The Analysis of Pixel Intensity (Myocardial Signal Density) Data: The Quantification of Myocardial Perfusion by Imaging Methods.

This paper described a number of important issues in the analysis of pixel intensity data, as well as approaches for dealing with these. We particularly emphasized the issue of clustering, which may be ubiquitous in studies of pixel intensity data. Clustering can take many forms, e.g., measurements of different sections of a heart or repeated measurements of the same research participant. Clustering typically has the effect of increasing variance estimates. When one fails to account for clustering, variance estimates may be unrealistically small, resulting in spurious significance. We illustrated several possible approaches to account for clustering, including adjusting standard errors for design effects and modeling the covariance structure within clusters using mixed models. These methods offer great flexibility for dealing with a wide variety of research designs and include the capability for adjusting for covariates and different case weights. Similar methods can be used to account for clustering in both superiority and equivalence analyses. In situations where clustering affects the true cluster mean, µ, but not the difference between measures of the mean, it is possible that clustering will have a much greater impact on superiority analyses than on equivalence analyses

Scaling Baroclinic Eddy Fluxes: Vortices and Energy Balance

The eddy heat flux generated by the statistically equilibrated baroclinic instability of a uniform, horizontal temperature gradient is studied using a two-mode f-plane quasigeostrophic model. An overview of the dependence of the eddy diffusivity D on the bottom friction κ, the deformation radius λ, the vertical variation of the large-scale flow U, and the domain size L is provided by numerical simulations at 70 different values of the two nondimensional control parameters κλ/U and L/λ. Strong, axisymmetric, well-separated baroclinic vortices dominate both the barotropic vorticity and the temperature fields. The core radius of a single vortex is significantly larger than λ but smaller than the eddy mixing length ℓ_mix. On the other hand, the typical vortex separation is comparable to ℓ_mix. Anticyclonic vortices are hot, and cyclonic vortices are cold. The motion of a single vortex is due to barotropic advection by other distant vortices, and the eddy heat flux is due to the systematic migration of hot anticyclones northward and cold cyclones southward. These features can be explained by scaling arguments and an analysis of the statistically steady energy balance. These arguments result in a relation between D and ℓ_mix. Earlier scaling theories based on coupled Kolmogorovian cascades do not account for these coherent structures and are shown to be unreliable. All of the major properties of this dilute vortex gas are exponentially sensitive to the strength of the bottom drag. As the bottom drag decreases, both the vortex cores and the vortex separation become larger. Provided that ℓ_mix remains significantly smaller than the domain size, then local mixing length arguments are applicable, and our main empirical result is ℓ_mix ≈ 4λ exp(0.3U/κλ)

Calculation of the Response of Angle Beam EMATs to Flaws in the Far Field

In the design of a system for NDE, it is necessary to quantify the relationship of flaw size and orientation to transducer signal levels. This is particularly true for automated systems, in which the transducer coordinates cannot be adjusted by an operator to maximize the signal. This paper presents the result of a model calculation for the case of angle beam inspection using EMATs, which appear likely to find extensive use in such systems. Included in the model are calculations of the elastic wave radiation pattern in three dimensions for plates, calculations of the elastic wave scattering from cracks using existent approximate models, and calculation of the electrical response to the scattered wave. Transducer apodization is used to reduce spurious side lobe signals and blind areas where flaws are weakly detected. Emphasis is placed on the case of SH wave generation

Half-Space Radiation by EMAT\u27s

A Green\u27s function calculation of the far field radiation patterns of EMAT\u27s is presented. The approach is based upon (a) closed form expressions for the eddy current and static magnetic field distributions, established by the EMAT, which react to produce the driving Lorentz forces and (b) a Green\u27s function derived from the steepest descent approximation to the far field response of an arbitary surface point force on a half space. Numerical results are presented, illustrating the radiation patterns of the three common EMAT designs. Included are vertically polarized shear waves as radiated by both meander coil and periodic magnet EMAT\u27s and horizontally polarized shear waves as radiated by the latter