Ueber einige asymptotische Gesetze der Zahlentheorie.

Mertens, Franz

doi:10.1515/crll.1874.77.289

Cited by 31 publications

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“…28 TAI-DANAE BRADLEY, YIN CHOI CHENG AND YAN FEI LUO Similar questions have also been studied for the case of rational integers. Originally, Mertens [1874] proved that the probability that a pair of rational integers chosen uniformly and independently at random from {1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

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2016

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Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance between such lists. Using an algorithm based on three basic DNA editing operations suggested by a model for ciliate micronuclear decryption, this study defines the distance between two permutations to be the number of ciliate operations the algorithm performs during such a transformation. Combining wellknown clustering methods with this distance function enables one to construct corresponding phylogenies. These ideas are illustrated by exploring the phylogenetic relationships among the chromosomes of eight fruit fly (Drosophila) species, using the well-known UPGMA algorithm on the distance function provided by the ciliate operations.Over evolutionary time, "local" DNA editing events such as nucleotide substitutions, deletions or insertions diversify the set of DNA sequences present in organisms. Results of whole genome sequencing suggest that also "global" DNA editing events diversify these DNA sequences.Consider two species S 1 and S 2 with a common ancestor whose genome was organized over n linear chromosomes. A gene G of the ancestor was inherited as gene G 1 by species S 1 and as gene G 2 by species S 2 . G 1 and G 2 are orthologous genes, or simply orthologs. Assume that the species S 1 and S 2 each also has n chromosomes, and that for each ancestral chromosome i, the orthologs of any ancestral gene on chromosome i are also in the descendant species S 1 and S 2 on the corresponding chromosome i. This assumption is known, in the context of certain MSC2010: 05E15,

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Section: Introductionmentioning

confidence: 99%