Therefore, to study the Riemannian 3-manifold Σ τ we have to use the geodesic exponential map as the main tool [39] [40], even if it is not clear its relationship with the differential structure of Dif f Σ τ .
Sample text:```Following past work, we show that such basis models can be learned from 2D annotations using techniques adapted from nonrigid structure from motion (SFM) [20, 19].```
Sample intent: method
Sample text:```In the first pass, we display the diffuse lobe of the BRDF through spherical harmonic environment map rendering [Ramamoorthi and Hanrahan 2001].```
Sample intent: background



Sample text:```This section contains a generalisation of the basic results on multifractal products of stochastic processes developed in Kahane (1985), Kahane (1987) and Mannersalo et al (2002).```
Sample intent: method



Sample text:```Because previous studies indicated that hexapeptides bind the junction core (29, 32), we tested two junctions, one with an AT-rich core and the other with a GC-rich core (Fig.```
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:```While this method is known to be generally reliable, there are some questions about the representativeness of the data used [25].```
Sample intent: background
Sample text:```For seeking the optimal value of Wh of the sub-problems which corresponds to the h-th level, we can solve the problem by the smoothing proximal gradient (SPG) method [6] fortunately.```
Sample intent: background



Sample text:```In the first pass, we display the diffuse lobe of the BRDF through spherical harmonic environment map rendering [Ramamoorthi and Hanrahan 2001].```
Sample intent: background



Sample text:```On the other hand, there are research works on the design of graph-based routing algorithms [3], [16], [17], [18], [19], [20], [21], [22], [23] to deal with the void problem.```
Sample intent: method



Sample text:```Following past work, we show that such basis models can be learned from 2D annotations using techniques adapted from nonrigid structure from motion (SFM) [20, 19].```
Sample intent: method



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:```Our results further confirm previous findings on the differential regulatory mechanisms for Hoxa3 and Hoxb3 expression in r5 and r6 by kreisler (Manzanares et al., 1997, 1999a,b, 2001).```
Sample intent: result



Sample text:```In-between methods can be subdivided into linear approximations [12,24] and quadratic interpolation methods [22,23,25–27] based on the degree of the polynomial approximation employed.```
Sample intent: method



Sample text:```A large part of Shannon’s seminal work [16] is devoted to both theoretical and practical aspects of products, and his invocation of the pastry dough mixing analogy [16, p.```
Sample intent: method



Sample text:```This section contains a generalisation of the basic results on multifractal products of stochastic processes developed in Kahane (1985), Kahane (1987) and Mannersalo et al (2002).```
Sample intent: method



Sample text:```Because previous studies indicated that hexapeptides bind the junction core (29, 32), we tested two junctions, one with an AT-rich core and the other with a GC-rich core (Fig.```
Sample intent: result