540 research outputs found

    Theorems on products of EPr matrices, II

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    AbstractThis paper gives necessary and sufficient conditions that the product of EPr matrices with entries from an arbitrary field be EPr. Results about the Reverse Order Law for generalized inverses of products of these matrices are included

    Delirium as a predictor of sepsis in post-coronary artery bypass grafting patients: a retrospective cohort study

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    Article deposited according to agreement with BMC, December 6, 2010.YesFunding provided by the Open Access Authors Fund

    Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues

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    We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for an egalitarian PS queue with KK customer classes, we show that the marginal queue length distribution for class kk factorizes over the number of other customer types. The factorizing coefficients equal the queue length probabilities of a PS queue for type kk in isolation, in which the customers of the other types reside \textit{ permanently} in the system. Similarly, the (conditional) mean sojourn time for class kk can be obtained by conditioning on the number of permanent customers of the other types. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian processor-sharing models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights. \u

    Multiple metrics of latitudinal patterns in insect pollination and herbivory for a tropical‐temperate congener pair

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    The biotic interactions hypothesis posits that biotic interactions are more important drivers of adaptation closer to the equator, evidenced by “stronger” contemporary interactions (e.g. greater interaction rates) and/or patterns of trait evolution consistent with a history of stronger interactions. Support for the hypothesis is mixed, but few studies span tropical and temperate regions while experimentally controlling for evolutionary history. Here, we integrate field observations and common garden experiments to quantify the relative importance of pollination and herbivory in a pair of tropical‐temperate congeneric perennial herbs. Phytolacca rivinoides and P. americana are pioneer species native to the Neotropics and the eastern USA, respectively. We compared plant‐pollinator and plant‐herbivore interactions between three tropical populations of P. rivinoides from Costa Rica and three temperate populations of P. americana from its northern range edge in Michigan and Ohio. For some metrics of interaction importance, we also included three subtropical populations of P. americana from its southern range edge in Florida. This approach confounds species and region but allows us, uniquely, to measure complementary proxies of interaction importance across a tropical‐temperate range in one system. To test the prediction that lower‐latitude plants are more reliant on insect pollinators, we quantified floral display and reward, insect visitation rates, and self‐pollination ability (autogamy). To test the prediction that lower‐latitude plants experience more herbivore pressure, we quantified herbivory rates, herbivore abundance, and leaf palatability. We found evidence supporting the biotic interactions hypothesis for most comparisons between P. rivinoides and north‐temperate P. americana (floral display, insect visitation, autogamy, herbivory, herbivore abundance, and young‐leaf palatability). Results for subtropical P. americana populations, however, were typically not intermediate between P. rivinoides and north‐temperate P. americana, as would be predicted by a linear latitudinal gradient in interaction importance. Subtropical young‐leaf palatability was intermediate, but subtropical mature leaves were the least palatable, and pollination‐related traits did not differ between temperate and subtropical regions. These nonlinear patterns of interaction importance suggest future work to relate interaction importance to climatic or biotic thresholds. In sum, we found that the biotic interactions hypothesis was more consistently supported at the larger spatial scale of our study
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