We construct a small arithmetic package operating on discrete sequences: u0, u1, u2, . . . treated as single mathematical entities. Applying functions to sequences by the generalized map, or adding them element-wise is quite trivial, but if the sequences are regular, e.g. if they are arithmetic or geometric progressions, a much more compact and in several cases much more efficient representatio...

background: about 15% of couples have infertility problems which 40% of them are related to the male factors. genetic factors are candidate for about 10% of male infertility conditions. among these, azfa, azfb, azfc and azfd regions on the yq are considered most important for spermatogenesis. microdeletions of these regions are thought to be involved in some cases of azoospermic or oligospermic...

BACKGROUND About 15% of couples have infertility problems which 40% of them are related to the male factors. Genetic factors are candidate for about 10% of male infertility conditions. Among these, AZFa, AZFb, AZFc and AZFd regions on the Yq are considered most important for spermatogenesis. Microdeletions of these regions are thought to be involved in some cases of azoospermic or oligospermic ...

The Y-chromosomal binary marker P25 is a paralogous sequence variant, rather than a SNP: three copies of the P25 sequence lie within the giant palindromic repeats on Yq, and one copy has undergone a C to A transversion to define haplogroup R1b (designated C/C/A). Since gene conversion is known to be active in the palindromic repeats, we reasoned that P25 might be liable to back-mutation by gene...