We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is K(n, 1 ). These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well. I. Definitions and ...

A similarity matrix is a covariance matrix generated by additive nested common factors having independent components. The set of such matrices is a structured subset of covariance matrices, closed under permutation and restriction, which makes it potentially useful as a sub-model for the joint dependence of several responses. It is also equal to the set of rooted trees. Some issues connected wi...

Medical researchers may be interested in disease processes‎  ‎that are not‎ ‎directly observable‎. ‎Imperfect diagnostic‎ ‎tests may be used repeatedly to monitor the‎ ‎condition of a patient in the absence of a gold standard.‎ ‎We consider parameter identifiability and estimability‎ ‎in a Markov model for alternating binary longitudinal ‎responses that may be misclassified.‎ ‎Exactly ...

We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the transform fractal measures, therefore improve results for Falconer distance set conjecture in three higher dimensions.