In blended-neighbor interpolation of scattered data, a tensor field represents a model of spatial correlation that is both anisotropic and spatially varying. In effect, this tensor field defines a non-Euclidean metric, a measure of distance that varies with direction and location. The tensors may be derived from secondary data, such as images. Alternatively, when the primary data to be interpol...

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchi...

BACKGROUND AND PURPOSE Tract-based analysis can be used to investigate required tracts extracted from other fiber tracts. However, the fractional anisotropy (FA) threshold influences tractography analysis. The current study evaluated the influence of the FA threshold in measuring diffusion tensor parameters for tract-based analysis of the uncinate fasciculus in subjects with Alzheimer disease (...

The quantum fluctuations of the stress tensor of a quantum field are discussed , as are the resulting spacetime metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the spacetime geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and ...

We have used solid-state 17O NMR experiments to determine the 17O quadrupole coupling (QC) tensor and chemical shift (CS) tensor for the carbonyl oxygen in p-nitro-[1-(17)O]benzaldehyde. Analyses of solid-state 17O NMR spectra obtained at 11.75 and 21.15 T under both magic-angle spinning (MAS) and stationary conditions yield the magnitude and relative orientation of these two tensors: CQ = 10.7...