Dong Xue

The percolation, as an important theoretical tool for studying the robustness of networks, is continuously improved and explored on both ordinary graphs and hypergraphs. Given that most existing studies treat percolation as a single random event and overlook the fact that the collapse of real-world networks is a targeted and gradual process, we propose a node-targeted multi-step percolation model. In this model, the network undergoes multiple rounds of percolation processes, with the input for each percolation being the residual network after the previous percolation ends. Additionally, during each round of percolation, the failure probability of each node is related to the structure of the current residual network. It is worth noting that we have proposed a theoretical framework based on generating functions to predict the changes in the giant connected components of the networks during the multi-step percolation process, which has satisfactory predictive performance when the network does not have extreme heavy-tailed characteristics. Furthermore, through tests on randomly generated ordinary graphs and hypergraphs, we find that networks with Poisson degree/hyperdegree distributions are often more vulnerable than those with power-law degree/hyperdegree distributions when facing the proposed node-targeted multi-step percolation process.

Opinion dynamics models that elucidate the evolution and formation of opinions conventionally focus on pairwise interactions within graphs, often overlooking the complex higher-order interactions that arise in real-world social networks, such as online meetings and group chats. In this article, a continuous-time dynamical system is developed to study opinion-forming processes over higher-order networks associated with undirected hypergraphs. The proposed model introduces a novel diffusion-like interaction function to characterize interactions of different orders over hypergraphs. The convergence and stability of the dynamical systems are further examined in both the presence and absence of stubborn individuals. Building on traditional opinion dynamics models and integrating weak-tie theory, we emphasize the critical role of higher-order interactions in shaping individual opinions, enhancing network communication efficiency, and mitigating opinion polarization. Finally, all theoretical results are extensively investigated and empirically validated through numerical experiments on both synthetic and real-world network datasets.

The labor-intensive nature of medical data annotation presents a significant challenge for respiratory disease diagnosis, resulting in a scarcity of high-quality labeled datasets in resource-constrained settings. Moreover, patient privacy concerns complicate the direct sharing of local medical data across institutions, and existing centralized data-driven approaches, which rely on amounts of available data, often compromise data privacy. This study proposes a federated few-shot learning framework with privacy-preserving mechanisms to address the issues of limited labeled data and privacy protection in diagnosing respiratory diseases. In particular, a meta-stochastic gradient descent algorithm is proposed to mitigate the overfitting problem that arises from insufficient data when employing traditional gradient descent methods for neural network training. Furthermore, to ensure data privacy against gradient leakage, differential privacy noise from a standard Gaussian distribution is integrated into the gradients during the training of private models with local data, thereby preventing the reconstruction of medical images. Given the impracticality of centralizing respiratory disease data dispersed across various medical institutions, a weighted average algorithm is employed to aggregate local diagnostic models from different clients, enhancing the adaptability of a model across diverse scenarios. Experimental results show that the proposed method yields compelling results with the implementation of differential privacy, while effectively diagnosing respiratory diseases using data from different structures, categories, and distributions.

The increasing integration of distributed energy resources into distribution feeders introduces significant uncertainties, stemming from volatile renewable sources and other fluctuating electrical elements, which pose substantial challenges for optimal power flow (OPF) analysis. This paper introduces a data-driven distributionally robust chance-constrained (DRCC) approach to address the stochastic Alternating Current (AC) OPF problem in distribution grids, where the exact probability distributions of uncertainties are unknown. The proposed method utilizes the Wasserstein metric to construct an ambiguity set based on empirical distributions derived from historical data, eliminating the need for prior knowledge of the underlying probability distributions. Notably, the size of the Wasserstein ball within the ambiguity set is inversely related to the volume of available data, allowing for adaptive robustness. Moreover, a computationally efficient reformulation of the DRCC-OPF model is developed using the LinDistFlow AC power flow approximation. The effectiveness and precision of the developed method are validated through multiple IEEE distribution test cases, demonstrating higher reliability of the security constraints compared with other methods. As more data become available, this reliability is systematically and securely adjusted to achieve greater economic efficiency.

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