The interaction between negative emotion contagion and the spread of extreme opinions on social media can lead to serious consequences, highlighting the need to understand the co-evolution of opinion and emotion. However, most existing studies treat opinion and emotion dynamics as independent processes. The few models that explore their interplay often do not fully capture their distinct dynamic mechanisms and tend to overlook the mutual reinforcement between opinion convergence and emotion contagion. To address these limitations, we propose the dynamics of opinion and emotion on social media (DOES) model, which employs two differential equations to represent the separate dynamics of opinion and emotion, and introduces coupling functions that describe their mutual reinforcement. We analyze the model’s steady-state conditions and validate the results through simulations. Prediction experiments on real-world datasets demonstrate the model’s ability to reproduce key patterns. DOES provides a novel framework for modeling the coevolution of opinion and emotion, offering insights into emotional regulation and discourse moderation on social media platforms.

Dynamic graphs evolve continuously, presenting challenges for traditional graph learning due to their changing structures and temporal dependencies. Recent advancements have shown potential in addressing these challenges by developing suitable meta-learning-based dynamic graph neural network models. However, most meta-learning approaches for dynamic graphs rely on fixed weight update parameters, neglecting the essential intrinsic complex high-order topological information of dynamically evolving graphs. We have designed Dowker Zigzag Persistence (DZP), an efficient and stable dynamic graph persistent homology representation method based on Dowker complex and zigzag persistence, to capture the high-order features of dynamic graphs. Armed with the DZP ideas, we propose TMetaNet, a new meta-learning parameter update model based on dynamic topological features. By utilizing the distances between high-order topological features, TMetaNet enables more effective adaptation across snapshots. Experiments on real-world datasets demonstrate TMetaNet’s state-of-the-art performance and resilience to graph noise, illustrating its high potential for meta-learning and dynamic graph analysis. Our code is available at https://github.com/Lihaogx/TMetaNet.

Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.

With the development of intelligent transportation systems, timely and accurate travel forecasting task has witnessed growing interest. Unlike most previous research that only considers the demand prediction in origin regions, this task aims to predict the origin-destination demand between all-region pairs. Its main challenges come from effectively capturing the direction, weight, and temporal information of links in dynamic traffic networks. To confront these challenges, we treat the dynamic traffic networks as multiple weighted directed network snapshots and propose a graph-based deep learning framework, Temporal Graph Autoencoder (TGAE). Specifically, TGAE encodes the fundamentally asymmetric nature of a directed graph via directed neighborhood aggregation and learns a pair of vector representations for each node. Meanwhile, we use the graph attention mechanism to capture the weight information of links. Next, TGAE preserves the temporal dependencies by independently reconstructing the existence and weight of links over two consecutive time steps. Furthermore, we employ the Long Short-Term Memory network (LSTM) to capture the evolution patterns of traffic networks and predict both the direction and weight of links based on the historical data. Experimental results demonstrate that TGAE outperforms several baseline methods on the travel forecasting task, which can help traffic management, resource preallocation, and services optimization.