The development of information technology has made it possible to collect large amounts of spatial data on a daily basis. It is of enormous significance when it comes to discovering implicit, non-trivial and potentially valuable information from this spatial data. Spatial co-location patterns reveal the distribution rules of spatial features, which can be valuable for application users. This book provides commercial software developers with proven and effective algorithms for detecting and filtering these implicit patterns, and includes easily implemented pseudocode for all the algorithms. Furthermore, it offers a basis for further research in this promising field. Preference-based co-location pattern mining refers to mining constrained or condensed co-location patterns instead of mining all prevalent co-location patterns. Based on the authors’ recent research, the book highlights techniques for solving a range of problems in this context, including maximal co-location pattern mining, closed co-location pattern mining, top-k co-location pattern mining, non-redundant co-location pattern mining, dominant co-location pattern mining, high utility co-location pattern mining, user-preferred co-location pattern mining, and similarity measures between spatial co-location patterns. Presenting a systematic, mathematical study of preference-based spatial co-location pattern mining, this book can be used both as a textbook for those new to the topic and as a reference resource for experienced professionals.
Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
The development of information technology has made it possible to collect large amounts of spatial data on a daily basis. It is of enormous significance when it comes to discovering implicit, non-trivial and potentially valuable information from this spatial data. Spatial co-location patterns reveal the distribution rules of spatial features, which can be valuable for application users. This book provides commercial software developers with proven and effective algorithms for detecting and filtering these implicit patterns, and includes easily implemented pseudocode for all the algorithms. Furthermore, it offers a basis for further research in this promising field. Preference-based co-location pattern mining refers to mining constrained or condensed co-location patterns instead of mining all prevalent co-location patterns. Based on the authors’ recent research, the book highlights techniques for solving a range of problems in this context, including maximal co-location pattern mining, closed co-location pattern mining, top-k co-location pattern mining, non-redundant co-location pattern mining, dominant co-location pattern mining, high utility co-location pattern mining, user-preferred co-location pattern mining, and similarity measures between spatial co-location patterns. Presenting a systematic, mathematical study of preference-based spatial co-location pattern mining, this book can be used both as a textbook for those new to the topic and as a reference resource for experienced professionals.
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
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