Community detection via network embedding has received increasing interest in applications. However, existing approaches mainly focus on detecting the communities themselves, while the relationships between these detected communities remain underexplored. In this paper, we propose a novel regularization term - the cosine similarity penalty - to the negative log-likelihood function, which avoids grouping nodes with small degrees into the same community as most existing methods that heavily rely on clustering embedding vectors using the ℓ _2 regularized penalty, i.e., the Euclidean distance. The proposed method not only promotes the community structure but also is robust to the heterogeneity of the node degrees and can offer a clear interpretation of the relationships between the detected communities. This regularization term effectively brings together the embedding vectors with smaller angles, leading to consistent directions among embedding vectors within the same community. To resolve the resultant optimization task, a novel algorithm is developed to detect communities and estimate link probability. Moreover, the asymptotic properties of the proposed method are established in terms of network embedding. Numerical simulations demonstrate the performance of our method, and the illustrations of three real applications provide an interpretation for our model.

Factor analysis is integrated with the Combination of a Uniform and a Binomial distribution (CUB) model to analyze multivariate ordinal data. By augmenting the CUB model with latent random factors, the proposed Factor Augmented CUB (FACUB) model generalizes the conventional multivariate CUB approach to capture complex correlations among items. This framework functions as a probabilistic principal component analysis tailored for multivariate ordinal data, enabling natural dimensionality reduction. For efficient inference, a maximum variational likelihood method is developed via a fast variational expectation-maximization algorithm. The consistency and asymptotic normality of the resulting estimator are established using profile M-estimation theory, and extensions for specific response styles are discussed. The effectiveness and practical utility of the model are demonstrated through comprehensive simulations and two complementary case studies: a low-dimensional application providing an intuitive illustration of the latent space, and a moderate-dimension application incorporating covariates to showcase the recovery of complex dependence structures.

Canonical polyadic (CP) decomposition is widely used for modeling multiway high-dimensional data, but it does not explicitly incorporate mode-specific structural information such as temporal smoothness, network cohesion, or functional regularity. We propose a structure-regularized CP (SR-CP) framework that uses a unified quadratic penalty to encode diverse structural priors through positive semidefinite matrices. A soft orthogonality-promoting penalty is further introduced to enhance component distinctiveness and numerical stability. For estimation, we develop a cyclic block-coordinate descent algorithm for both rank-one and rank-R decompositions. Each regularized mode-wise update is reformulated as a ridge-type problem, leading to a tensor-specific generalized cross-validation criterion for automatic selection of regularization parameters. We establish convergence rates, consistency, and whole-tensor reconstruction error bounds under general noise conditions. Simulations show improved factor recovery and tensor reconstruction relative to classical CP. A real-image completion study demonstrates robustness under severe missingness, and the FRED-MD application yields temporally coherent and interpretable macroeconomic factors. Overall, SR-CP offers a flexible and principled framework for incorporating structural priors into CP tensor decomposition.

This paper introduces a dynamic panel data quantile regression model with network-linked fixed effects, named DQR-NFE, in which unobserved individual heterogeneity is structured through an underlying network. The corresponding estimator is derived by incorporating a quantile network cohesion (QNC) penalty into the dynamic panel quantile regression framework. This penalty encourages connected units within the network to exhibit similar conditional quantiles, with a particularly increased capacity to capture tail network dependence. Relative to conventional fixed-effects specifications, the proposed framework improves the estimation of unobserved heterogeneity and enables more accurate prediction in cold-start settings where training data are unavailable. We establish the consistency and asymptotic normality of the DQR-NFE estimators within a general nonlinear structural framework. These theoretical guarantees hold under both correctly specified and misspecified network structures, with an explicit characterization of their dependence on the network topology. Simulation studies and empirical applications reveal that the proposed estimator outperforms competing approaches in terms of both estimation accuracy and out-of-sample forecasting.

Extreme risk plays an important role in financial supervision and financial investment, which can cause substantial loss in the financial market. To better manage the severe risks resulting from extreme events, the authors propose a novel fixed-k autoregressive conditional Fréchet (k-AcF) model. The proposed model incorporates the k-dimensional extremal distribution and an observation-driven evolution scheme for the key parameters, which accommodates well with the time-varying tail behavior of financial data. Compared to the existing dynamic methods under the extreme value theory framework that focus solely on maximum observations, the k-AcF model employs the largest k observations, which enhances the utilization of tail information and obtains a more accurate extreme risk estimation. Furthermore, this paper uses the maximum likelihood estimators to conduct the model estimation and investigates their statistical properties. Simulation studies validate the reliability of the estimators and confirm the theoretical properties of k-AcF. Empirical applications to the constituent stocks of two major stock indices in the U.S. demonstrate that the k-AcF model accurately captures the clustering and dynamics of extreme risk in the stock market. Moreover, the results show that the obtained model is more responsive and sensitive to a financial crisis than the benchmark model considering only the maximum observations.

In extreme value theory, the tail index parameter controls the tail behavior of a distribution function and is thus of primary interest in analyzing extreme events. Recent developments in modeling the tail index along with covariates have been in semi-parametric regression, but there is a lack of flexible models for time series data, especially for non stationary data. To handle such cases, this article proposes a novel tail single-index regression model incorporating locally stationary covariates to address time-varying tail behaviors. For the proposed model, we develop an estimation procedure by proposing an iterative algorithm and a selection method for the tuning parameter. The asymptotic properties of the estimators are constructed in the time-dependent context. Numerical studies and an analysis of Ozone data demonstrate the effectiveness of our model and corresponding theories.

This paper introduces a novel framework for network reconstruction and community detection, addressing two key challenges in network data analysis. One is to utilise rich but noisy data: in network analysis, observations between nodes typically contain substantial noise rather than directly reflecting network structure. Our framework effectively extracts useful information from this noisy data. Another is to consider the dependence on intracommunity connections: networks often exhibit group heterogeneity, where intracommunity members are more interconnected than intercommunity members. This paper integrates dependencies among intracommunity-connected edges using Bahadur representations. Using a mixture of two latent conditional distributions shared by nodes with the same community label, this paper offers a flexible and interpretable modelling method that introduces a generalised expectation-maximisation (EM) algorithm for computing approximate maximum likelihood estimates. The proposed approach provides a new network analysis method particularly suited for dealing with noisy data and complex community structures, and outperforms traditional methods in distinguishing similar communities, as validated by numerical simulations and two empirical data studies.

To mitigate severe fluctuations in engine power turbine speed caused by changes in coaxial rotors, propellers, and aero-surfaces during the mode transition in coaxial high-speed helicopter (CHH), this paper presents a nonlinear model predictive control (NMPC) method for the CHH power system based on an integrated onboard model. Firstly, a digital simulation framework is deployed, incorporating a CHH onboard model based on a T-S fuzzy model and an onboard composite model of variable speed turboshaft engine based on a stacked Long ShortTerm Memory-State Variable Model (LSTM-SVM). Subsequently, a nonlinear model predictive control method is devised for the CHH power system. By integrating flight prediction data from the integrated onboard model, an optimized objective function is formulated, taking into account both speed control objectives and the dynamic response characteristics of the turboshaft engine's output shaft. Through rolling optimization and feedback correction methods, real-time optimized control parameters for the turboshaft engine are obtained, ensuring rapid responsiveness in the engine control system. Simulation results demonstrate that the developed integrated onboard model accurately represents the variations in performance parameters during high-speed helicopter flight. Additionally, the nonlinear model predictive control law effectively tracks the variable speed reference commands of the power turbine, maintaining a maximum power turbine speed fluctuation of under 0.46%, thereby significantly enhancing both the engine's response and control quality while preserving computational real-time performance.

Frequency response analysis (FRA) is a well-established technique to detect transformer winding deformation faults. Its diagnostic application is based on the principle that a transformer winding can be represented by an equivalent circuit consisting of resistors, inductors, and capacitors. However, rapidly obtaining an accurate and physically meaningful broadband equivalent circuit model for windings remains challenging, limiting both the understanding of fault mechanisms and the generation of data for data-driven fault diagnosis methods. To address these difficulties, this study proposes a two-step broadband equivalent circuit modeling method for the transformer winding based on FRA and Bayesian optimization (BO), considering long-distance mutual inductances and capacitances. The proposed method is validated in a specially designed 10 kV power transformer. Subsequently, two kinds of winding deformation faults, including inter-disk short circuits (IDSCs) and disk space variations (DSVs), are simulated on the basis of the built model and compared with the experimental FRA data. The validation results confirm the accuracy and effectiveness of the proposed method in the construction of the equivalent winding circuit.

Winding short-circuit (SC) faults are a prevalent issue in synchronous machines, and the accurate and timely identification of these faults is critical for maintaining power system stability. Current methods for inspecting synchronous machine windings often rely on periodic inspections based on human expertise. Therefore, numerous studies have explored the application of deep learning (DL) models for detecting synchronous machine winding SC faults. However, these models often exhibit excessive complexity and overlook physical overhead, leading to inefficient utilization of computational power and data resources. To address these limitations, this study proposes a dual-channel DL model integrated with the active learning (AL) query strategy. In this study, winding SC faults are manually simulated on a 5-kVA synchronous machine, and corresponding frequency response analysis (FRA) data are recorded. Subsequently, the proposed method is validated on the test set and benchmarked against previous studies. Experimental results demonstrate that the proposed method significantly reduces the data annotation effort and accelerates model training to the order of seconds (under 5 s) while maintaining satisfactory accuracy (>= 95%). Comparative experimental results further indicate that the proposed model, requiring only 1/20th of the labeled training samples used in previous studies, achieves a substantial reduction of approximately 99.8% in both model parameters and training time.

In longitudinal data analysis, identifying subgroups of subjects with heterogeneous parameters is crucial for understanding complex data structures. To address the challenges posed by within-subject correlation and heteroscedasticity across subjects, we propose a novel grouped generalized estimating equation (GEE) method for quantile regression (QR). Under the assumption that subjects can be partitioned into a finite number of groups, where individuals within the same group share identical regression coefficients at a given quantile level, we develop a computationally efficient three-step algorithm that simultaneously performs subject grouping, estimates QR coefficients and infers the correlation matrix. Theoretically, we establish the asymptotic distribution of the group-specific QR coefficient estimator by demonstrating its asymptotic equivalence to the infeasible estimator with known group membership, even when both dimensions of the longitudinal data diverge. Numerical studies and theoretical analysis show that incorporating the estimated correlation matrix significantly improves the efficiency of both coefficient estimation and group identification, which provides an efficient and flexible framework for analysing heterogeneous longitudinal data.

The COVID-19 pandemic precipitated a surge in the non-performing assets held by financial institutions, elevating systemic risk in financial networks. Therefore, developing strategies to alleviate this risk, with a focus on non-performing assets, has become a research area of interest. Supported by policies related to the Chinese insurance market, this study proposes the establishment of a non-performing assets disposal fund backed by insurance capital. This fund will invest in the non-performing assets of financial institutions with the aim of mitigating systemic risk. Using a linear threshold model, we identify an asymptotically optimal scheme for disposing of non-performing assets. Additionally, we construct a payment model integrated with non-performing assets, from which we derive an optimal payment and clearing strategy. Our research also proposes a robust set of criteria to assist regulators in determining whether to use the non-performing assets disposal fund. To demonstrate the efficacy of the fund in reducing systemic risk, we conduct simulations and analyze data from the Chinese interbank financial network. Through this rigorous analysis, we confirm the role of the fund in enhancing the stability of the financial system.

Quantile vector autoregression (QVAR) models offer enhanced capabilities over vector autoregression (VAR) models in analyzing asymmetric interactions within multiple time series and are widely used in many areas, including finance and economics. However, in scenarios involving high-dimensional data where the number of time series N exceeds the length of the time series T, both parameter estimation and the theoretical establishment present significant challenges. Notably, existing research has not yet explored these challenges with the framework of QVAR models. To handle this problem, we propose a novel high-dimensional QVAR model that incorporates influencers and communities, which assumes that variables within distinct communities have shared dependency structures and are influenced by the same set of variables, called influencers. We develop an estimation procedure based on the alternating minimization algorithm and the convolution-smoothed approach. The local consistency results for the estimated parameters are established in high-dimensional settings with sub-Weibull innovations. Numerical studies illustrate that the proposed model performs well in finite samples. The proposed model is applied to identify the most influential macroeconomic variables in the United States across business cycles and construct a dynamic quantile network with influencers and communities for volatility spillover effects of global stock markets.

To better investigate potential risk contagion in guarantee networks, we propose risk contagion and threshold models based on a supply chain consisting of capital-constrained firms and suppliers. The results show that the optimal debt payment and asset liquidation strategy can help firms improve their payment ability and minimize liquidation losses suppliers, ultimately leading to agreement on debt repayment among all parties in the supply chain. When a guarantee network exists in the supply chain system, the optimal general guarantee under the threshold contagion model minimizes risk spillover and does not require the guarantee ratio to be necessarily full. In addition, we find that when product order quantity increases or actual market sales quantity increases, firms’ expected revenue increases or economic losses decrease, thereby reducing the likelihood of penalty guarantee agreements and decreasing supplier and firm defaults and asset losses. Similarly, during the network formation process, when the guarantee fee rate rises, some firms may refuse to accept suppliers’ guarantees, making it impossible to establish guarantee relationships. Finally, under certain conditions, we suggest that regulators recommend general guarantee schemes to supply chain systems to reduce systemic risk.

Due to the wide application of modular multilevel converters (MMCs) in hybrid AC/DC distribution grids, enhancing the fault ride-through (FRT) capability of MMC is essential to improve the reliability of the hybrid AC/DC distribution grids. In this paper, an individual arm capacitor voltage control based comprehensive FRT strategy is presented. To balance the active power transmitted in each arm, an individual arm capacitor voltage control (IACVC) method is presented to regulate arm capacitor voltage stable to their reference. The decoupled control for positive pole and negative pole is achieved. Besides, an improved arm current references calculation (ACRC) method is proposed. During pole-to-ground (PTG) fault, the current of the fault pole is reduced to 0, and the healthy pole still transmit rated active power with rated voltage. In addition to, the adverse effects of AC side voltage imbalance are eliminated. The presented control strategy is verified by simulations and experiments on a MMC prototype.

Achieving robust forecasts for a single time series with many covariates and possible nonlinear effects is a problem worth investigating. In this paper, a scaled factor-augmented quantile regression with aggregation (SFQRA) method is proposed for an effective prediction. It first estimates different conditional quantiles by introducing scaled covariates to the factor-augmented quantile regression, which not only combats the curse of dimensionality but also includes the target information in the estimation. Then the different conditional quantiles are aggregated appropriately to a robust forecast. Moreover, combining SFQRA with feature screening via an aggregated quantile correlation allows it to be extended to handle cases when only a portion of covariates is informative. The effectiveness of the proposed methods is justified theoretically, under the framework of large cross-sections and large time dimensions while no restriction is imposed on the relation between them. Various simulation studies and real data analyses demonstrate the superiority of the newly proposed method in forecasting.

The HVDC transmission system has played an important role in modern power system. In traditional HVDC transmission line protection, the differential protection is invulnerable to high fault resistance, but its time delay is too long due to the distributed capacitance current. In order to solve this problem, a novel pilot differential protection is proposed in this paper. The compensating voltage on the setting point on the line can be calculated by using the voltage and current at two terminals of the line, separately. The difference value of the compensating voltages calculated by the voltage and current at rectifier side terminal and the inverter side terminal are defined as the differential voltage in this paper. When external fault occurs, the compensating voltage on the setting point calculated by the rectifier side terminal and inverter side terminal should be almost the same, so the differential voltage should be relatively small. However, when internal fault occurs, the compensating voltage on the setting point calculated by the two terminals are different, so the differential voltage should be relatively large. The analysis proves that the differential voltage can be used to identify the fault. A +/- 800 kV UHVDC system is modeled for simulation in PSCAD/EMTDC, and the correctness and effectiveness of the proposed protection method is verified. (c) 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CCBY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).