Heat kernel transform for nilmanifolds associated to the Heisenberg group

We study the heat kernel transform on a nilmanifold $M$ of the Heisenberg group. We show that the image of $L^2(M)$ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.Comment: Revised version; to appear in Revista Mathematica Iberoamericana, 28

Discontinuous resistance change and domain wall scattering in patterned NiFe wires with a nanoconstriction

A nonlinear current-voltage (I-V) characteristic was observed in patterned NiFe wires with a central "bow-tie" point contact constriction. By passing a dc current through the wire, a sharp resistance drop was obtained for current densities in the range of 1.1-1.4 x 10(7) A/cm(2). This is attributed to current-induced domain wall drag, resulting in displacement of a domain wall away from the constriction. A maximum current-induced resistance change of 0.079% was obtained for a 100-nm constriction, which is comparable with the magnetoresistance due to domain wall scattering in NiFe

Empirical stationary correlations for semi-supervised learning on graphs

In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such proposals are equivalent to kriging predictors based on a fixed covariance matrix driven by the link structure of the graph. We then propose a data-driven estimator of the correlation structure that exploits patterns among the observed response values. By incorporating even a small fraction of observed covariation into the predictions, we are able to obtain much improved prediction on two graph data sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS293 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parameter estimation of GOES precipitation index at different calibration timescales

We examined two techniques that adjust the parameters of the GOES Precipitation Index (GPI) by combining the polar microwave and the geosynchronous infrared observations at three frequencies: daily, pentad, and monthly. The first technique is the adjusted GPI (AGPI), and the second is the universally adjusted GPI (UAGPI). The study shows that rainfall estimates can be improved by frequent calibrations providing there is sufficient superior (microwave) rainfall sampling within the calibration time and space domain. For this work, daily and pentad calibrations produce monthly rainfall estimates almost as good as monthly calibration. The daily calibration produced better daily rainfall estimates than pentad and monthly calibration, but it generates similar pentad rainfall estimates to these of the pentad calibration. The monthly calibrated scheme is not suitable for the daily and pentad rainfall estimates. Under the current twice-per-day sampling rate of polar-orbiting microwave observations, the pentad calibration scheme is suggested for the monthly, pentad, and daily rainfall. The potentials of applying the UAGPI and the AGPI techniques for daily rainfall estimation are also investigated. Copyright 2000 by the American Geophysical Union