Detection of positive selection signatures in populations around the world is helping to uncover recent human evolutionary history as well as the genetic basis of diseases. Most human evolutionary genomic studies have been performed in European, African and Asian populations. However, populations with Native American ancestry have been largely underrepresented. Here, we used a genome-wide local ancestry enrichment approach complemented with neutral simulations to identify post-admixture adaptations underwent by admixed Chileans through gene flow from Europeans into local Native Americans. The top significant hits (P = 2.4 x 10−7) are variants in a region on chromosome 12 comprising multiple regulatory elements. This region includes rs12821256, which regulates the expression of KITLG, a well-known gene involved in lighter hair and skin pigmentation in Europeans. Another variant from that region is associated with the long noncoding RNA RP11-13A1.1, which has been specifically involved in the innate immune response against infectious pathogens (Riege, et al. 2017). Our results suggest that these genes were relevant for adaption in Chileans following the Columbian exchange.
We simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius $R$. Computed frequency as a function of the radius $R$ follows to the well known Rayleigh formula. We discuss the simulation setup in the framework of the Lattice Boltzmann method.
There is a gap in the proof of the main theorem in the article  on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of  is true. We also describe a computer certification of this result.