lace expansion and suggesting that it might converge in five dimensions, and to Takashi Hara for the pleasure of four years of collaboration and for permission to include unpublished joint work. We gratefully acknowledge financial support from the Natural Sciences and Engineering Reearch Council of Canada. Finally we offer our thanks and deep appreciation to Joyce Kruskal and Joanne Nakonechny ...

The spatial orientation of vectors rigidly embedded in polymer chains are described in terms of time-dependent joint probability distribution functions. Serial expansion in terms of double spherical harmonics is adopted for the probability distribution functions, with the coefficients therein evaluated from Brownian dynamics simulations. Truncation of the series after the second-order harmonics...

We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the “adaptive cluster expansion”, or ACE for short. We present an application of this approach, based on a multilayer topographic mapping network, that adaptively estimates the joint probability density function of the pixel values of an image, and pr...

International data grids are now being built that support joint management of shared collections. An emerging strategy is to build multiple independent data grids, each managed by the local institution. The data grids are then federated to enable controlled sharing of files. We examine the management issues associated with maintaining federations of production data grids, including management o...

We develop two new multivariate statistical dependence measures. The first, based on the Kullback-Leibler distance, results in a single value that indicates the general level of dependence among the random variables. The second, based on an orthonormal series expansion of joint probability density functions, provides more detail about the nature of the dependence. We apply these dependence meas...

We consider the ensemble of real Ginibre matrices conditioned to have positive fraction α > 0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probabilit...

Abstract. The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of the linear representation of...

In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the “multiplicative golden mean shift” defined as the set of all reals in [0, 1] whose binary expansion (xk) satisfies xkx2k = 0 for all k ≥ 1. Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obta...