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The second dimension we used to classify instruments is domain.
In the sensory dimension, we used a numerical rating scale [ 7] to measure pain intensity.
However, to avoid contaminating measures of categorization along one dimension with effects actually attributable to categorization along the other dimension, we used a more conservative analysis strategy (see Stangor et al. 1992 for a similar approach).
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In the spatial dimension, we use Gaussian Markov random fields (GMRF) priors on activation characteristics parameters (location and magnitude) that embody our prior knowledge that evoked responses are spatially contiguous and locally homogeneous.
(15) On the other hand, to design the gain matrix K, for any matrix X of appropriate dimension, we use the following zero equality to avoid the nonlinear matrix inequality begin{aligned} begin{aligned}[b] 0=&2 bigl(e^{T} k)+Delta e^{T}(k) bigr)X bigl[Ae k-sigma -KCe k)+W_{0}f(k)+W_{1}f bigl[Ae k-sigma -KCe k-Kpsi(k)-e(k+1) bigl[Ae k-sigma -KCe ktorname{Sym}{Upsilon_{2} Upsilon_{3}}xi(k).
To assess positions on the economic dimension, we use the public services versus taxes scale, in which low values mean that the party 'promotes cutting public services to cut taxes' and high values that it 'promotes raising taxes to increase public services'.
In order to to visualize the 66-dimensional space in two- and/or three-dimensions, we used the Isomap algorithm for geodesic dimensionality reduction [27].
For the space and habitat dimensions, we used classification RFs of the strains into six continents (Africa, Asia, Australia, Europe, North America, and South America) and two habitats (clinical or environmental), respectively.
Because the cell membrane is a plane-like structure in three dimensions, we used anisotropic diffusion (Weickert, 1998) to enhance local consistency in structure and suppress noise.
To test whether these newly defined components still support the distinction between two phonological dimensions, we used confirmatory factor analysis to compare two models.
Because of the time-consuming nature of performing such investigation across a range of different parameters in three dimensions, we used a very small test domain.
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