The Hall algebra of a spherical object

We determine the Hall algebra, in the sense of Toen, of the algebraic triangulated category generated by a spherical object.Comment: references added, generalization to ground ring in section 3, 14 page

Quantile correlations and quantile autoregressive modeling

In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness

Advances in diagnosis and non-surgical treatment of Bell's palsy

AbstractBell's palsy is a commonly seen cranial nerve disease and can result in compromised facial appearance and functions. Its etiology, prognosis and treatment are still being debated. This paper is a review of recent development in the understanding of etiology, diagnosis and non-surgical treatment of Bell's palsy