Suppose A1, . . . , AN are rotation matrices on n-dimensional Euclidean space R, i.e., Aj ∈ SO(n). We want to consider some element of SO(n) that represents an “average” of these elements Aj . There are a number of possible ways to define the notion of an average in this context. One approach has been to write Aj = ej with Zj a real, skew-symmetric n × n matrix (i.e., Zj ∈ skew(n)), and define ...

We employ the recently developed multiphoton $R$-matrix method for molecular above-threshold photoionization to obtain second-order ionization amplitudes that govern interference in RABITT experiments. This allows us extract time delays are better agreement with nonperturbative time-dependent simulations of this process than typically used combination first-order (Wigner) and asymptotic correct...

We develop a family of techniques to align word embeddings which are derived from different source datasets or created using mechanisms (e.g., GloVe word2vec). Our methods simple and have closed form optimally rotate, translate, scale minimize root mean squared errors maximize the average cosine similarity between two same vocabulary into dimensional space. extend approaches known as absolute o...

Long time simulations of the dispersion prolate spheroids in a turbulent channel are performed to study effect averaging procedure on particle statistics. The flow at Reτ=180 is directly simulated (DNS) and 300000 ellipsoids, modelled as point-particles tracked produce After long time, an initially uniform distribution reaches steady state which almost all particles segregated viscous sublayer....

Abstract. Chemical shift tensors in 13C solid-state NMR provide valuable localized information on the chemical bonding environment organic matter, and deviations from isotropic static-limit powder line shapes sensitively encode dynamic-averaging or orientation effects. Studies natural abundance require magic-angle spinning (MAS), where analysis must thus focus sidebands. We propose an alternati...

Diffusion tensor magnetic resonance imaging (DT-MRI) is a non-invasive imaging method for assessing the characteristics and organization of tissue microstructure. The diffusion tensor provides information about the magnitude, anisotropy, and orientation of water diffusion in biological tissues. In brain white matter, the direction of greatest diffusivity is typically assumed to be parallel to t...

Among the most extraordinary phenomena in nuclear magnetic resonance (NMR) is the spin echo [1]. Although the original spin echo and its analogs in other areas of spectroscopy [2] result from reversing the dephasing due to independent, "inhomogeneous" interactions, a true many-body spin echo resulting from a reversal of the (seemingly irreversible) decay due to "homogeneous" spin-spin couplings...