Normalizers of tori

We determine the groups which can appear as the normalizer of a maximal torus in a connected 2-compact group. The technique depends on using ideas of Tits to give a novel description of the normalizer of the torus in a connected compact Lie group, and then showing that this description can be extended to the 2-compact case.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper31.abs.htm

Operating limits for acoustic measurement of rolling bearing oil film thickness

An ultrasonic pulse striking a thin layer of liquid trapped between solid bodies will be partially reflected. The proportion reflected is a function of the layer stiffness, which in turn depends on the film thickness and its bulk modulus. In this work, measurements of reflection have been used to determine the thickness of oil films in elastohydrodynamic lubricated (EHL) contacts. A very thin liquid layer behaves like a spring when struck by an ultrasonic pulse. A simple quasi-static spring model can be used to determine the proportion of the ultrasonic waves reflected. Experiments have been performed on a model EHL contact between a ball and a flat surface. A transducer is mounted above the contact such that the ultrasonic wave is focused onto the oil film. The reflected signals are captured and passed to a PC for processing. Fourier analysis gives the reflection spectrum that is then used to determine the stiffness of the liquid layer and hence its thickness. In further testing, an ultrasonic transducer has been mounted in the housing of a deep-groove ball bearing to measure the film generated at the outer raceway as each ball passes. Results from both the ball-flat and ball bearing measurements agree well with steady-state theoretical EHL predictions. The limits of the measuring technique, in terms of the measurable rolling bearing size and operating parameters, have been investigated

Finiteness in derived categories of local rings

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension, injective dimension, and Gorenstein dimension, are established. It is proved that these specialize to give results concerning modules over complete intersection local rings. A noteworthy feature is the use of techniques based on thick subcategories of derived categories.Comment: 40 pages. Minor revisions. To appear in Commentarii Math. Helvetic

A Site of Alcohol Action at the NMDA Receptor M3-M4 Domain Interface

The N-methyl-D-aspartate (NMDA) glutamate receptor is a major target of ethanol in the brain. Previous studies have identified positions in the third and fourth membrane-associated (M) domains of the NMDA receptor GluN1 and GluN2A subunits that influence alcohol sensitivity. The structural model of the NMDA receptor, predicted from the structure of the related GluA2 subunit, indicates a close apposition of the alcohol-sensitive positions in M3 and M4 between the two subunit types. We investigated possible interactions between the M3 and M4 domain positions of the two subunit types affecting the ethanol sensitivity of the receptor by using dual substitution mutants. In an initial screen of single-substitution mutants, we found that a position in both subunits adjacent to one previously identified, GluN1(G638) and GluN2A(F636), can strongly regulate ethanol sensitivity. Significant interactions affecting ethanol inhibition were observed at four pairs of positions in GluN1/GluN2A: G638/M823, F639/L824, M818/F636, and L819/F637. Two of these interactions involve a position in M4 of both subunits, GluN1(M818) and GluN2A(L824), that does not by itself alter ethanol sensitivity, and one of the previously identified positions affecting ethanol sensitivity, GluN2A(A825), did not appear to interact with any other position tested. These results also indicate a shift by one position of the predicted alignment of the GluN1 M4 domain. These findings have allowed for the refinement of the NMDA receptor M domain structure, and support the existence of four sites of alcohol action on the NMDA receptor at the M3-M4 domain intersubunit interfaces. These studies were supported by grants R01 AA015203-01A1 and AA015203-06A1 from the NIAAA to R.W.P

Stratifying derived categories of cochains on certain spaces

In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of localizing and thick subcategories in terms of subsets of the prime ideal spectrum of the given ring. In this paper two stratification results are presented: one for the derived category of a commutative ring-spectrum with polynomial homotopy and another for the derived category of cochains on certain spaces. We also give the stratification of cochains on a space a topological content.Comment: 27 page

DG algebras with exterior homology

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page

Incremental Grid-like Layout Using Soft and Hard Constraints

We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout---with predominantly axis-aligned edges---that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart.Comment: Accepted to Graph Drawing 201

Interactions Among Positions in the Third and Fourth Membrane-Associated Domains at the Intersubunit Interface of the N-Methyl-D-Aspartate Receptor Forming Sites of Alcohol Action

The N-methyl-d-aspartate (NMDA) glutamate receptor is a major target of ethanol in the brain. Previous studies have identified positions in the third and fourth membrane-associated (M) domains of the NMDA receptor GluN1 and GluN2A subunits that influence alcohol sensitivity. The predicted structure of the NMDA receptor, based on that of the related GluA2 subunit, indicates a close apposition of the alcohol-sensitive positions in M3 and M4 between the two subunit types. We tested the hypothesis that these positions interact to regulate receptor kinetics and ethanol sensitivity by using dual substitution mutants. In single-substitution mutants, we found that a position in both subunits adjacent to one previously identified, GluN1(Gly-638) and GluN2A(Phe-636), can strongly regulate ethanol sensitivity. Significant interactions affecting ethanol inhibition and receptor deactivation were observed at four pairs of positions in GluN1/GluN2A: Gly-638/Met-823, Phe-639/Leu-824, Met-818/Phe-636, and Leu-819/Phe-637; the latter pair also interacted with respect to desensitization. Two interactions involved a position in M4 of both subunits, GluN1(Met-818) and GluN2A(Leu-824), that does not by itself alter ethanol sensitivity, whereas a previously identified ethanol-sensitive position, GluN2A(Ala-825), did not unequivocally interact with any other position tested. These results also indicate a shift by one position of the predicted alignment of the GluN1 M4 domain. These findings have allowed for the refinement of the NMDA receptor M domain structure, demonstrate that this region can influence apparent agonist affinity, and support the existence of four sites of alcohol action on the NMDA receptor, each consisting of five amino acids at the M3-M4 domain intersubunit interfaces