1,721,414 research outputs found
Coarse medians and Property A
No full textWe prove that uniformly locally finite quasigeodesic coarse median spaces of finite rank and at most exponential growth have Property A. This offers an alternative proof of the fact that mapping class groups have property A
Neuropharmacology of the snail Helix aspersa and the scorpion Pandinus imperator central neurones
No full textThis thesis is divided into three sections. The first section concerns the responses of identified neurones in the right parietal ganglion of the snail Helix aspersa. Cells F4, 5 and 6 are excited by 5-hydroxy-tryptamine (5-HT) and inhibited by dopamine whereas cells in the F30 area are inhibited by both compounds. Tryptamine and 6-HT are able to activate both types of receptor on the F4, 5 and 6 cells in a dose dependent manner. Their dual action can also be separated by specific antagonists. Ergometrine blocks the dopamine response and reverses tryptamine and 6-HT inhibition into excitation while d-tubocurarine blocks the 5-HT response and reverses tryptamine and 6-HT excitation into inhibition. On F30 cells the compounds appear to act on a dopamine receptor. All are blocked by ergometrine, unaffected by d-tubocurarine and enhanced by low potassium Ringer. The second section utilises the same preparation but is concerned with the chloride-mediated inhibitory response of cell E4 of the visceral ganglion to applied acetylcholine. Four compounds, known to affect chloride movement in a variety of tissues, were tested on this response and compared with the sodium-mediated excitatory response of cells E1 and 2 to applied acetylcholine. Piretanide irreversibly blocked the inhibitory response only and the inhibition increased with time. Furosemide irreversibly blocked both types of response and the inhibition also increased with time. No recovery was seen with either compound. 4-acetamino-4-isothiocyano-2,2'-disulphonic acid stilbene (S.I.T.S.) and ethacrynic acid rapidly and reversibly blocked both types of response. No change in the chloride or sodium equilibrium potential values were noted. Piretanide and furosemide probably act non selectively on the structure of the cell membrane while S.I.T.S. and ethacrynic acid may interact directly with the acetylcholine receptor protein. The third section involves the application of various putative neurotransmitters onto the exposed central nervous system (C.N.S.) of the scorpion Pandinus imperator. Their effects on leg motoneurone output were monitored extracellularly and analysed using the EROS-PC data-logging system. Although the exact nature of the response was obscured as the compounds could act at all or any level of the C.N.S., most did produce definite changes in the recorded spike trains. Gamma-aminobutyric acid (GABA) and acetylcholine were strongly implicated as central transmitters with glycine, glutamate, octopamine, dopamine and 5-HT also having an effect.</p
Neurobiological and Emotional Influences: a realistic organic account of human decision making
No full textStratified Langlands duality in the A<sub>n</sub> tower
No full textLet S_k denote a maximal torus in the complex Lie group G = SL_n(C)/C_kand let T_k denote a maximal torus in its compact real form SU_n(C)/C_k, where k divides n. Let W denote the Weyl group of G, namely the symmetric group S_n. We elucidate the structure of the extended quotient S_k//W as an algebraic variety and of T_k//W as a topological space, in both cases describing them as bundles over unions of tori.Corresponding to the invariance of K-theory under Langlands duality, this calculationprovides a homotopy equivalence between T_k//W and its dual T_n //W. Hence there is an isomorphism in cohomology for the extended quotients. Moreover this is stratified as a direct sum over conjugacy classes of the Weyl group. We derive a formula for the periodic cyclic homology of the group ring of an extended affine Weyl group in terms of these extended quotients and use our formulae to compute a number of examples of homology, cohomology and K-theory
A four point characterisation for coarse median spaces
No full textCoarse median spaces simultaneously generalise the classes of hyperbolic spaces and median algebras, and arise naturally in the study of the mapping class groups and many other contexts. Their definition as originally conceived by Bowditch requires median approximations for all finite subsets of the space. Here we provide a simplification of the definition in the form of a 4-point condition analogous to Gromov's 4-point condition defining hyperbolicity. We give an intrinsic characterisation of rank in terms of the coarse median operator and use this to give a direct proof that rank 1 geodesic coarse median spaces are -hyperbolic, bypassing Bowditch's use of asymptotic cones. A key ingredient of the proof is a new definition of intervals in coarse median spaces and an analysis of their interaction with geodesics
Coarse median algebras: The intrinsic geometry of coarse median spaces and their intervals
No full textThis paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of δ-hyperbolicity.<br/
Centralisers, complex reflection groups and actions in the Weyl group E6
No full textThe compact, connected Lie group admits two forms: simply connected and adjoint type. As we previously established, the Baum-Connes isomorphism relates the two Langlands dual forms, giving a duality between the equivariant K-theory of the Weyl group acting on the corresponding maximal tori. Our study of the case showed that this duality persists at the level of homotopy, not just homology. In this paper we compute the extended quotients of maximal tori for the two forms of , showing that the homotopy equivalences of sectors established in the case also exist here, leading to a conjecture that the homotopy equivalences always exist for Langlands dual pairs. In computing these sectors we show that centralisers in the Weyl group decompose as direct products of reflection groups, generalising Springer's results for regular elements, and we develop a pairing between the component groups of fixed sets generalising Reeder's results. As a further application we compute the -theory of the reduced Iwahori-spherical -algebra of the p-adic group , which may be of adjoint type or simply connected
Property A and exactness of the uniform Roe algebra
No full textIn this short note, prepared for the volume of conjectures to celebrate Guido Mislin's retirement, we outline the conjecture that a uniformly discrete bounded geometry metric space X has property A if and only if the uniform Roe algebra C^?(X ) is exact
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
