One Dimensional Chain with Long Range Hopping

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude \expectation{|t_{ij}|} \propto |i-j|^{-\sigma} in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2

Multi-ancestry genome-wide gene–smoking interaction study of 387,272 individuals identifies new loci associated with serum lipids

The concentrations of high- and low-density-lipoprotein cholesterol and triglycerides are influenced by smoking, but it is unknown whether genetic associations with lipids may be modified by smoking. We conducted a multi-ancestry genome-wide gene–smoking interaction study in 133,805 individuals with follow-up in an additional 253,467 individuals. Combined meta-analyses identified 13 new loci associated with lipids, some of which were detected only because association differed by smoking status. Additionally, we demonstrate the importance of including diverse populations, particularly in studies of interactions with lifestyle factors, where genomic and lifestyle differences by ancestry may contribute to novel findings

Approximate Guarding of Monotone and Rectilinear Polygons

We show a constant factor approximation algorithm for interior guarding of monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is \OPT\ for a rectilinear polygon, our algorithm produces a guard set of size~O(\OPT^2)