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Abstract K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with interesting phenomena and a rich phase diagram. A key finding is the existence of a metastable phase where microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures spontaneously propagate the damage radially until the system collapses, a phenomenon analogous to the nucleation process.

The models of k -core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered exponents in IN have not been explored in k -core percolation, and the origin of the similarity still remains unclear. Thus, in this paper, by considering k -core percolation on random networks, we first verify that the two newly discovered exponents (fractal fluctuation dimension, $d^{^{\prime}}_\textrm{f}$ , and correlation length exponent, $\nu^{^{\prime}}$ ) observed in d -dimensional IN spatial networks also exist with the same values in k -core percolation. That is, the fractality of the k -core giant component fluctuations is manifested by a fractal fluctuation dimension, $\widetilde d_\textrm{f} = 3/4$ , within a correlation size N ʹ that scales as $N^{^{\prime}} \propto (p-p_c)^{-\widetilde\nu}$ , with $\widetilde\nu = 2$ . Here we define, $\widetilde\nu \equiv d\cdot \nu^{^{\prime}}$ and $\widetilde{d}_\textrm{f} \equiv d^{^{\prime}}_\textrm{f}/d$ . This implies that both models, IN and k -core, feature the same scaling behaviors with the same critical exponents, further reinforcing the similarity between the two models. Furthermore, we suggest that these two models are similar since both have two types of interactions: short-range (SR) connectivity links and long-range (LR) influences. In IN the LR are the influences of dependency links while in k -core we find here that for k = 1 and k = 2 the influences are SR and in contrast for $k\unicode{x2A7E}3$ the influence is LR. In addition, analytical arguments for a universal hyper-scaling relation for the fractal fluctuation dimension of the k -core giant component and for IN as well as for any mixed-order transition are established. Our analysis enhances the comprehension of k -core percolation and supports the generalization of the concept of fractal fluctuations in mixed-order phase transitions.

Abstract Background The clinical and virological course of patients with coronavirus disease 2019 (COVID-19) are lacking. We aimed to describe the clinical and virological characteristics of COVID-19 patients from 10 designated hospitals in 10 cities of Jiangsu province, China. The factors associated with the clearance of SARS-CoV-2 were investigated. Methods A total of 328 hospitalized patients with COVID-19 were retrospectively recruited. The epidemiological, clinical, laboratory, radiology and treatment data were collected. The associated factors of SARS-CoV-2 clearance were analyzed. Results The median duration of hospitalization was 16.0 days (interquartile range [IQR] 13.0–21.0 days). On multivariate Cox regression analysis, age > 60 years (hazard ratio [HR] 0.643, 95% confidence interval [CI] 0.454–0.911, P = 0.013) was associated with the delayed SARS-CoV-2 clearance, while the atomized inhalation of interferon α-2b could improve the clearance of SARS-CoV-2 (HR, 1.357, 95% CI 1.050–1.755, P = 0.020). Twenty-six (7.9%) patients developed respiratory failure and 4 (1.2%) patients developed ARDS. Twenty (6.1%) patients were admitted to the ICU, while no patient was deceased. Conclusions Our study found that age > 60 years was associated with the delayed SARS-CoV-2 clearance, while treated with atomized inhalation of interferon α-2b could promote the clearance of SARS-CoV-2.

The macro social influence is recognized as a non-negligible ingredient in innovation propagation: more adopters in the network lead to a higher adoption tendency for the rest individuals. A recent study to incorporate such a crucial mechanism shows that sufficient intensity of macro-level social influence can cause a change from a continuous to discontinuous transition, further indicating the existence of a tricritical point. Although network localization strength determines the tricritical point, it remains unclear what network quantities govern the performance of localization in regulating innovation diffusion. To address this issue, we herein consider the model incorporating both the micro- and macro-levels social influence. We present a dynamic message-passing method to analytically treat both the outbreak threshold and recovered population, and validate the predictions through agent-based simulations. Extensive analysis on the classical synthetic networks shows that sparsely available connections, and relatively heterogeneous degree distribution, either assortative or extremely disassortative configurations are favorable for continuous transition. In such cases, the employed network can yield a strong localization effect so that the innovation is trapped in the configurations composed of the hubs with high non-backtracking centrality. We further explore the dependence of both tricritical point and localization strength on three structural quantities: network density, heterogeneity, and assortativity, which gives a clear physical picture of the joint effects of the three structure quantities on the localization strength. Finally, we conclude that the core-periphery structure, being sensitive to the change of the three structure quantities, essentially determines localization strength, and further regulates the phase transition.

This study investigates the dynamic trading network structure of the international crude oil and gas market from year 2012 to 2017. We employed the dynamical similarity analysis at different time scales by inducing a multiscale embedding for dimensionality reduction. This analysis quantifies the effect of a global event on the dependencies and correlation stability at both the country and world level, which covers the top 53 countries. The response of China’s trading structure toward events after the unexpected 2014 price drop is compared with other major traders. China, as the world’s largest importing country, lacks strong stability under global events and could be greatly affected by a supply shortage, especially in the gas market. The trend of multi-polarization on the market share gives a chance for China to construct closer relationships with more stable exporters and join in the trade loop of major countries to improve its position in the energy trading networks. The hidden features of trade correlation may provide a deeper understanding of the robustness of relationship and risk resistance.

Limited data are available for clinical characteristics of patients with coronavirus disease 2019 (COVID-19) outside Wuhan. This study aimed to describe the clinical characteristics of COVID-19 and identify the risk factors for severe illness of COVID-19 in Jiangsu province, China. Clinical data of hospitalized COVID-19 patients were retrospectively collected in 8 hospitals from 8 cities of Jiangsu province, China. Clinical findings of COVID-19 patients were described and risk factors for severe illness of COVID-19 were analyzed. By Feb 10, 2020, 202 hospitalized patients with COVID-19 were enrolled. The median age of patients was 44.0 years (interquartile range, 33.0-54.0). 55 (27.2%) patients had comorbidities. At the onset of illness, the common symptoms were fever (156 [77.2%]) and cough (120 [59.4%]). 66 (32.7%) patients had lymphopenia. 193 (95.5%) patients had abnormal radiological findings. 11 (5.4%) patients were admitted to the intensive care unit and none of the patients died. 23 (11.4%) patients had severe illness. Severe illness of COVID-19 was independently associated with body mass index (BMI) ≥ 28 kg/m2 (odds ratio [OR], 9.219; 95% confidence interval [CI], 2.731 to 31.126; P