These significant refinements enable one to find optimal product and sum representations by minimizing the nesting depth (Schneider, 2005a, 2008, 2010c), by minimizing the number of sums arising within the summand (Schneider, 2004, 2015), or minimizing the degree of the sums and products arising in…
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:```The items are internally consistent and reproducible and the questionnaire may therefore be considered to have at least as favourable levels of reliability as clinical scores used to assess outcomes (Koran 1975).```
Sample intent: result



Sample text:```…between output and input, CNF achieves almost 10% relative improvement over CRF. CNF also outperforms other methods including SVMpro (Hua and Sun, 2001), SVMpsi (Kim and Park, 2003), YASSPP (Karypis, 2006), PSIPRED (Jones, 1999), SPINE (Dor and Zhou, 2007) and TreeCRFpsi (Dietterich et al., 2004).```
Sample intent: background



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-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 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:```The items are internally consistent and reproducible and the questionnaire may therefore be considered to have at least as favourable levels of reliability as clinical scores used to assess outcomes (Koran 1975).```
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:```The results for veridical recall replicated previous results in the literature (Bal-
lardini et al., 2008; McDermott & Watson, 2001), with the average recall of studied words increas-
ing monotonically as SOA increased.```
Sample intent: result



Sample text:```…between output and input, CNF achieves almost 10% relative improvement over CRF. CNF also outperforms other methods including SVMpro (Hua and Sun, 2001), SVMpsi (Kim and Park, 2003), YASSPP (Karypis, 2006), PSIPRED (Jones, 1999), SPINE (Dor and Zhou, 2007) and TreeCRFpsi (Dietterich et al., 2004).```
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:```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.```
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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).```
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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:```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