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Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications (Mathematics and Visualization)

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The deluge of data observed throughout research and industry has turned the analysis of the resulting information into the primary limiting factor for the rapid progress of science, engineering, and medicine. The field of visualization strives to tackle this data analysis challenge by devising visual representations that afford users an effective interface with their datasets. Driven by the explosion in data size and complexity experienced over the last decade, a prominent trend in today’s visualization research applies a data abstraction approach to yield high-level depictions emphasizing various salient properties of the phenomenon considered. Topology-based methods have proved especially compelling in this regard, as the topological abstraction provides a common mathematical language to identify remarkable structures in a broad range of applications and semantic contexts. Topological concepts and metaphors are therefore permeating the visualization literature and they are the focus of a significant research effort spanning theoretical, algorithmic, and practical aspects.

This book describes the research that was presented during the third Workshop on TopologicalMethods in Data Analysis and Visualization,which took place in Snowbird, Utah, on February 23-24, 2009. Following two successful, seminal TopoInVis workshops held in Europe, the 2009 edition was organized in the United States in response to the growing international interest in topological methods. As in previous years, this event offered international experts the opportunity to present their ongoing research in an informal and inspiring atmosphere, as well as to discuss the emerging trends and open challenges of the field. A defining feature of the 2009 edition was the attention paid to applications, reflecting the importance of topological techniques in practical data analysis scenarios and the increased prominence of problem-driven research. T he workshop featured two eminent invited speakers (Herbert Edelsbrunner, Duke University, and Jackie Chen, Sandia National Laboratory), who gave exciting lectures highlightingsignificant accomplishments and promising avenues for both fundamental and applied research on topological methods. All in all, TopoInVis ’09 was a resounding success thanks to the excellent contributions of over 60 participants.

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