Stochastic quantization of the linearized gravitational field

Stochastic field equations for linearized gravity are presented. The theory is compared with the usual quantum field theory and questions of Lorentz covariance are discussed. The classical radiation approximation is also presented.Comment: 14 page

A Correlation Between the Higgs Mass and Dark Matter

Depending on the value of the Higgs mass, the Standard Model acquires an unstable region at large Higgs field values due to RG running of couplings, which we evaluate at 2-loop order. For currently favored values of the Higgs mass, this renders the electroweak vacuum only meta-stable with a long lifetime. We argue on statistical grounds that the Higgs field would be highly unlikely to begin in the small field meta-stable region in the early universe, and thus some new physics should enter in the energy range of order, or lower than, the instability scale to remove the large field unstable region. We assume that Peccei-Quinn (PQ) dynamics enters to solve the strong CP problem and, for a PQ-scale in this energy range, may also remove the unstable region. We allow the PQ-scale to scan and argue, again on statistical grounds, that its value in our universe should be of order the instability scale, rather than (significantly) lower. Since the Higgs mass determines the instability scale, which is argued to set the PQ-scale, and since the PQ-scale determines the axion properties, including its dark matter abundance, we are led to a correlation between the Higgs mass and the abundance of dark matter. We find the correlation to be in good agreement with current data.Comment: 10 pages in double column format, 3 figures. v2: minor changes and added references. v3: some more clarifications; updated towards published versio

Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper bound is found by minimising the quadratic form for the operator over a test space consisting of separable functions. These bounds can be used to show that the negative part of the groundstate is small.Comment: 27 pages, 4 diagrams, 2 table

A Conversation with Leo Goodman

Leo A. Goodman was born on August 7, 1928 in New York City. He received his A.B. degree, summa cum laude, in 1948 from Syracuse University, majoring in mathematics and sociology. He went on to pursue graduate studies in mathematics, with an emphasis on mathematical statistics, in the Mathematics Department at Princeton University, and in 1950 he was awarded the M.A. and Ph.D. degrees. His statistics professors at Princeton were the late Sam Wilks and John Tukey. Goodman then began his academic career as a statistician, and also as a statistician bridging sociology and statistics, with an appointment in 1950 as assistant professor in the Statistics Department and the Sociology Department at the University of Chicago, where he remained, except for various leaves, until 1987. He was promoted to associate professor in 1953, and to professor in 1955. Goodman was at Cambridge University in 1953--1954 and 1959--1960 as visiting professor at Clare College and in the Statistical Laboratory. And he spent 1960--1961 as a visiting professor of mathematical statistics and sociology at Columbia University. He was also a research associate in the University of Chicago Population Research Center from 1967 to 1987. In 1970 he was appointed the Charles L. Hutchinson Distinguished Service Professor at the University of Chicago, a title that he held until 1987. He spent 1984--1985 at the Center for Advanced Study in the Behavioral Sciences in Stanford. In 1987 he was appointed the Class of 1938 Professor at the University of California, Berkeley, in the Sociology Department and the Statistics Department. Goodman's numerous honors include honorary D.Sc. degrees from the University of Michigan and Syracuse University, and membership in the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.Comment: Published in at http://dx.doi.org/10.1214/08-STS276 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Self-employment in Britain: when, who and why?

This work explores self-employment in Britain across recent years with a particular focus on when individuals became self-employed, who is more or less likely to enter self-employment and why individuals choose to enter self-employment. It complements previous microeconomic studies that focus on transitions into and out of selfemployment and presents new evidence on the returns to selfemployment and how these compare to the returns to paid employment. Lifetime employment history data from the British Household Panel Survey suggest that the large increase in self-employment in the 1980’s was due to increases in the inflow rate, while an increase in the outflow rate in the early 1990’s has stopped this trend. Panel data from the same source indicate that gender, parents occupation, assets and considering the work itself, the use of initiative or hours of work to be the most important aspect of a job emerge as key determinants of self-employment entry. Gender, age, occupation and elapsed duration in self-employment emerge as important determinants of selfemployment exit. Our analysis reveals that, all else equal, the selfemployed report higher levels of job satisfaction with pay and with the work itself than employees, but lower levels of satisfaction with job security

A study of interest survey results and elective technology education courses at Oshkosh West High School

Includes bibliographical references