According to the Expected Utility with Uncertain Probabilities (EUUP) proposed by Izhakian and Yermack (2017, 2020), this paper measures market uncertainty of the Chinese stock sectors. The cross-sector uncertainty connectedness is explored using a TVP-VAR based connectedness approach. The results suggest that most of the stock sectors have strong connectedness with each other. Their relationships are heterogeneous under different market states, as well as before and during the emergency events, including the COVID-19 pandemic and the Russia-Ukraine conflict. Three external uncertainty indices, including economic policy uncertainty, climate policy uncertainty, and trade policy uncertainty are employed to investigate their quantile effects on the market connectedness. Most of them have significantly negative effects on the connectedness under bear state, while they are insignificant under bull state. Moreover, their relationships have been changed greatly during the emergency events, compared with the results before. This study highlights the effects of market states and emergencies on the transmission mechanisms of cross-sector uncertainty.
The precision matrix is an essential tool for studying the conditional relationships among large groups of variables. This paper develops a Distributed Refitted Cross-Validation (DRCV) procedure to estimate a large precision matrix in distributed settings, whose communication complexity is proportional to the number of non-zero entries in the precision matrix. The proposed method designs two rounds of communication. The first round selects non-zero positions of the precision matrix via node-wise regressions, while the second round constructs a global-debiased estimation for the precision matrix. To address the overfitting issue regarding this inference-after-selection strategy, the proposed method splits observations at each machine into two parts, one for position selection and the other for parameter estimation. DRCV achieves the global estimation consistency with respect to the total sample size under certain conditions and allows the number of machines in distributed settings to increase as the total sample size increases. Numerical studies on simulated datasets and a real high-frequency stock dataset show that DRCV has good estimation performance and a low communication cost.
In this paper, the authors focus on the polynomial univariate representation (PUR) of zero-dimensional polynomial ideal I ⊂ k[x1, x2, ⋯, xn]. For a zero-dimensional polynomial ideal I of breadth at most one, the authors introduce fast linear algebra techniques to improve the existing algorithm. For a zero-dimensional polynomial ideal I of breadth κ (1 < κ ≤ n), the authors propose a computational procedure to transform I into an ideal of breadth at most one, ensuring that both ideals have the same zeros. The authors present a new algorithm to compute PUR of zero-dimensional polynomial ideals by linear algebra. Complexity analyses of all proposed methods and experimental examples are provided.
Topology optimization offers lightweight and high-performance solutions for structural design. With the rapid advancement of neural networks, topology optimization methods leveraging neural architectures have gained increasing attention. Among these methods, positional encoding is crucial for enabling neural networks to capture high-frequency geometry features, making its integration into neural network-based optimization methods a promising direction for exploration. This paper focuses on positional encoding by introducing a spline-based positional encoding into the neural topology optimization framework, in which spatial coordinates are transformed using spline basis functions before being input into the neural network. The performance of different classic spline basis functions is comprehensively evaluated, including the Bézier spline, B-spline, and NURBS spline. Experimental results demonstrate that positional encoding based on quadratic B-spline basis functions yields the highest structural stiffness. To further validate the effectiveness of the proposed method, a comparative analysis is performed against Fourier and super-Gaussian positional encoding schemes. The results show that spline-based encoding outperforms both alternatives in terms of structural compliance in most cases. Moreover, the resulting topologies exhibit smooth boundaries, free from oscillations and superfluous geometric details.
Drawing on industry convergence theory, this study develops an evaluation index system to quantify cultural-tourism integration. It applies the entropy weight method and a multiple-linear comprehensive index approach to measure both the levels and the spatiotemporal dynamics of culture-tourism integration in 31 selected Chinese provinces (municipalities and autonomous regions) from 2010 to 2022. A staggered Difference-in-Differences model is then used to estimate the driving effects of integration policies and to uncover the pathways. The results show a steady upward trend in integration, marked regional disparities consistent with a Matthew effect, and a significant overall policy effect on integration levels, with notable heterogeneity across regions. Pathways analysis indicates that policies primarily enhance resource and market integration and that the pathways of policies also influence differ by region. This study advances understanding of how policy drives cultural-tourism integration and provides guidance for promoting high-quality, balanced regional development of culture-tourism.
