This is followed by a proof of asymptotic stability in probability of a robust invariant set, which is novel in Stochastic MPC and shows the connection to tube based Robust MPC approaches like [3], [27].
Sample text:```NP3L [10] is consistently outperformed by our methods, while for UPnP [8] our NPnLupC outperforms it in the noisy cases.```
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:```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).```
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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:```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:```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:```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:```A rook pivoting scheme as in [3] and [11] can be implemented for tridiagonal matrices, but a full rook scheme for general banded matrices would probably lead to a ”chasing” scheme as in [5] or [15] .```
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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.```
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Sample text:```Indeed, strong correlations between inhibitions at different ISIs have been reported previously (Roshan et al. 2003) which would be consistent with this idea.```
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:```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:```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:```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 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