The isomorphism problem for profinite completions of residually finite groups

We consider pairs of finitely presented, residually finite groups $u:P\hookrightarrow \Gamma$. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not the associated map of profinite completions $\hat{u}: \widehat{P} \to \widehat{\Gamma}$ is an isomorphism. Nor do there exist algorithms that can decide whether $\hat{u}$ is surjective, or whether $\widehat{P}$ is isomorphic to $\widehat{\Gamma}$.Comment: 12 page

On the difficulty of presenting finitely presentable groups

We exhibit classes of groups in which the word problem is uniformly solvable but in which there is no algorithm that can compute finite presentations for finitely presentable subgroups. Direct products of hyperbolic groups, groups of integer matrices, and right-angled Coxeter groups form such classes. We discuss related classes of groups in which there does exist an algorithm to compute finite presentations for finitely presentable subgroups. We also construct a finitely presented group that has a polynomial Dehn function but in which there is no algorithm to compute the first Betti number of the finitely presentable subgroups.Comment: Final version. To appear in GGD volume dedicated to Fritz Grunewal

Subgroup separability in residually free groups

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type $\mathrm{FP}_\infty$ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.Comment: 8 pages, no figure

Limit groups, positive-genus towers and measure equivalence

By definition, an $\omega$-residually free tower is positive-genus if all surfaces used in its construction are of positive genus. We prove that every limit group is virtually a subgroup of a positive-genus $\omega$-residually free tower. By combining this with results of Gaboriau, we prove that elementarily free groups are measure equivalent to free groups.Comment: 10 pages; no figures. Minor changes; now to appear in Ergod. Th. & Dynam. Sy

Pressure-dependent 13C chemical shifts in proteins: Origins and applications

Pressure-dependent (13)C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH(3), CH(2) and CH carbon shifts change on average by +0.23, -0.09 and -0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the gamma-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual (13)C alpha shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas (13)C beta shifts retain significant dependence on local compression, making them less useful as structural restraints

Performance evaluation of the Boron Coated Straws detector with Geant4

The last decade has witnessed the development of several alternative neutron detector technologies, as a consequence of upcoming neutron sources and upgrades, as well the world-wide shortage of $^3$He. One branch of development is the family of $^{10}$B-based gaseous detectors. This work focuses on the boron coated straws (BCS) by Proportional Technologies Inc., a commercial solution designed for use in homeland security and neutron science. A detailed Geant4 simulation study of the BCS is presented, which investigates various aspects of the detector performance, e.g. efficiency, activation, absorption and the impact of scattering on the measured signal. The suitability of the BCS detector for Small Angle Neutron Scattering (SANS), direct chopper spectrometry and imaging is discussed.Comment: 50 pages, 37 figures, minor changes after review, results unchange