41 research outputs found

    How to compute the Frobenius-Schur indicator of a unipotent character of a finite Coxeter system

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    For each finite, irreducible Coxeter system (W,S)(W,S), Lusztig has associated a set of "unipotent characters" \Uch(W). There is also a notion of a "Fourier transform" on the space of functions \Uch(W) \to \RR, due to Lusztig for Weyl groups and to Brou\'e, Lusztig, and Malle in the remaining cases. This paper concerns a certain WW-representation ϱW\varrho_{W} in the vector space generated by the involutions of WW. Our main result is to show that the irreducible multiplicities of ϱW\varrho_W are given by the Fourier transform of a unique function \epsilon : \Uch(W) \to \{-1,0,1\}, which for various reasons serves naturally as a heuristic definition of the Frobenius-Schur indicator on \Uch(W). The formula we obtain for ϵ\epsilon extends prior work of Casselman, Kottwitz, Lusztig, and Vogan addressing the case in which WW is a Weyl group. We include in addition a succinct description of the irreducible decomposition of ϱW\varrho_W derived by Kottwitz when (W,S)(W,S) is classical, and prove that ϱW\varrho_{W} defines a Gelfand model if and only if (W,S)(W,S) has type AnA_n, H3H_3, or I2(m)I_2(m) with mm odd. We show finally that a conjecture of Kottwitz connecting the decomposition of ϱW\varrho_W to the left cells of WW holds in all non-crystallographic types, and observe that a weaker form of Kottwitz's conjecture holds in general. In giving these results, we carefully survey the construction and notable properties of the set \Uch(W) and its attached Fourier transform.Comment: 38 pages, 4 tables; v2, v3, v4: some corrections and additional reference

    Family Firms and Firm Performance: Evidence from Japan

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    Corrigendum: Nature Structural and Molecular Biology 16 (12), 1331 (2009) doi:10.1038/nsmb1209-1331bInternational audienceThioredoxins (Trxs) are oxidoreductase enzymes, present in all organisms, that catalyze the reduction of disulfide bonds in proteins. By applying a calibrated force to a substrate disulfide, the chemical mechanisms of Trx catalysis can be examined in detail at the single-molecule level. Here we use single-molecule force-clamp spectroscopy to explore the chemical evolution of Trx catalysis by probing the chemistry of eight different Trx enzymes. All Trxs show a characteristic Michaelis-Menten mechanism that is detected when the disulfide bond is stretched at low forces, but at high forces, two different chemical behaviors distinguish bacterial-origin from eukaryotic-origin Trxs. Eukaryotic-origin Trxs reduce disulfide bonds through a single-electron transfer reaction (SET), whereas bacterial-origin Trxs show both nucleophilic substitution (SN2) and SET reactions. A computational analysis of Trx structures identifies the evolution of the binding groove as an important factor controlling the chemistry of Trx catalysis

    A united statement of the global chiropractic research community against the pseudoscientific claim that chiropractic care boosts immunity.

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    BACKGROUND: In the midst of the coronavirus pandemic, the International Chiropractors Association (ICA) posted reports claiming that chiropractic care can impact the immune system. These claims clash with recommendations from the World Health Organization and World Federation of Chiropractic. We discuss the scientific validity of the claims made in these ICA reports. MAIN BODY: We reviewed the two reports posted by the ICA on their website on March 20 and March 28, 2020. We explored the method used to develop the claim that chiropractic adjustments impact the immune system and discuss the scientific merit of that claim. We provide a response to the ICA reports and explain why this claim lacks scientific credibility and is dangerous to the public. More than 150 researchers from 11 countries reviewed and endorsed our response. CONCLUSION: In their reports, the ICA provided no valid clinical scientific evidence that chiropractic care can impact the immune system. We call on regulatory authorities and professional leaders to take robust political and regulatory action against those claiming that chiropractic adjustments have a clinical impact on the immune system

    Advances in structure elucidation of small molecules using mass spectrometry

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    The structural elucidation of small molecules using mass spectrometry plays an important role in modern life sciences and bioanalytical approaches. This review covers different soft and hard ionization techniques and figures of merit for modern mass spectrometers, such as mass resolving power, mass accuracy, isotopic abundance accuracy, accurate mass multiple-stage MS(n) capability, as well as hybrid mass spectrometric and orthogonal chromatographic approaches. The latter part discusses mass spectral data handling strategies, which includes background and noise subtraction, adduct formation and detection, charge state determination, accurate mass measurements, elemental composition determinations, and complex data-dependent setups with ion maps and ion trees. The importance of mass spectral library search algorithms for tandem mass spectra and multiple-stage MS(n) mass spectra as well as mass spectral tree libraries that combine multiple-stage mass spectra are outlined. The successive chapter discusses mass spectral fragmentation pathways, biotransformation reactions and drug metabolism studies, the mass spectral simulation and generation of in silico mass spectra, expert systems for mass spectral interpretation, and the use of computational chemistry to explain gas-phase phenomena. A single chapter discusses data handling for hyphenated approaches including mass spectral deconvolution for clean mass spectra, cheminformatics approaches and structure retention relationships, and retention index predictions for gas and liquid chromatography. The last section reviews the current state of electronic data sharing of mass spectra and discusses the importance of software development for the advancement of structure elucidation of small molecules

    The maintenance of extreme amino acid diversity at the disease resistance gene, RPP13, in Arabidopsis thaliana.

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    We have used the naturally occurring plant-parasite system of Arabidopsis thaliana and its common parasite Peronospora parasitica (downy mildew) to study the evolution of resistance specificity in the host population. DNA sequence of the resistance gene, RPP13, from 24 accessions, including 20 from the United Kingdom, revealed amino acid sequence diversity higher than that of any protein coding gene reported so far in A. thaliana. A significant excess of amino acid polymorphism segregating within this species is localized within the leucine-rich repeat (LRR) domain of RPP13. These results indicate that single alleles of the gene have not swept through the population, but instead, a diverse collection of alleles have been maintained. Transgenic complementation experiments demonstrate functional differences among alleles in their resistance to various pathogen isolates, suggesting that the extreme amino acid polymorphism in RPP13 is maintained through continual reciprocal selection between host and pathogen
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