By Evangelos Triantaphyllou
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This ebook is aimed toward offering thoughts, tools and algorithms ableto take care of undersampled and constrained information. One such pattern that lately received acceptance and to some degree revolutionised sign processing is compressed sensing. Compressed sensing builds upon the remark that many signs in nature are approximately sparse (or compressible, as they're more often than not mentioned) in a few area, and hence they are often reconstructed to inside excessive accuracy from a long way fewer observations than commonly held to be worthy.
Automata thought lies on the origin of computing device technological know-how, and is key to a theoretical realizing of ways pcs paintings and what constitutes formal tools. This treatise provides a rigorous account of the subject and illuminates its actual that means by way of taking a look at the topic in numerous methods. the 1st a part of the publication is organised round notions of rationality and recognisability.
The improvement of Maxim Kontsevich's preliminary rules on motivic integration has abruptly motivated many different parts of arithmetic, starting from the Langlands software over harmonic research, to non-Archimedean research, singularity thought and birational geometry. This booklet assembles the several theories of motivic integration and their purposes for the 1st time, permitting readers to check various methods and determine their person strengths.
The Banach–Tarski Paradox is a such a lot notable mathematical development: it asserts strong ball might be taken aside into finitely many items that may be rearranged utilizing inflexible motions to shape a ball two times as huge. This quantity explores the results of the anomaly for degree idea and its connections with crew conception, geometry, set thought, and common sense.
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Extra resources for Data Mining and Knowledge Discovery via Logic-Based Methods: Theory, Algorithms, and Applications: 43 (Springer Optimization and Its Applications)
Data Mining and Knowledge Discovery via Logic-Based Methods: Theory, Algorithms, and Applications: 43 (Springer Optimization and Its Applications) by Evangelos Triantaphyllou