By Theorem 2.1 of Ansley and Kohn (1994), each of ( 3) and ( 4) has a unique solution, and the back-fitting algorithms for ( 5) and ( 6) can be applied in (3), and ( 7) and ( 8) can be applied in (4). This guarantees convergence to the unique solution given any initial value.Therefore, Algorithm 1 is equivalent to minimizing (3) and (4) iteratively.Note that minimizing (3) and (4) iteratively is a special case of Algorithm MBI (Chen et al., 2012) with two blocks. Therefore, following Theorem 3.1 of Chen et al. (2012), Algorithm 1 converges to a stationary point. This completes the proof.
The framing effect refers the tendency to be risk-averse when options are presented positively but be risk-seeking when the same options are presented negatively during decision-making. This effect has been found to be modulated by the serotonin transporter gene (SLC6A4) and the catechol-o-methyltransferase gene (COMT) polymorphisms, which are on the dopaminergic and serotonergic pathways and which are associated with affective processing. The current study aimed to identify new genetic variations of genes on dopaminergic and serotonergic pathways that may contribute to individual differences in the susceptibility to framing. Using genome-wide association data and the gene-based principal components regression method, we examined genetic variations of 26 genes on the pathways in 1317 Chinese Han participants. Consistent with previous studies, we found that the genetic variations of the SLC6A4 gene and the COMT gene were associated with the framing effect. More importantly, we demonstrated that the genetic variations of the aromatic-L-amino-acid decarboxylase (DDC) gene, which is involved in the synthesis of both dopamine and serotonin, contributed to individual differences in the susceptibility to framing. Our findings shed light on the understanding of the genetic basis of affective decision-making.
ere are a series of human or natural activities, including earthquakes, explosions, and rockbursts, which have caused a number of safety accidents in geotechnical engineering. is review paper summarized the theories and methods for dynamic stability analysis of rockmass. First, numerical simulation methods, including finite element method (FEM), discrete element method (DEM), finite difference method (FDM), boundary element method (BEM), discontinuous deformation analysis method (DDA), and numerical manifold method (NMM), are summarized. Second, the laboratory experiments, containing shaking table test, split-Hopkinson pressure bar test (SHPB), improved true-triaxial test, dynamic centrifugal model test, acoustic emission (AE) technique, and dynamic infrared monitoring, are considered. ird, the in situ tests including microseismic (MS) technique, velocity tomography, stress-strain monitoring, and electromagnetic radiation monitoring are considered. Finally, some comprehensive analysis methods based on statistical theories are also provided. It is pointed out that the study foundation for the dynamic stability of rockmass is weak to explain the mechanism. So, a set of general comprehensive theories integrating the different methods, including theoretical analysis, numerical methods, laboratory experiments, and in situ tests, should be completely established. is is the most effective way for further investigation.
Gravelly beach ridges, which are formed solely by swash processes, may accurately reflect past wave conditions. The thickness (or height) of a gravelly beach ridge approximately equals the height of wave inundation, which is the sum of the surge and wave run‐up. Their ancient counterparts, if well‐preserved and identified, can be used to estimate palaeowave conditions, which can later be converted to palaeowind intensities based on wind–wave relationships. A technique is described for estimating the palaeowind speed in this paper, which is referred to as the gravelly beach‐ridge thickness technique. By comparing these estimates with instrumental wind records obtained at a modern lake, Qinghai Lake in north‐western China, the beach‐ridge thickness technique is shown to be useful for estimating the average wind speed (Vavg). When applying this method to ancient fetch‐limited basins, five parameters are necessary: (i) the thickness of the isolated gravelly beach ridge; (ii) the average depth of the water body; (iii) the palaeofetch; (iv) the angle between the palaeowind direction and the normal to the shoreline; and (v) the particle size. This technique was applied to an ancient example in the Eocene Dongying Depression, located in eastern China. The results indicate that the average wind speed of the northern wind ranged between 2·27 m sec−1 and 8·36 m sec−1 from 45·0 Ma to 42·0 Ma, and displayed a generally decreasing trend that included early strengthening followed by weakening and later strengthening during this period. The beach‐ridge thickness technique provides a new perspective on delineating palaeowind conditions and can be applied to ancient fetch‐limited basins with gravelly beach ridges worldwide. Generally, if a water body is sufficiently large (fetch exceeding 40 km), deep (average depth exceeding 10 m) and waves (or winds) are determined to approach the shoreline with high angles (angle of incidence <35°), then the calculation errors will be small to negligible.
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