Some facts about functionals of location and scatter

Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for $d\geq 2$, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they must be identically 0. Results are stated on existence and differentiability of location and scatter functionals, defined on a weakly dense, weakly open set of laws, via elliptically symmetric t distributions on ${\Bbb{R}}^d$, following up on work of Kent, Tyler, and D\"{u}mbgen.Comment: Published at http://dx.doi.org/10.1214/074921706000000860 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Refrigerated cutting tools improve machining of superalloys

Freon-12 applied to tool cutting edge evaporates quickly, leaves no residue, and permits higher cutting rate than with conventional coolants. This technique increases cutting rate on Rene-41 threefold and improves finish of machined surface

How Well Does the U.S. Government Do Cost-Benefit Analysis?

To make prudent recommendations for improving the use of cost-benefit analysis in policy settings, some measures of how well it is actually done are essential. This paper develops new insights on the potential usefulness of government cost-benefit analysis by examining how it is actually performed in the U.S. We assess the quality of a particularly rich sample of cost-benefit analyses of federal regulations. The data set we use for assessing the quality of regulatory analysis is the largest assembled to date for this purpose. Theseventy-four analyses we examine span the Reagan administration, the first Bush and the Clinton administration. The paper is the first to assess systematically how government cost-benefit analysis has changed over time. There are three key findings. First, a significant percentage of the analyses in all three administrations do not provide some very basic economic information, such as information on net benefits and policy alternatives. For example, over 70% of the analyses in the sample failed to provide any quantitative information on net benefits. Second, there is no clear trend in the quality of cost-benefit analysis across administrations. Third, there is a great deal of variation in the quality of individual cost-benefit analyses.

Deaths Exceed Births in Most of Europe, But Not in the United States

In this brief, authors Kenneth Johnson, Layton Fields, and Dudley Poston, Jr. present important new findings about the diminishing number of births compared to deaths in Europe and the United States from their recent article in Population and Development Review. Their research focuses on the prevalence and dynamics of natural decrease in subareas of Europe and the United States in the first decade of the twenty-first century using counties (United States) or county-equivalents (Europe). The authors report that 58 percent of the 1,391 counties of Europe had more deaths than births during that period compared to just 28 percent of the 3,137 U.S. counties. Natural decrease is more widespread in Europe because its population is older, fertility rates are lower, and there are fewer women of child-bearing age. Natural decrease is a major policy concern because it drains the demographic resilience from a region, diminishing its economic viability and competitiveness. The implications of the recent European immigrant surge for natural decrease are uncertain, but the authors’ analysis suggests that natural decrease is likely to remain widespread in Europe for the foreseeable future

On the statistical interpretation of optical rogue waves

Numerical simulations are used to discuss various aspects of "optical rogue wave" statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show that the unfiltered statistical distribution can still exhibit a long-tail, but the extreme-events in this case correspond to collisions between solitons of different frequencies. These results confirm the importance of collision dynamics in supercontinuum generation. We also show that the collision-induced events satisfy an extended hydrodynamic definition of "rogue wave" characteristics.Comment: Paper accepted for publication in the European Physical Journal ST, Special Topics. Discussion and Debate: Rogue Waves - towards a unifying concept? To appear 201

Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation

Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulsesComment: 22 pages, 6 figure