3,075 research outputs found

    The efficacy of lymph node fine needle aspiration cytology

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    Fine needle aspiration cytology (FNAC) of lymph nodes is a safe, easy, cheap and quick diagnostic tool, which involves the examination of a random sample of cells from a lymph node. To assess the distribution of diagnostic categories and the efficacy of lymph node fine needle aspiration cytology at our institution. These were compared to the literature. Methodology: All of lymph node FNAC cases taken between the 1st January 2012 and the 31st December 2013 were retrieved from our Laboratory Information System. A total of 300 cases were retrieved and then placed into one of six categories; Category 1: Non-diagnostic, 2: Reactive, 3: Probably reactive but lymphoma cannot be excluded, 4: Non-Hodgkin lymphoma, 5: Hodgkin lymphoma, and 6: Metastasis. These were then correlated with the histology of the lymph node excision specimens. The proportion of diagnoses placed under categories 1, 2, 3, 4, 5 and 6 represent 14%, 53%, 4.3%, 5.7%, 1.7% and 21.3% of the total respectively. The overall efficacy of FNAC showed a sensitivity of 84.5%, specificity of 99.3%, a false negative rate of 10%, a false positive rate of 0.7%, accuracy of 93.1%, positive predictive value of 98.8% and negative predictive value of 89.9%. FNAC of lymph nodes is a very useful and effective tool in triaging patients with lymphadenopathy.peer-reviewe

    A multiplicity bound for graded rings and a criterion for the Cohen-Macaulay property

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    Let RR be a polynomial ring over a field. We prove an upper bound for the multiplicity of R/IR/I when II is a homogeneous ideal of the form I=J+(F)I=J+(F), where JJ is a Cohen-Macaulay ideal and F∉JF\notin J. The bound is given in terms of two invariants of R/JR/J and the degree of FF. We show that ideals achieving this upper bound have high depth, and provide a purely numerical criterion for the Cohen-Macaulay property. Applications to quasi-Gorenstein rings and almost complete intersections are given.Comment: 14 pages, comments are welcom

    Ideals with Larger Projective Dimension and Regularity

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    We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows asymptotically as sqrt{d}^(sqrt(d) - 1).Comment: 10 pages. This work was completed at the MRC for Commutative Algebra in Snowbird, UT, which was generously supported by the AM

    Adaptation without natural selection

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    PI Degree and Irreducible Representations of Quantum Determinantal Rings and their Associated Quantum Schubert Varieties

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    We study quantum determinantal rings at roots of unity and calculate the PI degree using results of Lenagan-Rigal and Haynal to reduce the problem to finding properties of their associated matrices. These matrices, in turn, correspond to Cauchon-Le diagrams from which we can calculate the required matrix properties. In particular, we show that any matrix corresponding to an m×nm\times n diagram has invariant factors which are powers of 2. Our calculations allow us to state an explicit expression for the PI degree of quantum determinantal rings when the deformation parameter qq is a primitive ℓth\ell^{\text{th}} root of unity with ℓ\ell odd. Using this newly calculated PI degree we present a method to construct an irreducible representation of maximal dimension. Building on these results, we use the strong connection between quantum determinantal rings and certain quantum Schubert varieties through noncommutative dehomogenisation to obtain expressions for the PI degree of such quantum Schubert varieties under the same conditions on qq.Comment: 36 page
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