Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

EFFECT OF ELECTRICAL DISCHARGE PATTERN ON SPARK IGNITED FLAME KERNEL DEVELOPMENT

Fuel-lean combustion and exhaust gas recirculation (EGR) in spark ignition engines improve engine efficiency and reduce emission. However, flame initiation becomes more difficult in lean and dilute fuel-air mixture with traditional spark discharge. This research proposal will first provide an intensive review on topics related to spark ignition including properties of electrical discharge, flame kernel behavior and spark ignition modeling and simulation. Focus will be laid on electrical discharge pattern effect as it is showing prospect in extending ignition limits in SI engines. An experimental setup has been built with an optically accessible constant volume combustion vessel. Multiple imaging techniques as well as spectroscopy will be applied. By varying spark discharge patterns, preliminary test results are available on consequent flame kernel development. In addition to experimental investigation of spark plasma and flame kernel development, spark ignition modeling with detailed description of plasma channel is also proposed for this study.

Montana In the 1970’s: Seen Through a Reporter’s Eyes -- Chuck Johnson “In the Crucible of Change”

It has been said that “journalism is the first rough draft of history.” If that be the case, much of Montana’s history since 1970 was first written by Chuck Johnson. He has covered the activities of 20 regular sessions of the Legislature plus an untold number of Special Sessions, the Constitutional Convention, nine Governors, eight US Senators and seven US Congressmen. Primary elections, general elections, state and national Party Conventions have been seen by Montanans through Johnson’s prism. Big and little news about policy, insights about politics, and a sense of the people behind the news (and history) has flowed from Chuck Johnson’s pen. Johnson’s first decade as a journalist coincides substantially with the period of “In the Crucible of Change.” Having been one of those who wrote the first draft of much of the history in the series “In the Crucible of Change,” and as “Dean of Montana’s Capitol Reporters,” Chuck’s reflections and insights about the period are conveyed in this film with a maturity and understanding that can only come from one who has spent decades honing is craft to perfection. Chuck Johnson is a journalist who has covered Montana state government and politics since 1970. Since 1992, he has been bureau chief of the Lee Newspapers State Bureau in Helena, writing for the Lee daily newspapers: the Billings Gazette, The Montana Standard (Butte), Helena Independent Record, The Missoulian, and the Ravalli Republic (Hamilton). Johnson, a Great Falls native raised in Helena, was exposed to politics early on when he was taken up to the Legislature one night to watch the debate on the raging issue of the day--whether stores should be allowed to give trading stamps to customers. He received a B.A. in journalism and an M.A. history from the University of Montana. Johnson spent a year studying politics and economics at Oxford University in England on a Rotary Foundation scholarship. He previously was chief of the Great Falls Tribune Capitol Bureau and worked for the Associated Press, Missoulian and Helena Independent Record. Chuck and his wife Pat reside in Helena.