Predicting the future popularity of information in online social networks is a crucial yet challenging task, due to the complex spatiotemporal dynamics underlying information diffusion. Existing methods typically use structural or sequential patterns within the observation window as direct inputs for subsequent popularity prediction. However, most approaches lack the ability to explicitly model the overall trend of popularity up to the prediction time, which leads to limited predictive capability. To address these limitations, we propose VNOIP, a novel method based on variational neural Ordinary Differential Equations (ODEs) for information popularity prediction. Specifically, VNOIP introduces bidirectional jump ODEs with attention mechanisms to capture long-range dependencies and bidirectional context within cascade sequences. Furthermore, by jointly considering both cascade patterns and overall trend temporal patterns, VNOIP explicitly models the continuous-time dynamics of popularity trend trajectories with variational neural ODEs. Additionally, a knowledge distillation loss is employed to align the evolution of prior and posterior latent variables. Extensive experiments on real-world datasets demonstrate that VNOIP is highly competitive in both prediction accuracy and efficiency compared to state-of-the-art baselines.

We study algorithmic strategies to effectively contain diffusion via edge immunization. We consider the scenarios where the epidemic characteristics are known and unknown, and accordingly present approaches relying upon the epidemic dynamics and the network topology. In particular, for the former, we propose the greedy and inverse greedy immune schemes to greedily minimize the immune edge set, whose performance is guaranteed by the exhaustive search. We also present strategies to scale up the associated methods such that they can more efficiently obtain better solutions. For the latter, we find that the epidemic incidence of the immunized network is determined by both local and global connection patterns, characterized by the critical threshold in network epidemiology and the largest connected component in network percolation, respectively. Thus, we propose network topology-based strategies that obtain the immune edge set by simultaneously minimizing both the factors. We conduct extensive experiments on synthetic and empirical social networks to evaluate the proposed methods. Results show that our methods outperform the state-of-the-art by a large margin. Besides, the developed topology-based strategies can always obtain comparable results to the greedy strategies, which are computationally much cheaper than existing approaches and thus favorable to tackle large-scale networks.

This paper studies the network dismantling (ND) problem and aims to develop more effective models and approaches to cope with it, such that a given network can be dismantled by a set of vital nodes of minimum size. To achieve that, we propose a three-phase framework—the Percolation coarsening, Belief propagation dismantling, and Fragmentation optimization fine-tuning (PBF) framework—consisting of PBF-I, PBF-II, and PBF-III, where we contribute three new and one improved algorithms. In particular, PBF-I studies strategies to effectively coarsen the studied network via the merger of less influential nodes, such that the computational efficiency of the follow-up PBF-II phase can be maximized. PBF-II considers the superiority of the belief propagation (BP) algorithm in the ND problem and proposes an improved BP to identify vital nodes from the coarse-grained network, which particularly focuses on the largest connected component and obtains the vital nodes from a filtered candidate set. In addition, PBF-III presents fine-tuning strategies to further improve the quality of solutions obtained in PBF-II. The effectiveness of the proposed framework is validated on over 10 empirical networks in regard to varied circumstances. Our results show that the developed framework can obtain dismantling node sets of much smaller sizes compared to the state-of-the-art in almost all cases. Meanwhile, our framework is also more effective, efficient, and stable compared to existing methods, and is capable of tackling the ND problem in extremely large networks. We are convinced that the model and methodology introduced in this paper could be applied to many applications, such as the robustness and resilience analysis of network-structural infrastructures, the suppression of epidemics, and the containment of misinformation on social networks. The source code of the proposed PBF framework will be made publicly available upon acceptance of the manuscript.

Accurate infectious disease forecasting is crucial for effective public health decision-making. Spatio-temporal graph neural networks (STGNNs) provide new insights and effective strategies for epidemic forecasting by modeling the spatio-temporal dynamics of disease transmission. However, most existing methods typically rely on fine-grained mobility and additional epidemiological information beyond reported infection cases, which are seldom accessible or practical to obtain in realworld scenarios. To address these limitations, we propose the Epidemiology-informed Adaptive Spatio-Temporal Graph neural network (EASTG), a novel forecasting framework requiring only reported infection cases. To model latent transmission dynamics, EASTG proposes an adaptive graph learning mechanism to capture both stable structural information and time-varying inter-regional dependencies directly from surveillance data. Then, a dual-stream temporal module is adopted to decompose and learn the trend and seasonal patterns inherent in epidemic time series. Furthermore, we introduce an epidemiology-informed next-generation matrix approach, which combines domain knowledge with an adaptive graph to model multi-regional epidemic transmission dynamics. Extensive experiments on three realworld datasets show that EASTG significantly outperforms state-of-the-art models. Our findings provide a practical solution for epidemic intelligence, offering reliable and meaningful forecasting even under data-constrained conditions.

Reasoning over temporal knowledge graphs (TKGs) is a challenging task that requires models to infer future events based on past facts. Currently, subgraph-based methods have become the state-of-the-art (SOTA) techniques for this task due to their superior capability to explore local information in knowledge graphs (KGs). However, while previous methods have been effective in capturing semantic patterns in TKG, they are hard to capture more complex topological patterns. In contrast, path-based methods can efficiently capture relation paths between nodes and obtain relation patterns based on the order of relation connections. But subgraphs can retain much more information than a single path. Motivated by this observation, we propose a new subgraph-based approach to capture complex relational patterns. The method constructs candidate-oriented relational graphs to capture the local structure of TKGs and introduces a variant of a graph neural network model to learn the graph structure information between query-candidate pairs. In particular, we first design a prior directed temporal edge sampling method, which is starting from the query node and generating multiple candidate-oriented relational graphs simultaneously. Next, we propose a recursive propagation architecture that can encode all relational graphs in the local structures in parallel. Additionally, we introduce a self-attention mechanism in the propagation architecture to capture the query's preference. Finally, we design a simple scoring function to calculate the candidate nodes' scores and generate the model's predictions. To validate our approach, we conduct extensive experiments on four benchmark datasets (ICEWS14, ICEWS18, ICEWS0515, and YAGO). Experiments on four benchmark datasets demonstrate that our proposed approach possesses stronger inference and faster convergence than the SOTA methods. In addition, our method provides a relational graph for each query-candidate pair, which offers interpretable evidence for TKG prediction results.

This article studies the diffusion-source-inference (DSI) problem, whose solution plays an important role in real-world scenarios such as combating misinformation and controlling diffusions of information or disease. The main task of the DSI problem is to optimize an estimator, such that the real source can be more precisely targeted. In this article, we assume that the state of a number of nodes, called observer set, in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the DSI problem. In particular, we find that the conventional error distance metric cannot precisely evaluate the effectiveness of varied DSI approaches in heterogeneous networks, and thus propose a novel and more general measurement, the candidate set, that is formulated to contain the diffusion source for sure. We propose the percolation-based evolutionary framework (PrEF) to optimize the observer set such that the candidate set can be minimized. Hence, one could further conduct more intensive investigation or search on only a few nodes to target the source. To achieve that, we first theoretically show that the size of the candidate set is bounded by the size of the largest component cover, and demonstrate that there are some similarities between the DSI problem and the network immunization problem. We find that, given the associated direction information of the diffusion is known on observers, the minimization of the candidate set is equivalent to the minimization of the order parameter if we view the observer set as the removal node set. Hence, PrEF is developed based on the network percolation and evolutionary algorithm. The effectiveness of the proposed method is validated on both synthetic and empirical networks in regard to varied circumstances. Our results show that the developed approach could achieve much smaller candidate sets compared to the state of the art in almost all cases, e.g., it is better in 26 out of 27 empirical networks and 155 out of 162 cases regarding the critical threshold. Meanwhile, our approach is also more stable, i.e., it works well irrespective of varied infection probabilities, diffusion models, and underlying networks. More importantly, we provide a framework for the analysis of the DSI problem in large-scale networks.

A great number of studies have demonstrated that many complex systems could benefit a lot from complex networks, through either a direct modeling on which dynamics among agents could be investigated in a global view or an indirect representation by the aid of that the leading factors could be captured more clearly. Hence, in the context of networks, this article copes with the continuous network dismantling problem which aims to find the key node set whose removal would break down a given network more thoroughly and thus is more capable of suppressing virus or misinformation. To achieve this goal effectively and efficiently, we propose the external-degree and internal-size component suppression (EDIS) framework based on the network percolation, where we constrain the search space by a well-designed local goal function and candidate selection approach such that EDIS could obtain better results than the-state-of-the-art in networks of millions of nodes in seconds. We also contribute two strategies with time complexity${\mathcal {O}}(m\log _{\vartheta } m)$and space complexity${\mathcal {O}}(m)$, of networks of m edges, under such framework by well studying the evolving characteristics of the associated connected components as nodes are occupied, where$\vartheta \gt 1$is a hyperparameter. Our results on 12 empirical networks from various domains demonstrate that the proposed method has far better performance than the-state-of-the-art over both effectiveness and computing time. Our study could play important roles in many real-world scenarios, such as the containment of misinformation or epidemics, the distribution of resources or vaccine, the decision of which group of individuals set to quarantine, or the detection of the resilience of a network-based system under intentional attacks.

Recently, the autoregressive framework based on large language models (LLMs) has achieved excellent performance in controlling the generated text to adhere to the required style. These methods guide LLMs through prompt learning to generate target text in an autoregressive manner. However, this manner possesses lower controllability and suffers from the challenge of accumulating errors, where early prediction inaccuracies might influence subsequent word generation. Furthermore, existing prompt-based methods overlook specific region editing, resulting in a deficiency of localized control over input text. To overcome these challenges, we propose a novel three-stage prompt-based approach for specific region editing. To alleviate the issue of accumulating errors, we transform the text style transfer task into a text infilling task, guiding the LLMs to modify only a small portion of text within the editing region to achieve style transfer, thus reducing the number of autoregressive iterations. To achieve an effective specific editing region, we adopt both prompt-based and word frequency-based strategies for region selection, subsequently employing a discriminator to validate the efficacy of the selected region. Experiments conducted on several publicly competitive datasets for text style transfer task confirm that our proposed approach achieves state-of-the-art performance. Keywords: text style transfer, natural language generation, large language models

Subgraph-based methods have proven to be effective and interpretable in predicting drug-drug interactions (DDIs), which are essential for medical practice and drug development. Subgraph selection and encoding are critical stages in these methods, yet customizing these components remains underexplored due to the high cost of manual adjustments. In this study, inspired by the success of neural architecture search (NAS), we propose a method to search for data-specific components within subgraph-based frameworks. Specifically, we introduce extensive subgraph selection and encoding spaces that account for the diverse contexts of drug interactions in DDI prediction. To address the challenge of large search spaces and high sampling costs, we design a relaxation mechanism that uses an approximation strategy to efficiently explore optimal subgraph configurations. This approach allows for robust exploration of the search space. Extensive experiments demonstrate the effectiveness and superiority of the proposed method, with the discovered subgraphs and encoding functions highlighting the model’s adaptability.

Network (or graph) sparsification accelerates many downstream analyses. For graph sparsification, sampling methods derived from local heuristic considerations are common in practice, due to their efficiency in generating sparse subgraphs using only local information. Filtering-based edge sampling is the most typical approach in this respect, yet it heavily depends on an appropriate definition of edge importance. Instead, we propose a generalized node-focused edge sampling framework by preserving scaled/expected local node characteristics. Apart from expected degrees, these local node characteristics include the expected number of triangles and the expected number of non-closed wedges associated with a node. From a technical point of view, we adapt a game-theoretic sampling method from uncertain graph generation to obtain sparse subgraphs that approximate the expected local properties. We include a tolerance threshold for much faster convergence. Within this framework, we provide appropriate algorithmic variants for sparsification. Moreover, we propose a network measure called tri-wedge assortativity for the selection of the most suitable variant when sparsifying a given network. Extensive experimental studies on functional climate, observed real-world, and synthetic networks show the effectiveness of our method in preserving overall structural network properties – on average consistently better than the state of the art.

We study the containment of diffusion in a network immunization perspective, whose solution also plays fundamental roles in scenarios such as the inference of rumor sources and the control of malicious viral marketings. In general, the network immunization aims to suppress the giant connected component of a network by removing as fewer nodes as possible, so that the intervention of the transmission could be achieved by only a few resources. Here, rather than that and based on the fact that removing edges might be cheaper and more applicable in some scenarios, we investigate which group of edges whose removal could boost the performance of an immunization strategy more effectively. We consider both cases that the network topology is known and unknown, and thus two approaches are accordingly developed based on the Edge RelationShip (ERS) and Explosive Percolation over Partial (EPP) information. We evaluate the performance of ERS by comparing it with strategies based on the edge betweenness, the product of eigenvector centralities of the nodes connected by edges, the epidemic link equations, etc. Results on over 30 real networks show that ERS could effectively acquire far better solutions by much less computing time. We also demonstrate the performance of EPP in the circumstances of decentralized, centralized, and delayed cases. We find that the performance of EPP would be in a degree degraded by the uncertainty of inferences from individuals, inaccuracy of predictions, and delay of reactions. But in almost all cases, the developed approach can more effectively suppress a diffusion compared to the currently random strategy, especially when a tough restriction is needed or a combination with the acquaintance immunization is conducted.

This paper addresses the Fast outbreak Sensing and Effective diffusion source Inferring (FSEI) problem, which assumes that the state of nodes in a particularly chosen observer set can be monitored if necessary and aims to optimize the observer set such that outbreaks can be timely detected and their sources can be effectively targeted. We propose three approaches to tackle the FSEI problem: Greedy Strategy (GS), Network-Topology-based Method (NTM), and Hybrid Method (HM). Among them, GS relies on collected outbreaks and constructs the observer set by iteratively choosing and removing the node that minimizes the product of sensing time and source targeting cost of the remaining network. For NTM, we also consider the remaining network and introduce a novel strategy to optimize its topology via simultaneously minimizing the adjoining component size and ratio of the first and second moments. HM is a combination of GS and NTM, considering the submodular property of GS on the minimization of the sensing time and well approximation of the component size on the optimization of the source targeting. We perform extensive experiments on over 200 empirical networks, using various diffusion models, to validate the proposed methods. The results demonstrate that our approaches consistently outperform the state-of-the-art. We believe that the model and methodology presented in this paper can be readily applied to real-world scenarios such as combating misinformation and controlling diffusions of information or disease.

There are many target methods that are efficient to tackle the robustness and immunization problem, in particular, to identify the most influential nodes in a certain complex network. Unfortunately, owing to the diversity of networks, none of them could be accounted as a universal approach that works well in a wide variety of networks. Hence, in this paper, from a percolation perspective, we connect the immunization and robustness problem with an evolutionary algorithm, i.e., a framework of an evolutionary algorithm for investigation of influential nodes in complex networks, in which we have developed procedures of selection, mutation, and initialization of population as well as maintaining the diversity of population. To validate the performance of the proposed framework, we conduct intensive experiments on a large number of networks and compare it to several state-of-the-art strategies. The results demonstrate that the proposed method has significant advantages over others, especially on empirical networks in most of which our method has over 10% advantages of both optimal immunization threshold and average giant fraction, even against the most excellent existing strategies. Additionally, our discussion reveals that there might be better solutions with various initial methods.