266 research outputs found

    On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

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    Given a finite simple graph \cG with nn vertices, we can construct the Cayley graph on the symmetric group SnS_n generated by the edges of \cG, interpreted as transpositions. We show that, if \cG is complete multipartite, the eigenvalues of the Laplacian of \Cay(\cG) have a simple expression in terms of the irreducible characters of transpositions, and of the Littlewood-Richardson coefficients. As a consequence we can prove that the Laplacians of \cG and of \Cay(\cG) have the same first nontrivial eigenvalue. This is equivalent to saying that Aldous's conjecture, asserting that the random walk and the interchange process have the same spectral gap, holds for complete multipartite graphs.Comment: 29 pages. Includes modification which appear on the published version in J. Algebraic Combi

    Veterinary practitioners’ selection of diagnostic tests for the primary evaluation of colic in the horse

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    The aim of this study was to survey veterinary practitioners’ selection of diagnostic tests for horses with clinical signs of abdominal pain. A questionnaire was distributed to veterinary surgeons involved in the primary evaluation of horses with abdominal pain, including the respondent's demographics, selection of diagnostic tests and factors affecting decision-making. Data analysis included descriptive analysis, categorisation of free text and simple univariable correlations to explore the relationships between independent variables and the relative self-estimated frequency that diagnostic tests were performed. A total of 228 responses were analysed. Participants worked in mixed practice (55.7 per cent), first opinion equine (22.8 per cent), first and second opinion equine (17.9 per cent) and referral practice (3.1 per cent). The majority (48.2 per cent, 105/218) were very confident managing a colic case (confidence level 4/5). The most frequently used diagnostic tests were ‘response to analgesia’ (87.2±24.0 per cent cases), rectal examination (75.9±21.2 per cent) and nasogastric intubation (43.8±27.6 per cent). Approach varied between practitioners, and for all diagnostic tests with frequency of use ranging from 0 to 100 per cent of cases. ‘Risk to personal safety’ was the most common reason for not using rectal examination. Practitioner's opinion of their confidence level in managing a colic case was associated with how frequently they used different diagnostic tests. There was marked variation in practitioners’ approaches, highlighting the need for further evidence to support decision-making

    Block-Transitive Designs in Affine Spaces

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    This paper deals with block-transitive tt-(v,k,λ)(v,k,\lambda) designs in affine spaces for large tt, with a focus on the important index λ=1\lambda=1 case. We prove that there are no non-trivial 5-(v,k,1)(v,k,1) designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-(v,k,1)(v,k,1) designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.Comment: 10 pages; to appear in: "Designs, Codes and Cryptography

    Adequate subgroups II

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    The Rolling Tachyon as a Matrix Model

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    We express all correlation functions in timelike boundary Liouville theory as unitary matrix integrals and develop efficient techniques to evaluate these integrals. We compute large classes of correlation functions explicitly, including an infinite number of terms in the boundary state of the rolling tachyon. The matrix integrals arising here also determine the correlation functions of gauge invariant operators in two dimensional Yang-Mills theory, suggesting an equivalence between the rolling tachyon and QCD_2.Comment: 22pages. 3 figures. v2: added reference, fixed minor typo
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