Trademark Surveys: Development of Computer-Based Survey Methods, 4 J. Marshall Rev. Intell. Prop. L. 91 (2004)

Courts have continually utilized surveys to show evidence of secondary meaning, genericness, dilution, and functionality in trademark litigation. In conducting a trademark survey, an expert must consider various factors that may affect the admissibility of the survey in court, including assuring the correct universe of respondents are questioned, implementing controls, and verifying the results. In light of these considerations, as well as the ever-changing environment of consumer shopping, the manner and mode of survey that a court accepts as appropriate must adapt to these conditions. The use and acceptance of online and computer-based surveys is not currently well received by the courts, but this should change due to the many advantages that on-line surveys offer to trademark litigants. These advantages, including more efficient, accurate and trustworthy results that far outweigh any perceived disadvantages a court may put forth in finding such surveys inadmissible

Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks

I study the Bona-Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks. For focusing singularities, I extend the original analysis of Bona et. al and show that both marginal and strong singularity avoidance can be obtained for certain types of behavior of the slicing condition as the lapse approaches zero. For the case of gauge shocks, I re-derive a condition found previously that eliminates them. Unfortunately, such a condition limits considerably the type of slicings allowed. However, useful slicing conditions can still be found if one asks for this condition to be satisfied only approximately. Such less restrictive conditions include a particular member of the 1+log family, which in the past has been found empirically to be extremely robust for both Brill wave and black hole simulations.Comment: 11 pages, revtex4. Change in acknowledgment

Recognizing normal reproductive biology: A comparative analysis of variability in menstrual cycle biomarkers in German and Bolivian women

The idealized “normal” menstrual cycle typically comprises a coordinated ebb and flow of hormones over a 28-day span with ovulation invariably shown at the midpoint. It's a pretty picture—but rare. Systematic studies have debunked the myth that cycles occur regularly about every 28 days. However, assumptions persist regarding the extent and normalcy of variation in other cycle biomarkers. The processes of judging which phenotypic variants are “normal” is context dependent. In everyday life, normal is that which is most commonly seen. In biomedicine normal is often defined as an arbitrarily bounded portion of the phenotype's distribution about its statistical mean. Standards thus defined in one population are problematic when applied to other populations; population specific standards may also be suspect. Rather, recognizing normal female reproductive biology in diverse human populations requires specific knowledge of proximate mechanisms and functional context. Such efforts should be grounded in an empirical assessment of phenotypic variability. We tested hypotheses regarding cycle biomarker variability in women from a wealthy industrialized population (Germany) and a resource-limited rural agropastoral population (Bolivia). Ovulatory cycles in both samples displayed marked but nonetheless comparable variability in all cycle biomarkers and similar means/medians for cycle and phase lengths. Notably, cycle and phase lengths are poor predictors of mid-luteal progesterone concentrations. These patterns suggest that global and local statistical criteria for “normal” cycles would be difficult to define. A more productive approach involves elucidating the causes of natural variation in ovarian cycling and its consequences for reproductive success and women's health

3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.Comment: 21 pages. To appear in PR

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.