We discretise the gradient descent equation (6) on a regular grid using finite differences and solve it efficiently using the recently proposed fast explicit diffusion (FED) [6].
Sample text:```The discretization is implemented within the DUNE numerics environment [3,4], centered around dune-gdt [23]: the dune-stuff [24] module provides classes for vectors, matrices and linear solvers (for instance the bicgstab.amg.ilu0 solver used in these experiments), dune-gdt provides the discretization building blocks (such as discrete function spaces, operators, products and functionals), and dune-hdd1 provides parametric discretizations compatible with pyMOR [22].```
Sample intent: background
Sample text:```The discretization is implemented within the DUNE numerics environment [3,4], centered around dune-gdt [23]: the dune-stuff [24] module provides classes for vectors, matrices and linear solvers (for instance the bicgstab.amg.ilu0 solver used in these experiments), dune-gdt provides the discretization building blocks (such as discrete function spaces, operators, products and functionals), and dune-hdd1 provides parametric discretizations compatible with pyMOR [22].```
Sample intent: background



Sample text:```5 concentrations were computed for each participant using a hierarchical spatiotemporal model fit with a pragmatic estimation procedure described elsewhere [30,31].```
Sample intent: background



Sample text:```In this study, we generalized previous results regarding the quasi-Gaussian shape and the scalar property using the SBF model [13,21,52].```
Sample intent: result



Sample text:```This transition was introduced first by Prince and Elder (2007) and it simplifies formulas for parameter update on Mstep of EM algorithm.```
Sample intent: background



Sample text:```The present observations support and extend earlier contentions that Parkinson patients prefer to adopt a closedloop control mode, adjusting their movements continuously on the basis of available visual information (Flowers 1976).```
Sample intent: result
Sample text:```The merging is based on the increase in the weighted-bycounts entropy [1] and is stopped by a threshold indicating the minimum number of training samples required to estimate a weight distribution.```
Sample intent: method



Sample text:```Over the last few years, many different local interest point detectors (like Harris3D [16], Cuboid [6], Hessian [35] or Dense sampling [33]) and many spatio-temporal descriptors (like HOG [17], HOG3D [14], HOF [17], Cuboid [6] or ESURF [35]) have been proposed.```
Sample intent: method



Sample text:```…methods rely on some additional and often heuristic step to generate an initial solution, such as adversarially-trained neural networks [Conneau et al., 2018, Zhang et al., 2017a,b], robust self-learning [Artetxe et al., 2018b] or
5This can be easily verified by noting that the…```
Sample intent: background



Sample text:```This seems to be the main drawback of the current implementation in comparison to the method of Black Jepson (“refined” in Table 1).```
Sample intent: result



Sample text:```This transition was introduced first by Prince and Elder (2007) and it simplifies formulas for parameter update on Mstep of EM algorithm.```
Sample intent: background



Sample text:```5 concentrations were computed for each participant using a hierarchical spatiotemporal model fit with a pragmatic estimation procedure described elsewhere [30,31].```
Sample intent: background



Sample text:```These are in keeping with earlier studies on the steadystate response (2, 5, 8), step-function response, (3, 5, 6, 14) and sinusoidal response ( 14) of the various vascular beds.```
Sample intent: result



Sample text:```Discrepancies analogous to those between our results and those of simulations have, indeed, recently been observed in the case of the binary perceptron [18], the pspin interaction spin glass [19], and in the case of fluctuating manifolds in random media [20], where dynamically frozen phases were observed in regions of parameter space in which static approaches yielded ergodic phases.```
Sample intent: result



Sample text:```In this study, we generalized previous results regarding the quasi-Gaussian shape and the scalar property using the SBF model [13,21,52].```
Sample intent: result



Sample text:```The discretization is implemented within the DUNE numerics environment [3,4], centered around dune-gdt [23]: the dune-stuff [24] module provides classes for vectors, matrices and linear solvers (for instance the bicgstab.amg.ilu0 solver used in these experiments), dune-gdt provides the discretization building blocks (such as discrete function spaces, operators, products and functionals), and dune-hdd1 provides parametric discretizations compatible with pyMOR [22].```
Sample intent: background