On Sampling of stationary increment processes

Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi by at most \epsilon, with a given probability, asymptotically as \epsilon \downarrow0. The canonical application is to discretization errors in computer simulation of stochastic processes.Comment: Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A technique for measuring vertically and horizontally polarized microwave brightness temperatures using electronic polarization-basis rotation

This technique for electronically rotating the polarization basis of an orthogonal-linear polarization radiometer is based on the measurement of the first three feedhorn Stokes parameters, along with the subsequent transformation of this measured Stokes vector into a rotated coordinate frame. The technique requires an accurate measurement of the cross-correlation between the two orthogonal feedhorn modes, for which an innovative polarized calibration load was developed. The experimental portion of this investigation consisted of a proof of concept demonstration of the technique of electronic polarization basis rotation (EPBR) using a ground based 90-GHz dual orthogonal-linear polarization radiometer. Practical calibration algorithms for ground-, aircraft-, and space-based instruments were identified and tested. The theoretical effort consisted of radiative transfer modeling using the planar-stratified numerical model described in Gasiewski and Staelin (1990)

On overload in a storage model, with a self-similar and infinitely divisible input

Let {X(t)}_{t\ge0} be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H>0. Pick constants \gamma >H and c>0. Let \nu be the L\'evy measure on R^{[0,\infty)} of X, and suppose that R(u)\equiv\nu({y\inR^{[0,\infty)}:supt\ge 0y(t)/(1+ct^{\gamma})>u}) is suitably ``heavy tailed'' as u\to\infty (e.g., subexponential with positive decrease). For the ``storage process'' Y(t)\equiv sup_{s\ge t}(X(s)-X(t)-c(s-t)^{\gamma}), we show that P{sup_{s\in[0,t(u)]}Y(s)>u}\sim P{Y(\hat t(u))>u} as u\to\infty, when 0\le \hat t(u)\le t(u) do not grow too fast with u [e.g., t(u)=o(u^{1/\gamma})]

Design, performance evaluation, and investigation of the theoretical capabilities of the NASA Millimeter-wave Imaging Radiometer (MIR)

The development of techniques for passive microwave retrieval of water vapor and precipitation parameters using millimeter- and sub-millimeter wavelength channels is reviewed. Channels of particular interest are in the tropospheric transmission windows at 90, 150, 220, and 340 GHz and centered around the water vapor lines at 183 and 325 GHz. Collectively, these channels have potential application in high-resolution mapping (e.g., from geosynchronous orbit), remote sensing of cloud and precipitation parameters, and retrieval of water vapor profiles. Both theoretical and experimental results to date are discussed

Joint Venture Law in the Soviet Union: The 1920s and the 1980s

Soviet law has only permitted the establishment of joint ventures within the Union of Soviet Socialist Republics (USSR) during two separate periods. Similar political and economic considerations were major catalysts for the enactment of both joint venture laws, as well as for the similar themes running through them, though the periods are separated by approximately sixty-five years. Examination of both situations, instead of merely the present one, not only will provide a broader perspective of how the Soviets view joint ventures themselves, but will illustrate how Soviet legislation itself has evolved in considering free-market economic principles

Joint Venture Law in the Soviet Union: The 1920s and the 1980s

Soviet law has only permitted the establishment of joint ventures within the Union of Soviet Socialist Republics (USSR) during two separate periods. Similar political and economic considerations were major catalysts for the enactment of both joint venture laws, as well as for the similar themes running through them, though the periods are separated by approximately sixty-five years. Examination of both situations, instead of merely the present one, not only will provide a broader perspective of how the Soviets view joint ventures themselves, but will illustrate how Soviet legislation itself has evolved in considering free-market economic principles

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Presented in this study are the results of controlled partially polarimetric measurements of thermal emission at 91.65 GHz from a striated water surface as corroborated by a geometrical optics radiative model. The measurements were obtained outdoors using a precision polarimetric radiometer which directly measured the first three modified Stokes' parameters. Significant variations in these parameters as a function of azimuthal water wave angle were found, with peak-to-peak variations in T(sub u) of up to approximately 10 K. The measurements are well corroborated by the GO model over a range of observations angles from near nadir up to approximately 65 degrees from nadir. The model incorporates both multiple scattering and a realistic downwelling background brightness field

Power to Change: Math as a Social-Emotional Language in a Classroom of 4 and 5 Year Olds

Tells the story of how mathematics influenced a long term investigation around feeling powerful within an early childhood classroom. Written by Early Childhood Teacher, Elinor J. Albin, and Dean of Faculty, Gretchen Vice, this essay outlines the guiding questions by which teachers at The Advent School in Boston, MA connect mathematics to overarching themes and social-emotional learning. “Power to Change” concludes with observations about how and why mathematics provided a language for building social-emotional intelligence in four and five year olds

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Activities within the period from July 1, 1992 through December 31, 1992 by Georgia Tech researchers in millimeter and submillimeter wavelength tropospheric remote sensing have been centered around the calibration of the Millimeter-wave Imaging Radiometer (MIR), preliminary flight data analysis, and preparation for TOGA/COARE. The MIR instrument is a joint project between NASA/GSFC and Georgia Tech. In the current configuration, the MIR has channels at 90, 150, 183(+/-1,3,7), and 220 GHz. Provisions for three additional channels at 325(+/-1,3) and 8 GHz have been made, and a 325-GHz receiver is currently being built by the ZAX Millimeter Wave Corporation for use in the MIR. Past Georgia Tech contributions to the MIR and its related scientific uses have included basic system design studies, performance analyses, and circuit and radiometric load design, in-flight software, and post-flight data display software. The combination of the above millimeter wave and submillimeter wave channels aboard a single well-calibrated instrument will provide unique radiometric data for radiative transfer and cloud and water vapor retrieval studies. A paper by the PI discussing the potential benefits of passive millimeter and submillimeter wave observations for cloud, water vapor and precipitation measurements has recently been published, and is included as an appendix