2 research outputs found
A BPS Interpretation of Shape Invariance
We show that shape invariance appears when a quantum mechanical model is
invariant under a centrally extended superalgebra endowed with an additional
symmetry generator, which we dub the shift operator. The familiar mathematical
and physical results of shape invariance then arise from the BPS structure
associated with this shift operator. The shift operator also ensures that there
is a one-to-one correspondence between the energy levels of such a model and
the energies of the BPS-saturating states. These findings thus provide a more
comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe
A GWAS in Latin Americans identifies novel face shape loci, implicating VPS13B and a Denisovan introgressed region in facial variation
To characterize the genetic basis of facial features in Latin Americans, we performed a genome-wide association study (GWAS) of more than 6000 individuals using 59 landmark-based measurements from two-dimensional profile photographs and ~9,000,000 genotyped or imputed single-nucleotide polymorphisms. We detected significant association of 32 traits with at least 1 (and up to 6) of 32 different genomic regions, more than doubling the number of robustly associated face morphology loci reported until now (from 11 to 23). These GWAS hits are strongly enriched in regulatory sequences active specifically during craniofacial development. The associated region in 1p12 includes a tract of archaic adaptive introgression, with a Denisovan haplotype common in Native Americans affecting particularly lip thickness. Among the nine previously unidentified face morphology loci we identified is the VPS13B gene region, and we show that variants in this region also affect midfacial morphology in mice