Web-Based Tool for Algebraic Modeling and Mathematical Optimization

In this article, we present a new open-source tool for algebraic modeling and mathematical optimization. We begin by distilling the main gaps within the existing algebraic modeling languages and tools (varying performance, limited cross-compatibility, complex syntax, and different solver, feature, and problem type support). Later, we propose a state-of-the-art web-based tool (WebAML and Optimization System) for algebraic modeling languages and mathematical optimization. The tool does not require specific algebraic language knowledge, allows solving problems using different solvers, and utilizes the best characteristics of existing algebraic modeling languages. We also provide clear extension points and ideas on how we could further improve such a tool.

Compatibility Complex for Black Hole Spacetimes

The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (Aksteiner and Bäckdahl in Phys Rev Lett 121:051104, 2018) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from Aksteiner and Bäckdahl (Phys Rev Lett 121:051104, 2018) with the first compatibility operator from that complex.

Complete loss of the MHC II pathway in an anglerfish, Lophius piscatorius

Genome studies in fish provide evidence for the adaptability of the vertebrate immune system, revealing alternative immune strategies. The reported absence of the major compatibility complex (MHC) class II pathway components in certain species of pipefish (genus Syngnathus ) and cod-like fishes (order Gadiformes) is of particular interest. The MHC II pathway is responsible for immunization and defence against extracellular threats through the presentation of exogenous peptides to T helper cells. Here, we demonstrate the absence of all genes encoding MHC II components (CD4, CD74 A/B, and both classical and non-classical MHC II α / β ) in the genome of an anglerfish, Lophius piscatorius , indicating loss of the MHC II pathway. By contrast, it has previously been reported that another anglerfish, Antennarius striatus , retains all MHC II genes, placing the loss of MHC II in the Lophius clade to their most recent common ancestor . In the three taxa where MHC II loss has occurred, the gene loss has been restricted to four or five core MHC II components, suggesting that, in teleosts, only these genes have functions that are restricted to the MHC II pathway.