We propose a unified framework based on persistent homology to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has been shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases. We also demonstrated that using a single variable enables a linear support vector machine to achieve nearly perfect three-phase classification. Inspired by this discovery, we define a nonparametric metric, the separation index, which not only achieves this classification without sacrificing significant performance but also establishes a connection between particle environments and the global phase structure. Our methods provide an effective framework for understanding and analyzing the properties of disordered materials, with broad potential applications in materials science and even wider studies of complex systems.

Communications networks such as vehicle and social contact networks are temporal networks, where autos/individuals are connected only when they are close to each other. These networks facilitate the propagation of information. Traffic between any two nodes demanded at any time is routed along the fastest time-respecting path. In this work, we investigate the vulnerability of information transport on temporal networks to link removal. The objective is to understand the removal of which types of links deteriorate the efficiency/speed of information transport the most. Identifying such critical links will enable better intervention to facilitate/prohibit the spread of (mis)information. To identify critical links, we propose link-removal strategies based on transport efficiency between two end nodes of each link, properties of links in the aggregated network, and in routing paths respectively. Each strategy ranks links according to their corresponding properties and removes links with the highest measures. Strategies are evaluated via the relative change in transport efficiency after link removal in real-world networks. We find that the path-based strategy performs the best: links appear more often and occur early in the fastest time-respecting paths tend to be critical. Via comprehensive analysis, we explain this strategy's out-performance and its dependency on network properties.

Temporal networks are networks whose topology changes over time. Two nodes in a temporal network are connected at a discrete time step only if they have a contact/interaction at that time. The classic temporal network prediction problem aims to predict the temporal network one time step ahead based on the network observed in the past of a given duration. This problem has been addressed mostly via machine learning algorithms, at the expense of high computational costs and limited interpretation of the underlying mechanisms that form the networks. Hence, we propose to predict the connection of each node pair one step ahead based on the connections of this node pair itself and of node pairs that share a common node with this target node pair in the past. The concrete design of our two prediction models is based on the analysis of the memory property of real-world physical networks, i.e., to what extent two snapshots of a network at different times are similar in topology (or overlap). State-of-the-art prediction methods that allow interpretation are considered as baseline models. In seven real-world physical contact networks, our methods are shown to outperform the baselines in both prediction accuracy and computational complexity. They perform better in networks with stronger memory. Importantly, our models reveal how the connections of different types of node pairs in the past contribute to the connection estimation of a target node pair. Predicting temporal networks like physical contact networks in the long-term future beyond short-term i.e., one step ahead is crucial to forecast and mitigate the spread of epidemics and misinformation on the network. This long-term prediction problem has been seldom explored. Therefore, we propose basic methods that adapt each aforementioned prediction model to address classic short-term network prediction problem for long-term network prediction task. The prediction quality of all adapted models is evaluated via the accuracy in predicting each network snapshot and in reproducing key network properties. The prediction based on one of our models tends to have the highest accuracy and lowest computational complexity.

Temporal networks are networks like physical contact networks whose topology changes over time. Predicting future temporal network is crucial e.g., to forecast and mitigate the spread of epidemics and misinformation on the network. Most existing methods for temporal network prediction are based on machine learning algorithms, at the expense of high computational costs and limited interpretation of the underlying mechanisms that form the networks. This motivates us to develop network-based models to predict the temporal network at the next time step based on the network observed in the past. Firstly, we investigate temporal network properties to motivate our network prediction models and to explain how the performance of these models depends on the temporal networks. We explore the similarity between the network topology (snapshot) at any two time steps with a given time lag/interval. We find that the similarity is relatively high when the time lag is small and decreases as the time lag increases. Inspired by such time-decaying memory of temporal networks and recent advances, we propose two models that predict a link’s future activity (i.e., connected or not), based on the past activities of the link itself or also of neighboring links, respectively. Via seven real-world physical contact networks, we find that our models outperform in both prediction quality and computational complexity, and predict better in networks that have a stronger memory. Beyond, our model also reveals how different types of neighboring links contribute to the prediction of a given link’s future activity, again depending on properties of temporal networks.

Temporal networks refer to networks like physical contact networks whose topology changes over time. Predicting future temporal network is crucial e.g., to forecast the epidemics. Existing prediction methods are either relatively accurate but black-box, or white-box but less accurate. The lack of interpretable and accurate prediction methods motivates us to explore what intrinsic properties/mechanisms facilitate the prediction of temporal networks. We use interpretable learning algorithms, Lasso Regression and Random Forest, to predict, based on the current activities (i.e., connected or not) of all links, the activity of each link at the next time step. From the coefficients learned from each algorithm, we construct the prediction backbone network that presents the influence of all links in determining each links future activity. Analysis of the backbone, its relation to the link activity time series and to the time aggregated network reflects which properties of temporal networks are captured by the learning algorithms. Via six real-world contact networks, we find that the next step activity of a particular link is mainly influenced by (a) its current activity and (b) links strongly correlated in the time series to that particular link and close in distance (in hops) in the aggregated network.