• Linear codes associated to symmetric determinantal varieties: Even rank case 

    Beelen, Peter; Johnsen, Trygve; Singh, Prasant (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-06-20)
    We consider linear codes over a finite field Fq, for odd q, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a codeword is derived. Using this formula, we have computed the minimum distance for the codes corresponding to matrices upperbounded by any fixed, even rank. A conjecture is proposed for the cases where the upper bound is ...
  • Matroid Stratifications of Hypergraph Varieties, Their Realization Spaces, and Discrete Conditional Independence Models 

    Clarke, Oliver; Grace, Kevin; Mohammadi, Fatemeh; Motwani, Harshit J. (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-11-01)
    We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be reducible and can have arbitrary singularities by the Mnëv–Sturmfels universality theorem. We focus on various families of hypergraph varieties for which we explicitly compute an irredundant irreducible decomposition. Our ...
  • Exceptionally simple super-PDE for F (4) 

    Santi, Andrea; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-01)
    For the largest exceptional simple Lie superalgebra F(4), having dimension (24|16), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively.
  • How many species of Mollusca are there in Brazil? A collective taxonomic effort to reveal this still unknown diversity 

    Machado, Fabrizio M.; Miranda, Marcel S.; Salvador, Rodrigo Brincalepe; Pimenta, Alexandre D. (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-11)
    The expression ‘you need to know to conserve’ is a well-known cliche among biologists. Documenting the richness of a group of organisms is the first step towards understanding biodiversity and preparing efficient conservation plans. In this context, many efforts have been made to quantify the number of species on Earth and estimate the number of species still unknown to science. A few countries have ...
  • The snails of Super Mario Bros 

    Salvador, Rodrigo Brincalepe (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-11)
    Nintendo has recently released a new Mario game, Super Mario Bros. Wonder, a multiplayer platformer involving a good dose of mushrooms, both in-game and presumably during development. But psychedelic trips aside, in the first few stages of the game we are introduced to a completely new (and arguably the best) “enemy” in Mario games: a snail with a fabulous pink shell. Figure 1. Snail (©Nintendo, ...

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