In this paper‎, ‎we first present some properties of lower and upper central series of pair of groups‎. ‎Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced‎, ‎and some of the structural properties of the created classes are proved‎. ‎Moreover some interesting theorems such as Baer Theorem‎, ‎Bioch Theorem‎, ‎Hirsh Theorem for pair of groups are generalized...

Using a new technique, based on the regularization of a càdlàg process via the double Skorohod map, we obtain limit theorems for integrated numbers of level crossings of diffusions. The results are related to the recent results on the limit theorems for the truncated variation. We also extend to diffusions the classical result of Kasahara on the “local" limit theorem for the number of crossings...

The discovery of genomic structural variants (SVs), such as copy number variants (CNVs), is essential to understand genetic variation of human populations and complex diseases. Over recent years, the advent of new high-throughput sequencing (HTS) platforms has opened many opportunities for SVs discovery, and a very promising approach consists in measuring the depth of coverage (DOC) of reads al...

In this paper we consider billiards in a square with a barrier. We use Ratner’s theorem to compute the asymptotics for the number of closed orbits.

Several bioinformatics methods have been proposed for the detection and characterization of genomic structural variation (SV) from ultra high-throughput genome resequencing data. Recent surveys show that comprehensive detection of SV events of different types between an individual resequenced genome and a reference sequence is best achieved through the combination of methods based on different ...