1 has been refined by results that count hyperbinary expansions with certain properties (see [1], [10], [14]), one purpose of this paper is to prove results that give the actual set of all hyperbinary expansions of n.
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 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:```have been proposed as potential alternatives to the Turing Test, specifically targeting its potential weaknesses and inadequacy [1].```
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 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:```13 indicates the comparison of the results of the mesh simplification method [2] after applying different mesh enhancement techniques.```
Sample intent: background
Sample text:```phi is a meta-program interpreted in [112, 24] as a second-order predicate which applies to the predicate p.```
Sample intent: method



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:```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:```have been proposed as potential alternatives to the Turing Test, specifically targeting its potential weaknesses and inadequacy [1].```
Sample intent: background



Sample text:```Following the experimental design proposed in Yannakakis and Hallam (2007c) and Yannakakis et al. (2008) for effectively capturing the level of entertainment, the test-bed game under investigation is played in variants.```
Sample intent: background



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:```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 adopted theoretical formulation expands on the USVA theory for two confocal beams in the case of lossless media [4,5], by also including absorption in the analytical model.```
Sample intent: method



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:```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