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An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic. In all four crashes, a persistent gap opens up in the Laplacian spectra when we go from a normal phase to a crash phase. In the crash phase, the persistent structure associated with the gap remains distinguishable up to a characteristic length scale ϵ * where the first non-zero Laplacian eigenvalue changes most rapidly. Before ϵ * , the distribution of components in the Fiedler vector is predominantly bi-modal, and this distribution becomes uni-modal after ϵ *. Our findings hint at the possibility of understanding market crashs in terms of both continuous and discontinuous changes. Beyond the graph Laplacian, we can also employ Hodge Laplacians of higher order for future research. [ABSTRACT FROM AUTHOR]

With increasing pressure to cut carbon emissions and develop sustainability plans, companies need carbon credits to offset emissions that cannot be eliminated from their operations, new global carbon exchange to launch in Singapore by 2021 end, the high-quality credit can bridge this gap and play an important role in the overall climate change mitigation strategy. The purpose of this research is to use the production data (including carbon emissions) of paper-making companies in Taiwan to establish a circular economy mathematical programming model and the concept based on the activity cost method (ABC) to explore the impact of different carbon emissions costs (such carbon tax, carbon cap-and-trade, etc.) on the company's production structure and profitability impact. The research results show that different carbon emission cost models have different effects on the company's optimal product-mix and profitability. The managerial implication is to combine the extensive application of the carbon emission credit mechanism, which can offset the carbon emissions in the production process and have a significant impact on the company's sustainable competitiveness. In addition, this study can also enable decision makers to understand the impact of different carbon emission cost models on the profitability of the company's product mix, which can be used as a reference for production planning decisions. [ABSTRACT FROM AUTHOR]

Precipitable water vapor (PWV) and zenith total delay (ZTD) are highly correlated indicators used for forecasting rainfall effectively. These two factors are widely used when establishing qualitative and quantitative rainfall forecast models. Another indicator, however, convective available potential energy (CAPE), is also highly correlated with the occurrence of rainfall, but has not been combined with PWV or ZTD in previous studies. Therefore, a novel rainfall forecast model based on support vector regression that combines CAPE and Global Navigation Satellite System (GNSS)-derived PWV is proposed in this paper. Moreover, annual, seasonal scales, and hourly autocorrelation for predictors were also considered, and wavelet coherence (WTC) was introduced to further reveal the correlation relationships between CAPE, PWV and rainfall in both time and frequency domains. Hourly PWV, CAPE, temperature (T) and rainfall over a time span of three years were collected from four stations in Singapore and Taiwan to evaluate the performance of the proposed model. The root mean square error (RMSE) and mean absolute error (MAE) between the measured and forecasted rainfall were calculated for each year and averaged. Subsequently, the average RMSE and MAE were determined for the annual seasonal rainfall. The annual average RMSE value was 0.71 mm and the average annual seasonal RMSE value was 0.69 mm. The annual average MAE value was 0.21 mm and the annual seasonal was 0.22 mm. The average correlation coefficient (R2) for the annual value was 0.94 and the annual seasonal R2 value was 0.93. These results indicate that the forecast accuracy at the seasonal scale is basically consistent with annual scale. Additionally, a measure called comparable RMSE (CRMS) was introduced to evaluate the forecasting accuracy across all grades of rainfall. This analysis showed that the accuracy of moderate rainfall (MR) and heavy rainfall (HR) forecasts is similar, but slight rainfall (SR) forecasts are the most accurate among seasons and schemes. • A short-term rainfall forecast method is proposed using convective available potential energy (CAPE) and GNSS-derived PWV. • The forecast accuracy of seasonal scales is consistent with annual scale. • Results showed that the forecast accuracy of moderate rainfall and heavy rainfall were comparable while that of slight rainfall was highest. [ABSTRACT FROM AUTHOR]

• Provide a comprehensive overview of the solidarity in health and long-term care sectors. • The overall direction of reforms is developing toward universal coverage. • Reforms might be possible without overall consensus on solidarity. • The pay-as-you-go financial arrangements will require strong intergenerational solidarity. • The capacity of informal caregiving of family could be considered. Different from the development of health sector, there are significant variations in the underpinnings and formation timings of solidarity-based long-term care (LTC) systems. This paper compares the historical developmental trajectories and identifies factors of the transitions of the actual practices of solidarity - the scope of community, the scope of interdependence, and the costs of joint action - in the health and LTC sectors in four East Asian countries: Japan, South Korea, Taiwan, and Singapore. Comparative policy analysis. Healthcare tends to be considered a universal value such that its boundary should include all residents, while LTC is closer to an entitlement of citizens. The differing solidarity reflects path dependency as well as historical legacies and policy diffusion between the health and LTC sectors. In both health and LTC sectors, the costs involved in collective service provision are not distributed evenly between generations. Centralized governance is a prevailing feature of health and LTC sectors in East Asia, allowing solidarity-based institutional arrangements to be established without an overall sense of solidarity. The relationship between solidarity and health and LTC systems is complex and dynamic. [ABSTRACT FROM AUTHOR]