Catastrophic cascade of failures in interdependent hypergraphs.

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.

Opinion cascade under perception bias in social networks.

Opinion cascades, initiated by active opinions, offer a valuable avenue for exploring the dynamics of consensus and disagreement formation. Nevertheless, the impact of biased perceptions on opinion cascade, arising from the balance between global information and locally accessible information within network neighborhoods, whether intentionally or unintentionally, has received limited attention. In this study, we introduce a threshold model to simulate the opinion cascade process within social networks. Our findings reveal that consensus emerges only when the collective stubbornness of the population falls below a critical threshold. Additionally, as stubbornness decreases, we observe a higher prevalence of first-order and second-order phase transitions between consensus and disagreement. The emergence of disagreement can be attributed to the formation of echo chambers, which are tightly knit communities where agents' biased perceptions of active opinions are lower than their stubbornness, thus hindering the erosion of active opinions. This research establishes a valuable framework for investigating the relationship between perception bias and opinion formation, providing insights into addressing disagreement in the presence of biased information.

Fine mapping of powdery mildew and stripe rust resistance genes Pm5V/Yr5V transferred from Dasypyrum villosum into wheat without yield penalty.

KEY MESSAGE: The novel wheat powdery mildew and stripe rust resistance genes Pm5V/Yr5V are introgressed from Dasypyrum villosum and fine mapped to a narrowed region in 5VS, and their effects on yield-related traits were characterized. The powdery mildew and stripe rust seriously threaten wheat production worldwide. Dasypyrum villosum (2n = 2x = 14, VV), a relative of wheat, is a valuable resource of resistance genes for wheat improvement. Here, we describe a platform for rapid introgression of the resistance genes from D. villosum into the wheat D genome. A complete set of new wheat-D. villosum V (D) disomic substitution lines and 11 D/V Robertsonian translocation lines are developed and characterized by molecular cytogenetic method. A new T5DL·5V#5S line NAU1908 shows resistance to both powdery mildew and stripe rust, and the resistances associated with 5VS are confirmed to be conferred by seedling resistance gene Pm5V and adult-plant resistance gene Yr5V, respectively. We flow-sort chromosome arm 5VS and sequence it using the Illumina NovaSeq 6000 system that allows us to generate 5VS-specific markers for genetic mapping of Pm5V/Yr5V. Fine mapping shows that Pm5V and Yr5V are closely linked and the location is narrowed to an approximately 0.9 Mb region referencing the sequence of Chinese Spring 5DS. In this region, a NLR gene in scaffold 24,874 of 5VS orthologous to TraesCS5D02G044300 is the most likely candidate gene for Pm5V. Soft- and hard-grained T5DL·5V#5S introgressions confer resistance to both powdery mildew and stripe rust in diverse wheat genetic backgrounds without yield penalty. Meanwhile, significant decrease in plant height and increase in yield were observed in NIL-5DL·5V#5S compared with that in NIL-5DL·5DS. These results indicate that Pm5V/Yr5V lines might have the potential value to facilitate wheat breeding for disease resistance.

Asymmetry in interdependence makes a multilayer system more robust against cascading failures.

Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation-induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: Once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first to second order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light on the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.

The "weak" interdependence of infrastructure systems produces mixed percolation transitions in multilayer networks.

Previous studies of multilayer network robustness model cascading failures via a node-to-node percolation process that assumes "strong" interdependence across layers-once a node in any layer fails, its neighbors in other layers fail immediately and completely with all links removed. This assumption is not true of real interdependent infrastructures that have emergency procedures to buffer against cascades. In this work, we consider a node-to-link failure propagation mechanism and establish "weak" interdependence across layers via a tolerance parameter α which quantifies the likelihood that a node survives when one of its interdependent neighbors fails. Analytical and numerical results show that weak interdependence produces a striking phenomenon: layers at different positions within the multilayer system experience distinct percolation transitions. Especially, layers with high super degree values percolate in an abrupt manner, while those with low super degree values exhibit both continuous and discontinuous transitions. This novel phenomenon we call mixed percolation transitions has significant implications for network robustness. Previous results that do not consider cascade tolerance and layer super degree may be under- or over-estimating the vulnerability of real systems. Moreover, our model reveals how nodal protection activities influence failure dynamics in interdependent, multilayer systems.

Percolation on networks with weak and heterogeneous dependency.

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdos-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.

Cascading failures in coupled networks: The critical role of node-coupling strength across networks.

The robustness of coupled networks against node failure has been of interest in the past several years, while most of the researches have considered a very strong node-coupling method, i.e., once a node fails, its dependency partner in the other network will fail immediately. However, this scenario cannot cover all the dependency situations in real world, and in most cases, some nodes cannot go so far as to fail due to theirs self-sustaining ability in case of the failures of their dependency partners. In this paper, we use the percolation framework to study the robustness of interdependent networks with weak node-coupling strength across networks analytically and numerically, where the node-coupling strength is controlled by an introduced parameter α. If a node fails, each link of its dependency partner will be removed with a probability 1-α. By tuning the fraction of initial preserved nodes p, we find a rich phase diagram in the plane p-α, with a crossover point at which a first-order percolation transition changes to a second-order percolation transition.

Cascading failures in coupled networks with both inner-dependency and inter-dependency links.

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We find that when most of dependency links are inner- or inter-ones, the coupled networks system is fragile and makes a discontinuous percolation transition. However, when the numbers of two types of dependency links are close to each other, the system is robust and makes a continuous percolation transition. This indicates that the high density of dependency links could not always lead to a discontinuous percolation transition as the previous studies. More interestingly, although the robustness of the system can be optimized by adjusting the ratio of the two types of dependency links, there exists a critical average degree of the networks for coupled random networks, below which the crossover of the two types of percolation transitions disappears, and the system will always demonstrate a discontinuous percolation transition. We also develop an approach to analyze this model, which is agreement with the simulation results well.

Percolation on interacting networks with feedback-dependency links.

When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here, we develop a mathematical framework and study numerically and analytically the percolation of interacting networks with feedback-dependency links. For the case that all degree distributions of intra- and inter- connectivity links are Poissonian, we find that for a low density of inter-connectivity links, the system undergoes from second order to first order through hybrid phase transition as coupling strength increases. It implies that the average degree k of inter-connectivity links has a little influence on robustness of the system with a weak coupling strength, which corresponds to the second order transition, but for a strong coupling strength corresponds to the first order transition. That is to say, the system becomes robust as k increases. However, as the average degree k of each network increases, the system becomes robust for any coupling strength. In addition, we find that one can take less cost to design robust system as coupling strength decreases by analyzing minimum average degree kmin of maintaining system stability. Moreover, for high density of inter-connectivity links, we find that the hybrid phase transition region disappears, the first order region becomes larger and second order region becomes smaller. For the case of two coupled scale-free networks, the system also undergoes from second order to first order through hybrid transition as the coupling strength increases. We find that for a weak coupling strength, which corresponds to the second order transitions, feedback dependency links have no effect on robustness of system relative to no-feedback condition, but for strong coupling strength which corresponds to first order or hybrid phase transition, the system is more vulnerable under feedback condition comparing with no-feedback condition. Thus, for designing resilient system, designers should try to avoid the feedback dependency links, because the existence of feedback-dependency links makes the system extremely vulnerable and difficult to defend.

Cascading dynamics on random networks: crossover in phase transition.

In a complex network, random initial attacks or failures can trigger subsequent failures in a cascading manner, which is effectively a phase transition. Recent works have demonstrated that in networks with interdependent links so that the failure of one node causes the immediate failures of all nodes connected to it by such links, both first- and second-order phase transitions can arise. Moreover, there is a crossover between the two types of transitions at a critical system-parameter value. We demonstrate that these phenomena can occur in the more general setting where no interdependent links are present. A heuristic theory is derived to estimate the crossover and phase-transition points, and a remarkable agreement with numerics is obtained.

Information filtering based on transferring similarity.

In this Brief Report, we propose an index of user similarity, namely, the transferring similarity, which involves all high-order similarities between users. Accordingly, we design a modified collaborative filtering algorithm, which provides remarkably higher accurate predictions than the standard collaborative filtering. More interestingly, we find that the algorithmic performance will approach its optimal value when the parameter, contained in the definition of transferring similarity, gets close to its critical value, before which the series expansion of transferring similarity is convergent and after which it is divergent. Our study is complementary to the one reported in [E. A. Leicht, P. Holme, and M. E. J. Newman, Phys. Rev. E 73, 026120 (2006)], and is relevant to the missing link prediction problem.