If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori...

The aim of this paper is to explain how, starting from a Goppa code C(X,G, P1, ..., Pn) and a cyclic covering π : Y → X of degree m, one can twist the initial code to another one C(X,G + Dχ, P1, ..., Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y/X), in the hope that `X(G + Dχ) > `X(G). We give, using a MAGMA program, several examples where this occu...

Linking fluids as they twist and writhe Helicity is a measure of corkscrew-like motion described by the amount of twisting, writhing, and linking in a fluid. Total helicity is conserved for ideal fluids, but how helicity changes in real fluids with even tiny amounts of viscosity has been an open question. Scheeler et al. provide a complete measurement of total helicity in a real fluid by using ...

In contrast to the classical and semiclassical settings, the Coxeter element (12 . . . n) which cycles the columns of an m×n matrix does not determine an automorphism of the quantum grassmannian. Here, we show that this cycling can be obtained by defining a cocycle twist. A consequence is that the torus invariant prime ideals of the quantum grassmannian are permuted by the action of the Coxeter...

The mechanism by which the ligand occupancy state of the T cell receptor complex is converted into intracellular signaling information has been a controversial topic. Although the majority of structural studies argue against a conformational change, recent studies support the possibility for such a change within the CD3 components of the TCR complex. In this commentary, the evidence for TCR con...

A fascinating class of patterns, often encountered in nature as wiggling cracks on rocks, dried out fields and tectonic plates, is produced by the fracture of solids 1. Here we report the observation and modeling of an unusual type of patterns consisting of spiral cracks within fragments of a thin layer of drying precipitate. We find that this symmetry-breaking cracking mode arises naturally no...