Unless otherwise stated, the matrix functions and FreÃÅchet derivatives were computed using the following algorithms:
 ‚Äî matrix exponential: scaling and squaring algorithms from [Al-Mohy and Higham 2009a], [Al-Mohy and Higham 2009b], ‚Äî matrix logarithm: inverse scaling and squaring algorithms from [Al-Mohy and Higham 2012], [Al-Mohy et al. 2013], ‚Äî real matrix powers: Schur‚ÄìPadeÃÅ algorithm [Higham and Lin 2013], ‚Äî general matrix functions: Schur‚ÄìParlett algorithm [Davies and Higham 2003].
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:```The sequence of intermediates in the hR photocycle and their interconversions have been the subject of numerous studies (Va´ró et al., 1995a, b; Hazemoto et al., 1984; Zimányi and Lanyi, 1989a, b; Zima´nyi et al., 1989; Spencer and Dewey, 1990; Ames et al., 1992; Dioumaev and Braiman, 1997a).```
Sample intent: method



Sample text:```Our results confi rm previous studies that reached the same conclusion (Boushey et al 1994; Vermeulen et al 2000; Till et al 2005; Marcucci et al 2005).```
Sample intent: result



Sample text:```phi is a meta-program interpreted in [112, 24] as a second-order predicate which applies to the predicate p.```
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Sample text:```Note that in their pioneering paper Calvet and Fisher (2002) proposed the simplified version of the construction of Mannersalo et al (2002).```
Sample intent: method



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:```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:```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 sequence of intermediates in the hR photocycle and their interconversions have been the subject of numerous studies (Va´ró et al., 1995a, b; Hazemoto et al., 1984; Zimányi and Lanyi, 1989a, b; Zima´nyi et al., 1989; Spencer and Dewey, 1990; Ames et al., 1992; Dioumaev and Braiman, 1997a).```
Sample intent: method



Sample text:```Note that in their pioneering paper Calvet and Fisher (2002) proposed the simplified version of the construction of Mannersalo et al (2002).```
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:```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:```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:```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:```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.```
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Sample text:```We screened for potential TF binding sites using STAMP [59], with the motifs’ position weight matrices (PWMs) retrieved from the TRANSFAC database [60].```
Sample intent: background