The classification of 2-compact groups

We prove that any connected 2-compact group is classified by its 2-adic root datum, and in particular the exotic 2-compact group DI(4), constructed by Dwyer-Wilkerson, is the only simple 2-compact group not arising as the 2-completion of a compact connected Lie group. Combined with our earlier work with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one-to-one correspondence between compact Lie groups and finite loop spaces admitting a maximal torus. Our proof is a general induction on the dimension of the group, which works for all primes. It refines the Andersen-Grodal-Moeller-Viruel methods to incorporate the theory of root data over the p-adic integers, as developed by Dwyer-Wilkerson and the authors, and we show that certain occurring obstructions vanish, by relating them to obstruction groups calculated by Jackowski-McClure-Oliver in the early 1990s.Comment: 47 page

Driving steady-state visual evoked potentials at arbitrary frequencies using temporal interpolation of stimulus presentation

Date of Acceptance: 29/10/2015 We thank Renate Zahn for help with data collection. This work was supported by Deutsche Forschungsgemeinschaft (AN 841/1-1, MU 972/20-1). We would like to thank A. Trujillo-Ortiz, R. Hernandez-Walls, A. Castro-Perez and K. BarbaRojo (Universidad Autonoma de Baja California) for making Matlab code for non-sphericity corrections freely available.Peer reviewedPublisher PD

The C*-algebra of an affine map on the 3-torus

We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is completely determined for all strongly transitive affine maps on a torus of dimension one, two or three

Weak and saturable protein-surfactant interactions in the denaturation of apo-α-lactalbumin by acidic and lactonic sophorolipid

Biosurfactants are of growing interest as sustainable alternatives to fossil-fuel-derived chemical surfactants, particularly for the detergent industry. To realize this potential, it is necessary to understand how they affect proteins which they may encounter in their applications. However, knowledge of such interactions is limited. Here, we present a study of the interactions between the model protein apo-alpha-lactalbumin (apo-aLA) and the biosurfactant sophorolipid (SL) produced by the yeast Starmerella bombicola. SL occurs both as an acidic and a lactonic form; the lactonic form (lactSL) is sparingly soluble and has a lower critical micelle concentration (cmc) than the acidic form [non-acetylated acidic sophorolipid (acidSL)]. We show that acidSL affects apo-aLA in a similar way to the related glycolipid biosurfactant rhamnolipid (RL), with the important difference that RL is also active below the cmc in contrast to acidSL. Using isothermal titration calorimetry data, we show that acidSL has weak and saturable interactions with apo-aLA at low concentrations; due to the relatively low cmc of acidSL (which means that the monomer concentration is limited to ca. 0-1 mM SL), it is only possible to observe interactions with monomeric acidSL at high apo-aLA concentrations. However, the denaturation kinetics of apo-aLA in the presence of acidSL are consistent with a collaboration between monomeric and micellar surfactant species, similar to RL and non-ionic or zwitterionic surfactants. Inclusion of diacetylated lactonic sophorolipid (lactSL) as mixed micelles with acidSL lowers the cmc and this effectively reduces the rate of unfolding, emphasizing that SL like other biosurfactants is a gentle anionic surfactant. Our data highlight the potential of these biosurfactants for future use in the detergent and pharmaceutical industry

Band structure and atomic sum rules for x-ray dichroism

Corrections to the atomic orbital sum rule for circular magnetic x-ray dichroism in solids are derived using orthonormal LMTOs as a single-particle basis for electron band states.Comment: 7 pages, no figure

Orbital fluctuations in the different phases of LaVO3 and YVO3

We investigate the importance of quantum orbital fluctuations in the orthorhombic and monoclinic phases of the Mott insulators LaVO3 and YVO3. First, we construct ab-initio material-specific t2g Hubbard models. Then, by using dynamical mean-field theory, we calculate the spectral matrix as a function of temperature. Our Hubbard bands and Mott gaps are in very good agreement with spectroscopy. We show that in orthorhombic LaVO3, quantum orbital fluctuations are strong and that they are suppressed only in the monoclinic 140 K phase. In YVO3 the suppression happens already at 300 K. We show that Jahn-Teller and GdFeO3-type distortions are both crucial in determining the type of orbital and magnetic order in the low temperature phases.Comment: 4 pages, 3 figures, final version. To appear in PR

An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation