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The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vec...
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This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.
This book constitutes the refereed proceedings of the 10th International Conference on Text, Speech and Dialogue, TSD 2007, held in Pilsen, Czech Republic, September 3-7, 2007. The 80 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 198 submissions. The papers present a wealth of state-of-the-art research results in the field of natural language processing with an emphasis on text, speech, and spoken dialogue ranging from theoretical and methodological issues to applications in various fields and with special focus on corpora, texts and tra.
This book constitutes the proceedings of the 20th International Conference on Text, Speech, and Dialogue, TSD 2017, held in Prague, CzechRepublic, in August 2017. The 56 regular papers presented together with 3 abstracts of keynote talks were carefully reviewed and selected from 117 submissions. They focus on topics such as corpora and language resources; speech recognition; tagging, classification and parsing of text and speech; speech and spoken language generation; semantic processing of text and speech; integrating applications of text and speech processing; automatic dialogue systems; as well as multimodal techniques and modelling.