156 research outputs found

    On the Calogero-Moser space associated with dihedral groups

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    International audienceUsing the geometry of the associated Calogero-Moser space, R. Rouquier and the author have attached to any finite complex reflection group WW several notions (Calogero-Moser left, right or two-sided cells, Calogero-Moser cellular characters), completing the notion of Calogero-Moser families defined by Gordon. If moreover WW is a Coxeter group, they conjectured that these notions coincide with the analogous notions defined using the Hecke algebra by Kazhdan and Lusztig (or Lusztig in the unequal parameters case). In the present paper, we aim to investigate these conjectures whenever WW is a dihedral group

    The renal resistive index: is it a misnomer?

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    Progress in digital ultrasound technology and diffusion of Doppler ultrasound evaluation of the kidney enable a widespread non-invasive evaluation of renal haemodynamics. Initially most attention has been paid to the study of extraparenchymal renal arteries, mainly to detect renovascular disease. However, this approach has low reproducibility and accuracy. Therefore, interest has gradually moved towards the duplex evaluation of intrarenal anatomy, where the best and most reliable signals are obtained from the large segmental or interlobar arteries that run directly towards the transducer. Among the sonographic parameters used in the last decade, great emphasis has been placed on the intrarenal resistive index (RRI), which is defined as the dimensionless ratio of the difference between maximum and minimum (end-diastolic) flow velocity to maximum flow velocity. It has been used for a long time for the diagnostic and prognostic assessment of renovascular disease . One of the earliest prospective uses of the RRI was in the prediction of kidney function outcomes following intervention for renal artery stenosis. In the pioneering study of Radermacher et al., an RRI[0.80 is associated with poorer outcomes, when surgery or angioplasty is used to correct renal artery stenosis ..

    Computational aspects of Calogero-Moser spaces

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    International audienceWe present a series of algorithms for computing geometric and representationtheoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated with complex reflection groups. Especially, we are concerned with Calogero-Moser families (which correspond to the C×{\mathbb{C}}^\times-fixed points of the Calogero-Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig's constructible characters based on a Galois covering of the Calogero-Moser space). To compute the former, we devised an algorithm for determining generators of the center of the rational Cherednik algebra (this algorithm has several further applications), and to compute the latter we developed an algorithmic approach to the construction of cellular characters via Gaudin operators. We have implemented all our algorithms in the Cherednik Algebra Magma Package (CHAMP) by the second author and used this to confirm open conjectures in several new cases. As an interesting application in birational geometry we are able to determine for many exceptional complex reflection groups the chamber decomposition of the movable cone of a Q-factorial terminalization (and thus the number of non-isomorphic relative minimal models) of the associated symplectic singularity

    Computational aspects of Calogero-Moser spaces

    No full text
    We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated to complex reflection groups. Especially, we are concerned with Calogero-Moser families (which correspond to the C×\mathbb{C}^\times-fixed points of the Calogero-Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig's constructible characters based on a Galois covering of the Calogero-Moser space). To compute the former, we devised an algorithm for determining generators of the center of the rational Cherednik algebra (this algorithm has several further applications), and to compute the latter we developed an algorithmic approach to the construction of cellular characters via Gaudin operators. We have implemented all our algorithms in the Cherednik Algebra Magma Package (CHAMP) by the second author and used this to confirm open conjectures in several new cases. As an interesting application in birational geometry we are able to determine for many exceptional complex reflection groups the chamber decomposition of the movable cone of a Q\mathbb{Q}-factorial terminalization (and thus the number of non-isomorphic relative minimal models) of the associated symplectic singularity.Comment: 42 page

    Identification of a peptide binding to the HIV-1 nucleocapsid protein (NCP7)

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    In HIV-1 the nucleocapsid protein (NC) is essential in the virion assembly process. The discovery of substances able to interfere with the HIV-1 NC functions could be a starting point for the design of new drugs that might inhibit the HIV-1 viral infectivity. A single peptide sequence binding to the NC was isolated using a conformationally homogeneous phage displayed-peptide library. The minimal requirement for the NCp7/peptide interaction was the NCp7 region encompassing the second zinc finger

    Classical hydrodynamics of Calogero-Sutherland models

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    The Calogero Sutherland model is system of particle moving on a line and interacting with long-range forces. In this thesis we consider the classical case where the particles may or may not possess a spin degree of freedom. We demonstrate the intimate connection between the Calogero-Sutherland system and the Benjamin Ono equation. We then directly obtain a classical hydrodynamical limit of both the spineless and spinful Calogero system. The continuum limit of the spinless system is known to exhibit solition solutions. We show numerically that the spinful system also exhibits localized solutions with the soliton property. This is a strong evidence that the continuum spin-Calogero model is exactly integrable.Item withdrawn by Laura Spradlin ([email protected]) on 2014-07-21T22:07:40Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 thesis_Lei_Xing.pdf: 1820398 bytes, checksum: bc21ce5c13ad47d9e5c6786d0694a567 (MD5) dissertation_Lei_Xing.pdf: 1820723 bytes, checksum: 5114afb422a47701f09721e20066ee10 (MD5)Made available in DSpace on 2015-01-21T19:58:50Z (GMT). No. of bitstreams: 1 Lei_Xing.pdf: 1820689 bytes, checksum: 9c67500f26f00003c20ac323e9966226 (MD5)Embargo set by: Seth Robbins for item 73233 Lift date: 2017-01-21T19:59:39Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD systemLimited Restriction Lifted for Item 73233 on 2017-01-22T10:15:29Z
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