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Search Results: 1 - 10 of 10110 matches for " Benjamin Harris "
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Fourier Transforms of Nilpotent, Coadjoint Orbits for GL(n,R)
Benjamin Harris
Mathematics , 2012,
Abstract: The main result of this paper is an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n,R). This paper also includes some results on limit formulas for reductive Lie groups including new proofs of classical limit formulas of Rao and Harish-Chandra.
Tempered Representations and Nilpotent Orbits
Benjamin Harris
Mathematics , 2012,
Abstract: Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation pi such that O occurs in the wave front cycle of pi. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.
Wave Front Sets of Reductive Lie Group Representations II
Benjamin Harris
Mathematics , 2014,
Abstract: In this paper it is shown that the wave front set of a direct integral of singular, irreducible representations of a real, reductive algebraic group is contained in the singular set. Combining this result with the results of the first paper in this series, the author obtains asymptotic results on the occurrence of tempered representations in induction and restriction problems for real, reductive algebraic groups.
Wave Front Sets of Reductive Lie Group Representations III
Benjamin Harris,Tobias Weich
Mathematics , 2015,
Abstract: In this article, the authors prove an upper bound for the wave front set of an induced Lie group representation under a uniformity condition, which is verified for several large classes of examples. As a corollary, if $X$ is a homogeneous space for a real, reductive algebraic group $G$ with a nonzero invariant density, the authors give a complete description of the regular, semisimple asymptotics of the support of the Plancherel measure for $L^2(X)$.
Modes of Neighbouring Group Participation by the Methyl Selenyl Substituent in β-Methylselenylmethyl-substituted 1-Phenylethyl Carbenium Ions
Benjamin L. Harris,Jonathan M. White
Molecules , 2013, DOI: 10.3390/molecules181011705
Abstract: Selenium substituents which are disposed β to an electron deficient centre, such as a carbocation p-orbital, or the π* orbital of an electron deficient p-system, interact in a stabilising way by a combination of C-Se hyperconjugation (σ Se-C– π* interaction), and a through-space homoconjugative n Se–π* interaction. The relative importance of these two modes of interaction is dependant on the electron demand of the cation, with hyperconjugation predominating for low electron demand systems, and the n Se–π* interaction predominating for high electron demand cations.
The Continuous Spectrum in Discrete Series Branching Laws
Benjamin Harris,Hongyu He,Gestur Olafsson
Mathematics , 2012,
Abstract: If $G$ is a reductive Lie group of Harish-Chandra class, $H$ is a symmetric subgroup, and $\pi$ is a discrete series representation of $G$, the authors give a condition on the pair $(G,H)$ which guarantees that the direct integral decomposition of $\pi|_H$ contains each irreducible representation of $H$ with finite multiplicity. In addition, if $G$ is a reductive Lie group of Harish-Chandra class, and $H\subset G$ is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in the direct integral decomposition of $\pi|_H$ is constant along `continuous parameters'. In obtaining these results, the authors develop a new technique for studying multiplicities in the restriction $\pi|_H$ via convolution with Harish-Chandra characters. This technique has the advantage of being useful for studying the continuous spectrum as well as the discrete spectrum.
Wave Front Sets of Reductive Lie Group Representations
Benjamin Harris,Hongyu He,Gestur Olafsson
Mathematics , 2013,
Abstract: If $G$ is a Lie group, $H\subset G$ is a closed subgroup, and $\tau$ is a unitary representation of $H$, then the authors give a sufficient condition on $\xi\in i\mathfrak{g}^*$ to be in the wave front set of $\operatorname{Ind}_H^G\tau$. In the special case where $\tau$ is the trivial representation, this result was conjectured by Howe. If $G$ is a real, reductive algebraic group and $\pi$ is a unitary representation of $G$ that is weakly contained in the regular representation, then the authors give a geometric description of $\operatorname{WF}(\pi)$ in terms of the direct integral decomposition of $\pi$ into irreducibles. Special cases of this result were previously obtained by Kashiwara-Vergne, Howe, and Rossmann. The authors give applications to harmonic analysis problems and branching problems.
Post-conflict transition and HIV
Manuel Carballo,Calixte Clérisme,Benjamin Harris,Patrick Kayembe
Forced Migration Review , 2010,
Abstract: Research in Bosnia, the Democratic Republic of Congo, Haiti and Liberia has highlighted worrying neglect of HIV issues in the aftermath of conflict and displacement.
Cost-Effectiveness Analysis of Diagnostic Options for Pneumocystis Pneumonia (PCP)
Julie R. Harris, Barbara J. Marston, Nalinee Sangrujee, Desiree DuPlessis, Benjamin Park
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0023158
Abstract: Background Diagnosis of Pneumocystis jirovecii pneumonia (PCP) is challenging, particularly in developing countries. Highly sensitive diagnostic methods are costly, while less expensive methods often lack sensitivity or specificity. Cost-effectiveness comparisons of the various diagnostic options have not been presented. Methods and Findings We compared cost-effectiveness, as measured by cost per life-years gained and proportion of patients successfully diagnosed and treated, of 33 PCP diagnostic options, involving combinations of specimen collection methods [oral washes, induced and expectorated sputum, and bronchoalveolar lavage (BAL)] and laboratory diagnostic procedures [various staining procedures or polymerase chain reactions (PCR)], or clinical diagnosis with chest x-ray alone. Our analyses were conducted from the perspective of the government payer among ambulatory, HIV-infected patients with symptoms of pneumonia presenting to HIV clinics and hospitals in South Africa. Costing data were obtained from the National Institutes of Communicable Diseases in South Africa. At 50% disease prevalence, diagnostic procedures involving expectorated sputum with any PCR method, or induced sputum with nested or real-time PCR, were all highly cost-effective, successfully treating 77–90% of patients at $26–51 per life-year gained. Procedures using BAL specimens were significantly more expensive without added benefit, successfully treating 68–90% of patients at costs of $189–232 per life-year gained. A relatively cost-effective diagnostic procedure that did not require PCR was Toluidine Blue O staining of induced sputum ($25 per life-year gained, successfully treating 68% of patients). Diagnosis using chest x-rays alone resulted in successful treatment of 77% of patients, though cost-effectiveness was reduced ($109 per life-year gained) compared with several molecular diagnostic options. Conclusions For diagnosis of PCP, use of PCR technologies, when combined with less-invasive patient specimens such as expectorated or induced sputum, represent more cost-effective options than any diagnostic procedure using BAL, or chest x-ray alone.
IL-1β Suppresses Innate IL-25 and IL-33 Production and Maintains Helminth Chronicity
Mario M. Zaiss,Kendle M. Maslowski,Ilaria Mosconi,Nadine Guenat,Benjamin J. Marsland,Nicola L. Harris
PLOS Pathogens , 2013, DOI: 10.1371/journal.ppat.1003531
Abstract: Approximately 2 billion people currently suffer from intestinal helminth infections, which are typically chronic in nature and result in growth retardation, vitamin A deficiency, anemia and poor cognitive function. Such chronicity results from co-evolution between helminths and their mammalian hosts; however, the molecular mechanisms by which these organisms avert immune rejection are not clear. We have found that the natural murine helminth, Heligmosomoides polygyrus bakeri (Hp) elicits the secretion of IL-1β in vivo and in vitro and that this cytokine is critical for shaping a mucosal environment suited to helminth chronicity. Indeed in mice deficient for IL-1β (IL-1β?/?), or treated with the soluble IL-1βR antagonist, Anakinra, helminth infection results in enhanced type 2 immunity and accelerated parasite expulsion. IL-1β acts to decrease production of IL-25 and IL-33 at early time points following infection and parasite rejection was determined to require IL-25. Taken together, these data indicate that Hp promotes the release of host-derived IL-1β that suppresses the release of innate cytokines, resulting in suboptimal type 2 immunity and allowing pathogen chronicity.
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