We present a variation of James Propp’s generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification is specially tailored to deal with cases when some of the weights are zero. This allows us to tile efficiently a large class of planar graphs, by embedding them in a large enough Aztec diamond. We also give a sufficient co...

We have exact formulas for the number of tilings of only a small number of regions: Aztec Diamonds, Fortresses, and regions composed of Lozenge Tiles. However, these regions, particularly aztec diamonds and lozenge tilings are fundamental, and numerous other regions types can be reduced to weighted versions of these graphs using urban renewal techniques. This paper will illustrate the process b...

From DNA replication to satellite communication, identifying and fixing errors is an essential part of building robust large-scale systems. Common approaches to error correction make use of redundancy (encoding copies of information across more than one entity) and rely on the fact that multiple errors are less likely to occur than a single error. For error correction in quantum information pro...

Abstract The thick mantle lithosphere beneath cratons consists of strongly reduced rocks that have reacted with oxidized melts. These low-silica, incipient melts are rich in CO 2 and H O react surrounding forming an enriched zone at the base lithosphere, which is source region for many diamonds. Here, we reproduce these reactions novel experiments oxidised, hydrous carbonate-rich reduced, deple...

In recent years a number of methods have been developed for subdividing the surface of the earth to meet the needs of applications in dynamic modeling, survey sampling, and information storage and display. One set of methods uses the surfaces of Platonic solids, or regular polyhedra, as approximations to the surface of the earth. Diamond partitions are similar to recursive subdivisions of the t...