Solutions to the Yang-Baxter equation -an important equation in mathematics and physics -and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum information science. In particular, unitary representations of the braid group are desired because they generate braiding quantum gates. These are actively studied in the ongoing research into topological quantum computing. A generalized Yang-Baxter equation was proposed a few years ago by Eric Rowell et al. By finding solutions to the generalized Yang-Baxter equation, we obtain new unitary braid group representations. Our representations give rise to braiding quantum gates and thus have the potential to aid in the construction of useful quantum computers.

Much debate surrounds the importance of top-down and bottom-up effects in the Southern Ocean, where the harvesting of over two million whales in the mid twentieth century is thought to have produced a massive surplus of Antarctic krill. This excess of krill may have allowed populations of other predators, such as seals and penguins, to increase, a top-down hypothesis known as the ‘krill surplus hypothesis’. However, a lack of pre-whaling population baselines has made it challenging to investigate historical changes in the abundance of the major krill predators in relation to whaling. Therefore, we used reduced representation sequencing and a coalescent-based maximum composite likelihood approach to reconstruct the recent demographic history of the Antarctic fur seal, a pinniped that was hunted to the brink of extinction by 18th and 19th century sealers. In line with the known history of this species, we found support for a demographic model that included a substantial reduction in population size around the time period of sealing. Furthermore, maximum likelihood estimates from this model suggest that the recovered, post-sealing population at South Georgia may have been around two times larger than the pre-sealing population. Our findings lend support to the krill surplus hypothesis and illustrate the potential of genomic approaches to shed light on long-standing questions in population biology.

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