Mapping class groups and outer automorphism groups of free groups are C*-simple

We prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups.Comment: 10 pages, amstex. J. Functional Analysis, to be publishe

The Chabauty space of closed subgroups of the three-dimensional Heisenberg group

When equipped with the natural topology first defined by Chabauty, the closed subgroups of a locally compact group $G$ form a compact space \Cal C(G). We analyse the structure of \Cal C(G) for some low-dimensional Lie groups, concentrating mostly on the 3-dimensional Heisenberg group $H$. We prove that \Cal C(H) is a 6-dimensional space that is path--connected but not locally connected. The lattices in $H$ form a dense open subset \Cal L(H) \subset \Cal C(H) that is the disjoint union of an infinite sequence of pairwise--homeomorphic aspherical manifolds of dimension six, each a torus bundle over $(\bold S^3 \smallsetminus T) \times \bold R$, where $T$ denotes a trefoil knot. The complement of \Cal L(H) in \Cal C(H) is also described explicitly. The subspace of \Cal C(H) consisting of subgroups that contain the centre $Z(H)$ is homeomorphic to the 4--sphere, and we prove that this is a weak retract of \Cal C(H).Comment: Minor edits. Final version. To appear in the Pacific Journal. 41 pages, no figure

In silico prediction of mutant HIV-1 proteases cleaving a target sequence

HIV-1 protease represents an appealing system for directed enzyme re-design, since it has various different endogenous targets, a relatively simple structure and it is well studied. Recently Chaudhury and Gray (Structure (2009) 17: 1636 -- 1648) published a computational algorithm to discern the specificity determining residues of HIV-1 protease. In this paper we present two computational tools aimed at re-designing HIV-1 protease, derived from the algorithm of Chaudhuri and Gray. First, we present an energy-only based methodology to discriminate cleavable and non cleavable peptides for HIV-1 proteases, both wild type and mutant. Secondly, we show an algorithm we developed to predict mutant HIV-1 proteases capable of cleaving a new target substrate peptide, different from the natural targets of HIV-1 protease. The obtained in silico mutant enzymes were analyzed in terms of cleavability and specificity towards the target peptide using the energy-only methodology. We found two mutant proteases as best candidates for specificity and cleavability towards the target sequence

Core Precession and Global Modes in Granular Bulk Flow

A transition from local to global shear zones is reported for granular flows in a modified Couette cell. The experimental geometry is a slowly rotating drum which has a stationary disc of radius R_s fixed at its bottom. Granular material, which fills this cell up to height H, forms a wide shear zone which emanates from the discontinuity at the stationary discs edge. For shallow layers (H/R_s < 0.55), the shear zone reaches the free surface, with the core of the material resting on the disc and remaining stationary. In contrast, for deep layers (H/R_s > 0.55), the shear zones meet below the surface and the core starts to precess. A change in the symmetry of the surface velocities reveals that this behavior is associated with a transition from a local to a global shear mode.Comment: 4 pages, 7 figures, submitte

Theory for the optimal control of time-averaged quantities in open quantum systems

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed

On the Stability of Compactified D=11 Supermembranes

We prove D=11 supermembrane theories wrapping around in an irreducible way over $S^{1} \times S^{1}\times M^{9}$ on the target manifold, have a hamiltonian with strict minima and without infinite dimensional valleys at the minima for the bosonic sector. The minima occur at monopole connections of an associated U(1) bundle over topologically non trivial Riemann surfaces of arbitrary genus. Explicit expressions for the minimal connections in terms of membrane maps are presented. The minimal maps and corresponding connections satisfy the BPS condition with half SUSY.Comment: 15 pages, latex. Added comments in conclusions and more reference

Effects of repeated consumption on sensory-enhanced satiety

Previous research suggests that sensory characteristics of a drink modify the acute satiating effects of its nutrients, with enhanced satiety evident when a high energy drink was thicker and tasted creamier. The present study tested whether this modulation of satiety by sensory context was altered by repeated consumption. Participants (n=48) consumed one of four drinks mid-morning on seven non-consecutive days with satiety responses measured pre-exposure (day 1), post-exposure (day 6) and at a one month follow-up. Drinks combined two levels of energy (lower energy, LE, 326 KJ: higher energy, HE, 1163KJ) with two levels of satiety-predictive sensory characteristics (low-sensory, LS, or enhanced sensory, ES). Test lunch intake 90 minutes after drink consumption depended on both the energy content and sensory characteristics of the drink before exposure, but on energy content alone at post-exposure and the follow-up. The largest change was an increase in test meal intake over time in the LE/LS condition. Effects on intake were reflected in appetite ratings, with rated hunger and expected filling affected by sensory characteristics and energy content pre-exposure, but were largely determined by energy content post exposure and at follow up. In contrast, a measure of expected satiety reflected sensory characteristics regardless of energy content on all three test days. Overall these data suggest that some aspects of the sensory-modulation of satiety are changed by repeated consumption, with covert energy becoming more effective in suppressing appetite over time, but also suggest that these behavioural changes are not readily translated into expectations of satiety