A general urban spreading pattern of COVID-19 and its underlying mechanism.

Currently, the global situation of COVID-19 is aggravating, pressingly calling for efficient control and prevention measures. Understanding the spreading pattern of COVID-19 has been widely recognized as a vital step for implementing non-pharmaceutical measures. Previous studies explained the differences in contagion rates due to the urban socio-political measures, while fine-grained geographic urban spreading pattern still remains an open issue. Here, we fill this gap by leveraging the trajectory data of 197,808 smartphone users (including 17,808 anonymous confirmed cases) in nine cities in China. We find a general spreading pattern in all cities: the spatial distribution of confirmed cases follows a power-law-like model and the spreading centroid human mobility is time-invariant. Moreover, we reveal that long average traveling distance results in a high growth rate of spreading radius and wide spatial diffusion of confirmed cases in the fine-grained geographic model. With such insight, we adopt the Kendall model to simulate the urban spreading of COVID-19 which can well fit the real spreading process. Our results unveil the underlying mechanism behind the spatial-temporal urban evolution of COVID-19, and can be used to evaluate the performance of mobility restriction policies implemented by many governments and to estimate the evolving spreading situation of COVID-19.

The Intrinsic Similarity of Topological Structure in Biological Neural Networks.

Most previous studies mainly have focused on the analysis of structural properties of individual neuronal networks from C. elegans. In recent years, an increasing number of synapse-level neural maps, also known as biological neural networks, have been reconstructed. However, it is not clear whether there are intrinsic similarities of structural properties of biological neural networks from different brain compartments or species. To explore this issue, we collected nine connectomes at synaptic resolution including C. elegans, and analyzed their structural properties. We found that these biological neural networks possess small-world properties and modules. Excluding the Drosophila larval visual system, these networks have rich clubs. The distributions of synaptic connection strength for these networks can be fitted by the truncated pow-law distributions. Additionally, compared with the power-law model, a log-normal distribution is a better model to fit the complementary cumulative distribution function (CCDF) of degree for these neuronal networks. Moreover, we also observed that these neural networks belong to the same superfamily based on the significance profile (SP) of small subgraphs in the network. Taken together, these findings suggest that biological neural networks share intrinsic similarities in their topological structure, revealing some principles underlying the formation of biological neural networks within and across species.

Resilience centrality in complex networks.

Resilience describes a system's ability to adjust its activity to retain the basic functionality when errors or failures occur in components (nodes) of the network. Due to the complexity of a system's structure, different components in the system exhibit diversity in the ability to affect the resilience of the system, bringing us a great challenge to protect the system from collapse. A fundamental problem is therefore to propose a physically insightful centrality index, with which to quantify the resilience contribution of a node in any systems effectively. However, existing centrality indexes are not suitable for the problem because they only consider the network structure of the system and ignore the impact of underlying dynamic characteristics. To break the limits, we derive a new centrality index: resilience centrality from the 1D dynamic equation of systems, with which we can quantify the ability of nodes to affect the resilience of the system accurately. Resilience centrality unveils the long-sought relations between the ability of nodes in a system's resilience and network structure of the system: the capacity is mainly determined by the degree and weighted nearest-neighbor degree of the node, in which weighted nearest-neighbor degree plays a prominent role. Further, we demonstrate that weighted nearest-neighbor degree has a positive impact on resilience centrality, while the effect of the degree depends on a specific parameter, average weighted degree ß_{eff}, in the 1D dynamic equation. To test the performance of our approach, we construct four real networks from data, which corresponds to two complex systems with entirely different dynamic characteristics. The simulation results demonstrate the effectiveness of our resilience centrality, providing us theoretical insights into the protection of complex systems from collapse.