Half-isomorphisms of Moufang loops

We prove that if the squaring map in the factor loop of a Moufang loop $Q$ over its nucleus is surjective, then every half-isomorphism of $Q$ onto a Moufang loop is either an isomorphism or an anti-isomorphism. This generalizes all earlier results in this vein.Comment: 8 pages; v.2: fixed typo

Loops and the Lagrange property

Let \cF be a family of finite loops closed under subloops and factor loops. Then every loop in \cF has the strong Lagrange property if and only if every simple loop in \cF has the weak Lagrange property. We exhibit several such families, and indicate how the Lagrange property enters into the problem of existence of finite simple loops.Comment: 4 pages, LaTeX2e, uses natbib.sty, submitted to Results in Mathematic

Constructions of commutative automorphic loops

A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate the classification of commutative A-loops of small orders and also of order $p^3$, where $p$ is a prime.Comment: v2: final version to appear in Communications in Algebr

Temperature dependence of protein dynamics simulated with three different water models

The effect of variation of the water model on the temperature dependence of protein and hydration water dynamics is examined by performing molecular dynamics simulations of myoglobin with the TIP3P, TIP4P, and TIP5P water models and the CHARMM protein force field at temperatures between 20 and 300 K. The atomic mean-square displacements, solvent reorientational relaxation times, pair angular correlations between surface water molecules, and time-averaged structures of the protein are all found to be similar, and the protein dynamical transition is described almost indistinguishably for the three water potentials. The results provide evidence that for some purposes changing the water model in protein simulations without a loss of accuracy may be possible

Time-resolved structural studies of protein reaction dynamics: a smorgasbord of X-ray approaches

Time-resolved structural studies of proteins have undergone several significant developments during the last decade. Recent developments using time-resolved X-ray methods, such as time-resolved Laue diffraction, low-temperature intermediate trapping, time-resolved wide-angle X-ray scattering and time-resolved X-ray absorption spectroscopy, are reviewed