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In the grey prediction, the nonlinear Grey Bernoulli model NGBM (1, 1) is an important type. The NGBM (1, 1) has good adaptability to data fitting and then small prediction errors, and thus has been applied widely. However, if we improve the modelling method, the prediction precision shall be improved to some extent. The important factors of prediction error are the approximation of background value and the approximation of power exponent. Therefore, the paper tries to combine the optimisation of background value with the optimisation of the power exponent of NGBM (1, 1) model and then improves the model from parameter estimation. The paper gives three methods for the following three cases respectively: the background value in the form of exponential curve, the background value in the form of the polynomial curve and the background value in the form of interpolation function, to combine background value optimisation with power exponent optimisation for parameter optimisation. The final section of the paper builds the NGBM (1, 1) models of China's GDP and energy consumption with three improvement methods. The simulation and prediction results show the three improvement methods all have high precision. The methods given offer good approaches for the in-depth study on nonlinear grey Bernoulli model, enrich the method system of grey modelling and can be applied to the studies on other grey models to promote the study and wide application of the grey model. [ABSTRACT FROM AUTHOR]

Background: Depression and anxiety disorders are common conditions among general hospital inpatients, but are believed to be under-recognized in China. Methods: A short, practical questionnaire termed the happiness index scale (HIS) was developed for screening co-morbid mental disorders in non-psychiatric clinical settings. The HIS was completed by 1,005 non-psychiatric inpatients in a general hospital in China. The reliability and validity of the HIS were then assessed. Results: The HIS comprised eight items which loaded onto four dimensions: (a) sleep quality; (b) suicidal tendency; (c) depression; and (d) anxiety. These dimensions explained 84.2% of the total variance. Confirmatory factor analysis showed reasonably good fit of the four-factor model (χ2/df = 1.27, p < 0.001, goodness-of-fit index = 0.95, comparative fit index = 0.99, root-mean-square error of approximation = 0.008). The correlation coefficients between each item and the corresponding factor were all > 0.5. Cronbach's α of the entire scale was 0.83, indicating good internal consistency. The area under the ROC curve was 0.95 compared with the original 31-item scale. Using the optimal cut-off score of HIS (mild happiness), the sensitivity and specificity were 0.933 and 0.882, respectively. Conclusions: The new HIS scale is a practical screening tool composed of eight items covering the four most common and important dimensions of mental disorder. The HIS exhibited good reliability and specificity. The HIS is potentially suitable for large-scale screening in busy non-psychiatric clinical settings in China. Further verification using larger samples is warranted. [ABSTRACT FROM AUTHOR]

Background: The psychometric properties of the simplified Chinese version of the Patient-Reported Outcomes version of the Common Terminology Criteria for Adverse Events (PRO-CTCAE) have not been assessed. Therefore, we aimed to assess its validity, reliability, and responsiveness.Patients and Methods: A Chinese version of the PRO-CTCAE and the European Organization for Research and Treatment of Cancer Core Quality of Life Questionnaire (QLQ-C30) were distributed to 1580 patients from four cancer hospitals in China. Validity assessments included construct validity, measured by Pearson's correlations and confirmatory factor analysis (CFA), and known-groups validity, measured by t-tests. The assessment of reliability included internal consistency, measured by Cronbach's ɑ, and test-retest reliability, measured by the intraclass correlation (ICC). Responsiveness was assessed by standardized response means (SRMs).Results: Data from 1555 patients who completed the instruments were analyzed. The correlations were high between PRO-CTCAE items and parallel QLQ-C30 symptom scales (r > 0.60, p < 0.001), except for fatigue (severity: r = 0.49). Moreover, CFA showed the PRO-CTCAE structure was a good fit with the data (Root Mean Square Error of Approximation = 0.046). Known-groups validity was also confirmed. Cronbach's ɑ of all item clusters were greater than 0.9 and the median test-retest reliability coefficients of the 38 items were 0.85 (range = 0.71-0.91). In addition, the SRMs of PRO-CTCAE items were greater than 0.8, indicating strong responsiveness.Conclusion: The simplified Chinese version of the PRO-CTCAE showed good reliability, validity, and responsiveness. [ABSTRACT FROM AUTHOR]

Local volatility model is widely used in the fields of risk management, options pricing, etc. The model can not only describe the "smile" and the term structure of volatility, but can also ensure the completeness of the market. The core goal of local volatility research is to calculate the implied volatility. In this paper, the implied volatility surfaces arc built with both parametric and non-parametric methods to obtain smoother volatility surfaces. Parametric method can ensure the absence of arbitrage. Meanwhile, a closed form of solving the local volatility model with non-parametric method is proposed, which can eliminate the approximation error. In addition, the pricing of Shanghai 50ETF option in China based on the local volatility model is studied by comparing effects of the models from aspects of in-the-sample, out-of-the sample and hedging pricing errors. The empirical results show that the non-parametric method is better than the parametric method for errors in-the-samplc; the parametric method has better results for out-of-sample and hedging effects. Particularly, both the options pricing and hedging effects of the implied volatility modeling methods are better than nn-modeled method in the aspects that the pricing errors can be decreased by more than half and the mean square error can be reduced by 1~2 orders of magnitude. [ABSTRACT FROM AUTHOR]

The first-order grey model is appropriate for monotonic time series, while the grey Verhulst model is appropriate for periodic time series. The grey Verhulst model is widely used for predicting practical nonlinear time series that contain fluctuations. Despite the successful application of the grey models in practice, researchers show that grey models still have room for improvement. Moreover, recent research shows that grey models are sensitive to initial conditions. In many practical problems, the value of initial conditions is not accurate and suffers from noise or approximation errors, resulting in inaccurate prediction. To address these difficulties, an improved grey Verhulst method using particle swarm optimization is proposed in this paper. The proposed model consists of two stages. In the first stage, a second-order polynomial with unknown coefficients is used to approximate the 1- AGO. In the second stage, the initial element of the time series is modified to improve the accuracy of the prediction. The particle swarm optimization method is used to search for the unknown coefficients. It is found that PSO is a suitable optimization method for the proposed method because it is stable and generates a sequence of points that converges to a globally optimal solution. To demonstrate the efficiency and stability of the proposed method, it was applied to five practical problems, namely, gas production in China, the number of hazardous chemical accidents, CO2 emissions in Russia, the number of domestic tourists in China, and traffic flows in Canada. Numerical results show that the method is more accurate and robust than existing methods. • The proposed method needs only four elements for predicting the future elements of time series. • The paper proposes a second order polynomial for approximating 1-AGO. • The method makes more accurate prediction than existed methods. • The proposed method is applied on various practical forecasting problems successfully. [ABSTRACT FROM AUTHOR]

Large deformations and displacements of rock blocks may occur under high stresses around deep underground rock engineering works such as deep mines. The original discontinuous deformation analysis (DDA) developed by Shi and Goodman was dedicated to analyze large deformations, rotations and displacements of rock blocks by accumulating small components of these quantities in a time-marching scheme. The small rotation angle approximation adopted in the original DDA may induce block expansion with rotation (rotation error). Based on solid mechanics, the free expansion is caused by (1) the error due to the approximation of the real behavior using a displacement function, and (2) the theory used to describe the geometrical relationship between movement (displacement and rotation) and deformation. The original DDA uses the geometrical relationship that is based on small strain theory. Small strain theory assumes a linear relationship between displacement and strain that does not consider the high order components and the decomposition of rotation and displacement. The finite deformation theory, however, decomposes the displacement and rotation and gives a nonlinear relationship between displacement and strain. Therefore, the finite deformation theory can solve the block rotation problem at a higher accuracy. The DDA method is extended by coupling with the finite deformation theory. The implementation of this method is first verified by three illustration examples, and later employed to modelling a work face excavation of a coal mine in China. The stress field and displacement field are investigated. The results show that the occurrence of the first fracture of the key stratum increases the displacement and the stress. The second fracture of the key stratum partially releases the stress. The periodic weighting phenomenon is also reflected in this modelling. [ABSTRACT FROM AUTHOR]