Discrete Mathematics

Get Algorithms on Strings, Trees and Sequences: Computer Science PDF

By Dan Gusfield

ISBN-10: 0521585198

ISBN-13: 9780521585194

ISBN-10: 1352542552

ISBN-13: 9781352542554

Typically a space of research in machine technological know-how, string algorithms have, lately, turn into an more and more vital a part of biology, rather genetics. This quantity is a entire examine machine algorithms for string processing. as well as natural laptop technological know-how, Gusfield provides huge discussions on organic difficulties which are forged as string difficulties and on equipment built to resolve them. this article emphasizes the basic rules and methods relevant to contemporary functions. New methods to this advanced fabric simplify tools that prior to now were for the professional by myself. With over four hundred workouts to enhance the fabric and advance extra subject matters, the e-book is appropriate as a textual content for graduate or complicated undergraduate scholars in desktop technology, computational biology, or bio-informatics

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Extra resources for Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology

Example text

For any Lebesgue measurable set J ⊆ [0, 1]2 we have λ2 (J ) = σ2 ( (J )), where (J ) = { (x) : x ∈ J }. In order to obtain points on the sphere S2 , we proceed in the following way. We map the points {x 0 , x 1 , . . , x N −1 } ∈ [0, 1]2 to (x 0 ), (x 1 ), . . , (x N −1 ) ∈ S2 . It was shown by Aistleitner et al. [3] that if x 0 , x 1 , . . , x N −1 have low discrepancy with respect to anchored boxes in the square, then (x 0 ), (x 1 ), . . , (x N −1 ) have low spherical cap discrepancy. 1 shows some numerical results for a digital net mapped to the sphere S2 .

57] A. Winterhof, Recent results on recursive nonlinear pseudorandom number generators. Sequences and their Applications–SETA 2010. Lecture Notes in Computer Science, volume 6338, pp. 113–124. Springer, Berlin, 2010. [58] A. Winterhof, Generalizations of complete mappings of finite fields and some applications. J. Symbolic Comput. 64, 42–52, 2014. [59] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points. Monatsh. Math. 127, 219–241, 1999. 2 Partially bent functions and their properties Ayça Çe¸smelio˘glu Istanbul Kemerburgaz University, Istanbul Wilfried Meidl and Alev Topuzo˘glu Sabancı University, Istanbul Dedicated to Harald Niederreiter on the occasion of his 70th birthday.

Today Niederreiter’s work forms one of the essential pillars of QMC integration. 18 Some highlights of Harald Niederreiter’s work Acknowledgements G. ” F. ” C. Xing is supported by Singapore Ministry of Education Tier 1 grant 2013-T1-002-033. A. ” References [1] J. Dick and H. Niederreiter, Duality for digital sequences. J. Complexity 25, 406–414, 2009. [2] J. Dick and F. Pillichshammer, Digital Nets and Sequences. Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, Cambridge, 2010.

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Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology by Dan Gusfield

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