and Machines' (LHM), launched by Peter Reimann and Hans Spada, and funded by the European Science Foundation. This program aimed to develop a multidisciplinary dialogue on learning, involving mainly scholars from cognitive psychology, educational science, and artificial intelligence (including machine learning). During the preparation of the program, Agnes Blaye, Claire O'Malley, Michael Baker and I developed a theme on collaborative learning. When the program officially began, 12 members were selected to work on this theme and formed the so-called 'task force 5'. I became the coordinator of the group. This group organised two workshops, in Sitges (Spain, 1994) and Aix-en-Provence (France, 1995). In 1996, the group was enriched with new members to reach its final size. Around 20 members met in the subsequent workshops, at Samoens (France, 1996), Houthalen (Belgium, 1996) and Mannheim (Germany, 1997). Several individuals joined the group for some time but have not written a chapter. I would nevertheless like to acknowledge their contributions to our activities: George Bilchev, Stevan Harnad, Calle Jansson and Claire O'Malley. Three experiments were conducted to determine the psychometric properties of language in dyadic interactions. Using text-analysis, it was possible to assess the degree to which people coordinate their word use in natural conversations. In Experiments 1 (n = 130) and 2( n = 32), college students interacted in dyadic conversations in laboratory-based private Internet chat rooms. Experiment 3 analyzed the official transcripts of the Watergate tapes involving the dyadic interactions between President Richard Nixon and his aids H. R. Haldeman, John Erlichman, and John Dean. The results of the three studies offer sub- stantial evidence that individuals in dyadic interactions exhibit linguistic style matching (LSM) on both the conversation level as well as on a turn-by-turn level. Furthermore, LSM is unrelated to ratings of the quality of the interaction by both participants and judges. We propose that a coordination-engagement hypothesis is a better description of linguistic behaviors than the coordination-rapport hypothesis that has been proposed in the nonver- bal literature. For years social psychologists have exalted the power of the situa- tion. We comfortably acknowledge that across different situations, with different people, we may act in a range of ways, or even talk using a variety of styles. Aware of this tendency, Gergen (1972) began his explorations of our shifting masks of identity. In writing letters to close friends, he realized that he came across as a "completely different per- son" in each letter. "In one, I was morose, pouring out a philosophy of existential sorrow; in another I was a lusty realist: in a third I was a lighthearted jokester" (p. 32). Based merely on his word choices, Gergen inadvertently varied his style to adapt to the recipients of his letters. This is a prime demonstration of our inherent knowledge of the mutability of our language with respect to varying social contexts. This paper presents data from a four month ethnographic study of professional pair programmers from two software development teams. Contrary to the current conception of pair programmers, the pairs in this study did not hew to the separate roles of "driver" and "navigator". Instead, the observed programmers moved together through different phases of the task, considering and discussing issues at the same strategic "range " or level of abstraction and in largely the same role. This form of interaction was reinforced by frequent switches in keyboard control during pairing and the use of dual keyboards. The distribution of expertise among the members of a pair had a strong influence on the tenor of pair programming interaction. Keyboard control had a consistent secondary effect on decisionmaking within the pair. These findings have implications for software development managers and practitioners as well as for the design of software development tools. Researchers in both machine translation (e.g., 1990) and bilingual lexicography (e.g., Klavans and Tzoukermann 1990) have recently become interested in studying bilingual corpora, bodies of text such as the Canadian Hansards (parliamentary proceedings), which are available in multiple languages (such as French and English). One useful step is to align the sentences, that is, to identify correspondences between sentences in one language and sentences in the other language.This paper will describe a method and a program (align) for aligning sentences based on a simple statistical model of character lengths. The program uses the fact that longer sentences in one language tend to be translated into longer sentences in the other language, and that shorter sentences tend to be translated into shorter sentences. A probabilistic score is assigned to each proposed correspondence of sentences, based on the scaled difference of lengths of the two sentences (in characters) and the variance of this difference. This probabilistic score is used in a dynamic programming framework to find the maximum likelihood alignment of sentences.It is remarkable that such a simple approach works as well as it does. An evaluation was performed based on a trilingual corpus of economic reports issued by the Union Bank of Switzerland (UBS) in English, French, and German. The method correctly aligned all but 4 of the sentences. Moreover, it is possible to extract a large subcorpus that has a much smaller error rate. By selecting the best-scoring 80 of the alignments, the error rate is reduced from 4 to 0.7 . There were more errors on the English-French subcorpus than on the English-German subcorpus, showing that error rates will depend on the corpus considered; however, both were small enough to hope that the method will be useful for many language pairs.To further research on bilingual corpora, a much larger sample of Canadian Hansards (approximately 90 million words, half in English and and half in French) has been aligned with the align program and will be available through the Data Collection Initiative of the Association for Computational Linguistics (ACL DCI). In addition, in order to facilitate replication of the align program, an appendix is provided with detailed c-code of the more difficult core of the align program.