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Titlebook: Metric Algebraic Geometry; Paul Breiding,Kathlén Kohn,Bernd Sturmfels Textbook‘‘‘‘‘‘‘‘ 2024 The Editor(s) (if applicable) and The Author(s

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樓主
發(fā)表于 2025-3-21 16:24:58 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Metric Algebraic Geometry
編輯Paul Breiding,Kathlén Kohn,Bernd Sturmfels
視頻videohttp://file.papertrans.cn/633/632456/632456.mp4
概述brings algebraic and differential geometry together in a computational setting.provides a modern view on this connection, motivated by data science and AI.focuses on concrete examples from a wide vari
叢書名稱Oberwolfach Seminars
圖書封面Titlebook: Metric Algebraic Geometry;  Paul Breiding,Kathlén Kohn,Bernd Sturmfels Textbook‘‘‘‘‘‘‘‘ 2024 The Editor(s) (if applicable) and The Author(s
描述.Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances..After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties.?Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety..This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry.. This is an openaccess book..
出版日期Textbook‘‘‘‘‘‘‘‘ 2024
關(guān)鍵詞Algebraic Variety; Data Science; Differential Geometry; Euclidean Distance; Integrals; Maximum Likelihood
版次1
doihttps://doi.org/10.1007/978-3-031-51462-3
isbn_softcover978-3-031-51461-6
isbn_ebook978-3-031-51462-3Series ISSN 1661-237X Series E-ISSN 2296-5041
issn_series 1661-237X
copyrightThe Editor(s) (if applicable) and The Author(s) 2024
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書目名稱Metric Algebraic Geometry影響因子(影響力)




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沙發(fā)
發(fā)表于 2025-3-21 23:42:58 | 只看該作者
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發(fā)表于 2025-3-22 00:50:05 | 只看該作者
Maximum Likelihood,ty distributions, and we used the Wasserstein metric to measure the distance from . to .. Finally, in Chapter 9, we considered the distance from a polynomial system . to the discriminant in the context of numerical analysis.
地板
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發(fā)表于 2025-3-22 17:06:59 | 只看該作者
Polar Degrees,cognized this point for Euclidean distance optimization in Section 2.3, and we will see it again in Theorem 5.5 for polyhedral norms, with focus on theWasserstein metric from optimal transport theory. The punchline is that polar degrees govern linear programming over real algebraic varieties.
8#
發(fā)表于 2025-3-22 21:21:23 | 只看該作者
Curvature, curvature. Our main point is to explore how curvature connects to algebraic geometry. We start out with plane curves, and we then turn to more general real algebraic varieties. The third section addresses the fundamental question of how to compute the volume of a tubular neighborhood of a variety.
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