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Introduction to Topology
Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology.
Practical Theories and Empirical Practice
There is a perceived tension between empirical and theoretical approaches to the study of language. Many recent works in the discipline emphasise that linguistics is an 'empirical science'. This volume argues for a nuanced view, highlighting that theory and practice necessarily and as a matter of fact complement each other in linguistic research. Its contributions ranging from experimental studies in psychology via linguistic fieldwork and cross-linguistic comparisons to the application of formal and logical approaches to language exemplify the mutual relationship between empirical and theoretical work. The volume illustrates how selected topics are addressed by different contributions and methodological stances. Topics include the cognitive grounding of language, social cognition and the construction of meaning in interaction, and, closely related, pragmatics from a typological perspective and beyond. Anyone interested in these topics and more generally in meta-theoretical considerations will find great value in this volume.
Spatial Data Science
Spatial Data Science introduces fundamental aspects of spatial data that every data scientist should know before they start working with spatial data. These aspects include how geometries are represented, coordinate reference systems (projections, datums), the fact that the Earth is round and its consequences for analysis, and how attributes of geometries can relate to geometries. In the second part of the book, these concepts are illustrated with data science examples using the R language. In the third part, statistical modelling approaches are demonstrated using real world data examples. After reading this book, the reader will be well equipped to avoid a number of major spatial data analy...
Lectures on Morse Homology
This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory.
Advances in Spatial Databases
The Third International Symposium on Large Spatial Databases (SSD '93) was held at the National University of Singapore in June 1993. The previous meetings of the series were at Sanata Barbara (1989) and Zurich (1991). The meetings are planned as a forum for researchers and practitioners specializing in database theory for and advanced applications of Spatial Information Systems. This volume constitutes the proceedings of the symposium. It contains 25 selected papersand three keynotes papers: "Spatial data management in database systems: research directions" (W. Kim), "From extensible databases to interoperability between multiple databases and GIS applications" (H.-J. Schek), and "The SEQUOIA 2000 project" (M. Stonebraker). The selectedpapers are collected into sections on: data modeling, spatial indexing, indexing mechanisms, handling of raster and vector data, spatial database systems, topology, storage management, query retrieval,knowledge engineering in SDS, and 3-dimensional data handling.
Classics from IJGIS
The past 20 years can be regarded as the adolescence of geographic information science (GIS), as it grew from a burgeoning area of study into a mature and thriving field. During those two decades, the International Journal of Geographic Information Science (formerly Systems) (IJGIS) was one of the most prominent academic guiding forces in GIScience
Literary Mathematics
Across the humanities and social sciences, scholars increasingly use quantitative methods to study textual data. Considered together, this research represents an extraordinary event in the long history of textuality. More or less all at once, the corpus has emerged as a major genre of cultural and scientific knowledge. In Literary Mathematics, Michael Gavin grapples with this development, describing how quantitative methods for the study of textual data offer powerful tools for historical inquiry and sometimes unexpected perspectives on theoretical issues of concern to literary studies. Student-friendly and accessible, the book advances this argument through case studies drawn from the Early...
Qualitative Spatial Reasoning with Topological Information
Spatial knowledge representation and reasoning with spatial knowledge are relevant issues for many application areas such as robotics, geographical information systems, and computer vision. Exceeding purely quantitative approaches, more recently initiated qualitative approaches allow for dealing with spatial information on a more abstract level that is closer to the way humans think and speak. Starting out with the qualitative, topological constraint calculus RCC8 proposed by Randell, Cui, and Cohn, this work presents answers to a variety of open questions regarding RCC8. The open issues concerning computational properties are solved by exploiting a broad variety of results and methods from logic and theoretical computer science. Questions concerning practical performance are addressed by large-scale empirical computational experiments. The most impressive result is probably the complete classification of computational properties for all fragments of RCC8.
Rough Sets and Current Trends in Computing
This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Rough Sets and Current Trends in Computing, RSCTC 2000, held in Banff, Canada in October 2000. The 80 revised papers presented together with an introduction and three keynote presentations have gone through two rounds of reviewing and revision. The papers are organized in topical sections on granual computing, rough sets and systems, fuzzy sets and systems, rough sets and data mining, nonclassical logics and reasoning, pattern recognition and image processing, neural networks and genetic algorithms, and current trends in computing.
