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

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

Graphite/epoxy composite adapters for the Space Shuttle/Centaur vehicle

The decision to launch various NASA satellite and Air Force spacecraft from the Space Shuttle created the need for a high-energy upper stage capable of being deployed from the cargo bay. Two redesigned versions of the Centaur vehicle which employed a graphite/epoxy composite material for the forward and aft adapters were selected. Since this was the first time a graphite/epoxy material was used for Centaur major structural components, the development of the adapters was a major effort. An overview of the composite adapter designs, subcomponent design evaluation test results, and composite adapter test results from a full-scale vehicle structural test is presented

Reduced, tame and exotic fusion systems

We define here two new classes of saturated fusion systems, reduced fusion systems and tame fusion systems. These are motivated by our attempts to better understand and search for exotic fusion systems: fusion systems which are not the fusion systems of any finite group. Our main theorems say that every saturated fusion system reduces to a reduced fusion system which is tame only if the original one is realizable, and that every reduced fusion system which is not tame is the reduction of some exotic (nonrealizable) fusion system

The size of the nucleosome

The structural origin of the size of the 11 nm nucleosomal disc is addressed. On the nanometer length-scale the organization of DNA as chromatin in the chromosomes involves a coiling of DNA around the histone core of the nucleosome. We suggest that the size of the nucleosome core particle is dictated by the fulfillment of two criteria: One is optimizing the volume fraction of the DNA double helix; this requirement for close-packing has its root in optimizing atomic and molecular interactions. The other criterion being that of having a zero strain-twist coupling; being a zero-twist structure is a necessity when allowing for transient tensile stresses during the reorganization of DNA, e.g., during the reposition, or sliding, of a nucleosome along the DNA double helix. The mathematical model we apply is based on a tubular description of double helices assuming hard walls. When the base-pairs of the linker-DNA is included the estimate of the size of an ideal nucleosome is in close agreement with the experimental numbers. Interestingly, the size of the nucleosome is shown to be a consequence of intrinsic properties of the DNA double helix.Comment: 11 pages, 5 figures; v2: minor modification

Taylor’s focal cortical dysplasia revisited: History, original specimens and impact

50 years ago back in 1971, David C. Taylor and colleagues from England reported on a small series of surgical epilepsy cases proposing a new type of tissue lesion as a cause of difficult-to-treat focal epilepsy: a localized malformation of cerebral cortex. The lesion is now known as focal cortical dysplasia (FCD) Type II or Taylor’s cortical dysplasia. FCD II is not rare, and today is a frequent finding in neurosurgical epilepsy specimens. Medical progress has been achieved in that the majority of FCD II is diagnosed non-invasively by magnetic resonance imaging today. Detailed studies on FCD revealed that the lesion belongs to a spectrum of mTOR-o-pathies, thereby confirming the authors´ initial hypothesis of a relationship to tuberous sclerosis. Here, selected original materials from Taylor´s series are presented as virtual slides, supplemented by original clinical records, in order to give a first-hand impression of this milestone finding in neuropathology of epilepsy