The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Correction of hypertension by normalization of endothelial levels of fibroblast growth factor and nitric oxide synthase in spontaneously hypertensive rats.

Acidic and basic fibroblast growth factors (FGFs) share a wide range of diverse biological activities. To date, low levels of FGF have not been correlated with a pathophysiologic state. We report that blood vessels of spontaneously hypertensive rats are shown to be associated with a marked decrement in endothelial basic FGF content. This decrement correlates both with hypertension and with a decrease in the endothelial content of nitric oxide synthase. Restoration of FGF to physiological levels in the vascular wall, either by systemic administration or by in vivo gene transfer, significantly augmented the number of endothelial cells with positive immunostaining for nitric oxide synthase, corrected hypertension, and ameliorated endothelial-dependent responses to vasoconstrictors. These results suggest an important role for FGFs in blood pressure homeostasis and open new avenues for the understanding of the etiology and treatment of hypertension.