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The failures of individual agents can significantly impact the functionality of associated groups in interconnected systems. To reveal these impacts, we develop a threshold model to investigate cascading failures in double-layer hypergraphs with interlayer interdependence. We hypothesize that a hyperedge disintegrates when the proportion of failed nodes within it exceeds a threshold. Due to the interdependence between a node and its replica in the other layer, the disintegrations of these hyperedges could trigger a cascade of events, leading to an iterative collapse across these two layers. We find that double-layer hypergraphs undergo abrupt, discontinuous first-order phase transitions during systemic collapse regardless of the specific threshold value. Additionally, the connectivity measured by average cardinality and hyperdegree plays a crucial role in shaping system robustness. A higher average hyperdegree always strengthens system robustness. However, the relationship between system robustness and average cardinality exhibits non-monotonic behaviors. Specifically, both excessively small and large average cardinalities undermine system robustness. Furthermore, a higher threshold value can boost the system's robustness. In summary, our study provides valuable insights into cascading failure dynamics in double-layer hypergraphs and has practical implications for enhancing the robustness of complex interdependent systems across domains. [ABSTRACT FROM AUTHOR]

Polyhedral boranes are a class of well-known boron molecular clusters with unique physical and chemical properties, and great efforts have been made in the past decades to find more effective synthetic methods. However, the established synthetic methods suffer from low efficiency and low selectivity because the mechanism of the B–H bond condensation reaction, critical for the synthesis of the polyhedral boranes, is not well understood. Here we report highly selective and efficient synthetic methods of the salts of the tetradecahydridoundecaborate (1–) (B11H14−) and dodecahydrido-dodecaborates (2–) (B12H122−) anions by employing commercially available and inexpensive starting materials. Both theoretical and experimental investigations are carried out to elucidate the reaction mechanisms. We have found that the nature of the B–H bond condensation is the dihydrogen bonding interaction in which the positively charged hydrogens (bridged hydrogens) play a crucial role. The current study has not only led to more effective and selective synthetic methods for B11H14− and B12H122− but also unveiled the nature of the B–H bond condensation and the general formation mechanisms of polyhedral boranes. This finding will facilitate the development of more effective synthetic methods for polyhedral boranes and spur their wide application. [ABSTRACT FROM AUTHOR]

Due to structural heterogeneity, the main function and structure of networked systems are significantly influenced by some important nodes rather than each member. In practical, the properties of important nodes could be different from network to network, and thus a variety of algorithms have been specially designed to identify important nodes of different networks and of different dynamics. In this paper we propose a widely applicable algorithm by employing the percolation model in statistical physics, which describes the behavior of connected clusters when nodes are connected randomly. This algorithm appropriately combines the local and global properties of a network, thus it stresses the significance of nodes that neither have a visibly local importance, such as degree and clustering, nor have a visibly global importance, such as betweenness. The effectiveness of our algorithm has been illustrated in a series of networks, including model networks with different degree distributions and different degree correlations, and empirical networks. As a shell decomposition process, the framework of our algorithm has extensive application prospects in analyzing network structure, such as community, core–periphery structure, and shell structures. [ABSTRACT FROM AUTHOR]