Spectral Duality Between Heisenberg Chain and Gaudin Model

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page

Report on noninvasive prenatal testing: classical and alternative approaches [version 1; referees: 2 approved]

Concerns of traditional prenatal aneuploidy testing methods, such as low accuracy of noninvasive and health risks associated with invasive procedures, were overcome with the introduction of novel noninvasive methods based on genetics (NIPT). These were rapidly adopted into clinical practice in many countries after a series of successful trials of various independent submethods. Here we present results of own NIPT trial carried out in Moscow, Russia. 1012 samples were subjected to the method aimed at measuring chromosome coverage by massive parallel sequencing. Two alternative approaches are ascertained: one based on maternal/fetal differential methylation and another based on allelic difference. While the former failed to provide stable results, the latter was found to be promising and worthy of conducting a large-scale trial. One critical point in any NIPT approach is the determination of fetal cell-free DNA fraction, which dictates the reliability of obtained results for a given sample. We show that two different chromosome Y representation measures—by real-time PCR and by whole-genome massive parallel sequencing—are practically interchangeable (r=0.94). We also propose a novel method based on maternal/fetal allelic difference which is applicable in pregnancies with fetuses of either sex. Even in its pilot form it correlates well with chromosome Y coverage estimates (r=0.74) and can be further improved by increasing the number of polymorphisms