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.

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.

The nature of jets in active galactic nuclei (AGNs) in the early Universe and their feedback to the host galaxy remains a highly topical question. Observations of the radio structure of high-redshift AGNs enabled by very long baseline interferometry (VLBI) provide indispensable input into studies of their properties and role in the galaxies' evolution. To date, only five AGNs at redshift z 6 have been studied with the VLBI technique. Aims. VIK J2318-3113 is a recently discovered quasar at z = 6:44 that had not been imaged with VLBI before the current work. Here we present the first VLBI imaging results of this high-redshift quasar, with the aim of corroborating its high-resolution appearance with the physical model of the object. Methods. We carried out VLBI phase-referencing observations of VIK J2318-3113 using the Very Long Baseline Array at two frequencies, 1.6 and 4.7 GHz, and obtained the first view at the radio structure on the milliarcsecond scale. Results. The source was clearly detected at 1.6 GHz. We found that almost all of its radio emission comes from the parsec-scale core region. Our dual-frequency observations constrain the spectral index and brightness temperature of the radio core. Its properties are similar to those of other known high-redshift radio-loud AGNs.