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Indeed, regularized field models tend to provide a smoothed estimate (i.e., weighted time average) of the SV coefficient series towards high degrees.
It differs from regularized field models in the sense that the information contained into observations is complemented with a stochastic a priori information derived from temporal spectra of geomagnetic series, following Gillet et al. (2013).
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The fiber tract segmentation method does not need a regularized tensor field since the surface is automatically smoothed as it propagates.
Since the extension of the classical model for multiple phases is widely used (Nestler et al. 2005), the natural multiphase-field model, as well as the regularized multiphase-field models are poorly studied.
The regularized multiphase-field model was also presented by Ghosh et al.
CCMpred implements the approach taken in plmDCA and GREMLIN, which is based on maximizing the pseudo-likelihood of an L2-regularized Markov random field (see Supplementary Information for details).
Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression.
In this paper, we first present a regularized lattice Boltzmann model for temperature field or concentration field, and then validate the present model through numerical simulations of two-dimensional (2D) Rayleigh-Bénard convection in a square cavity.
The material delamination propagation rate as a function of the energy release rate and the stress-ratio is similarly obtained combining the aforementioned damage evolution law with a regularized expression for the stress field at the crack tip.
We propose, too, an approximation for the SV-matrix inversion, under the assumption of having a smoothly varying PSF field and enough regularization as to ensure its local regularized inverse also changes smoothly in the space.
These are described by a collection of regularized point forces, and the velocity field they induce is computed directly on a regular Cartesian grid via a smoothed dipole potential.
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