Vulnerability Analysis Method Based on Network and Copula Entropy.

With the deepening of the diversification and openness of financial systems, financial vulnerability, as an endogenous attribute of financial systems, becomes an important measurement of financial security. Based on a network analysis, we introduce a network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with the previous network curvature analysis method, the CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

Frequency Stability Prediction of Power Systems Using Vision Transformer and Copula Entropy.

This paper addresses the problem of frequency stability prediction (FSP) following active power disturbances in power systems by proposing a vision transformer (ViT) method that predicts frequency stability in real time. The core idea of the FSP approach employing the ViT is to use the time-series data of power system operations as ViT inputs to perform FSP accurately and quickly so that operators can decide frequency control actions, minimizing the losses caused by incidents. Additionally, due to the high-dimensional and redundant input data of the power system and the O(N2) computational complexity of the transformer, feature selection based on copula entropy (CE) is used to construct image-like data with fixed dimensions from power system operation data and remove redundant information. Moreover, no previous FSP study has taken safety margins into consideration, which may threaten the secure operation of power systems. Therefore, a frequency security index (FSI) is used to form the sample labels, which are categorized as "insecurity", "relative security", and "absolute security". Finally, various case studies are carried out on a modified New England 39-bus system and a modified ACTIVSg500 system for projected 0% to 40% nonsynchronous system penetration levels. The simulation results demonstrate that the proposed method achieves state-of-the-art (SOTA) performance on normal, noisy, and incomplete datasets in comparison with eight machine-learning methods.

Vine copula selection using mutual information for hydrological dependence modeling.

Hydrological risk analysis and management entails multivariate modeling which requires modeling the structure of dependence among different variables. Vine copulas have been increasing applied in multivariate modeling wherein the selection of vine copula structure plays a critical role. Inspired by the relationship between Mutual information (MI) and copula entropy (CE), this study discussed the connection between conditional mutual information (CMI) and CE and developed a mutual information-based sequential approach to select a vine structure which was based on original observations, and model-independent. Then, to reduce the complexity of R-vine copulas, a statistical method-based truncation procedure was applied. Finally, an MI-based approach for hydrological dependence modeling was developed. Two types of hydrological processes with different dependence structures were utilized to show the performance of the proposed approach: (i) drought characterization: showing a D-vine structure; and (ii) multi-site streamflow dependence: showing a C-vine structure. Results indicated that the MI-based approach satisfactorily modeled different kinds of dependence structure and yielded more information on variables in comparison with traditional tau-based approach.

A Copula Entropy Approach to Dependence Measurement for Multiple Degradation Processes.

Degradation analysis has been widely used in reliability modeling problems of complex systems. A system with complex structure and various functions may have multiple degradation features, and any of them may be a cause of product failure. Typically, these features are not independent of each other, and the dependence of multiple degradation processes in a system cannot be ignored. Therefore, the premise of multivariate degradation modeling is to capture and measure the dependence among multiple features. To address this problem, this paper adopts copula entropy, which is a combination of the copula function and information entropy theory, to measure the dependence among different degradation processes. The copula function was employed to identify the complex dependence structure of performance features, and information entropy theory was used to quantify the degree of dependence. An engineering case was utilized to illustrate the effectiveness of the proposed method. The results show that this method is valid for the dependence measurement of multiple degradation processes.

Research on Establishing Corneal Edema after Phacoemulsification Prediction Model Based on Variable Selection with Copula Entropy.

BACKGROUND: Corneal edema (CE) affects the outcome of phacoemulsification. Effective ways to predict the CE after phacoemulsification are needed. METHODS: On the basis of data from patients conforming to the protocol of the AGSPC trial, 17 variables were selected to predict CE after phacoemulsification by constructing a CE nomogram through multivariate logistic regression, which was improved via variable selection with copula entropy. The prediction models were evaluated using predictive accuracy, the area under the receiver operating characteristic curve (AUC), and decision curve analysis (DCA). RESULTS: Data from 178 patients were used to construct prediction models. After copula entropy variable selection, which shifted the variables used for prediction in the CE nomogram from diabetes, best corrected visual acuity (BCVA), lens thickness and cumulative dissipated energy (CDE) to CDE and BCVA in the Copula nomogram, there was no significant change in predictive accuracy (0.9039 vs. 0.9098). There was also no significant difference in AUCs between the CE nomogram and the Copula nomogram (0.9637, 95% CI 0.9329-0.9946 vs. 0.9512, 95% CI 0.9075-0.9949; p = 0.2221). DCA suggested that the Copula nomogram has clinical application. CONCLUSIONS: This study obtained a nomogram with good performance to predict CE after phacoemulsification, and showed the improvement of copula entropy for nomogram models.

CRIA: An Interactive Gene Selection Algorithm for Cancers Prediction Based on Copy Number Variations.

Genomic copy number variations (CNVs) are among the most important structural variations of genes found to be related to the risk of individual cancer and therefore they can be utilized to provide a clue to the research on the formation and progression of cancer. In this paper, an improved computational gene selection algorithm called CRIA (correlation-redundancy and interaction analysis based on gene selection algorithm) is introduced to screen genes that are closely related to cancer from the whole genome based on the value of gene CNVs. The CRIA algorithm mainly consists of two parts. Firstly, the main effect feature is selected out from the original feature set that has the largest correlation with the class label. Secondly, after the analysis involving correlation, redundancy and interaction for each feature in the candidate feature set, we choose the feature that maximizes the value of the custom selection criterion and add it into the selected feature set and then remove it from the candidate feature set in each selection round. Based on the real datasets, CRIA selects the top 200 genes to predict the type of cancer. The experiments' results of our research show that, compared with the state-of-the-art related methods, the CRIA algorithm can extract the key features of CNVs and a better classification performance can be achieved based on them. In addition, the interpretable genes highly related to cancer can be known, which may provide new clues at the genetic level for the treatment of the cancer.