Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a positive-stranded single-stranded RNA virus with an envelope frequently altered by unstable genetic material, making it extremely difficult for vaccines, drugs, and diagnostics to work. Understanding SARS-CoV-2 infection mechanisms requires studying gene expression changes. Deep learning methods are often considered for large-scale gene expression profiling data. Data feature-oriented analysis, however, neglects the biological process nature of gene expression, making it difficult to describe gene expression behaviors accurately. In this article, we propose a novel scheme for modeling gene expression during SARS-CoV-2 infection as networks (gene expression modes, GEM), to characterize their expression behaviors. On this basis, we investigated the relationships among GEMs to determine SARS-CoV-2's core radiation mode. Our final experiments identified key COVID-19 genes by gene function enrichment, protein interaction, and module mining. Experimental results show that ATG10, ATG14, MAP1LC3B, OPTN, WDR45, and WIPI1 genes contribute to SARS-CoV-2 virus spread by affecting autophagy.

Summary Behavior is autonomous, convergent, and uncertain, which brings challenges to the modeling of social network behavior spread. In this article, we propose a behavior spread model based on group cohesion under uncertain environments. First, for behavioral convergence, we define group cohesion to quantify the convergent effects of group. Second, based on the game theory to model the autonomy of behavior, according to the characteristics of the game payoffs changing with time and the depth of spread, and integrating group cohesion, a dynamic game payoffs calculation method is designed. Finally, aiming at the uncertainty of behavior, a group behavior spread model based on random utility theory is established. Experiments on multiple real social network behavior spread datasets demonstrate the effectiveness of the proposed model in modeling and predicting behavior spread processes under uncertain environments.

Let c, k be two positive integers. Given a graph $$G=(V,E)$$ , the c-Load Coloring problem asks whether there is a c-coloring $$\varphi : V \rightarrow [c]$$ such that for every $$i \in [c]$$ , there are at least k edges with both endvertices colored i. Gutin and Jones (Inf Process Lett 114:446–449, 2014) studied this problem with $$c=2$$ . They showed 2-Load Coloring to be fixed-parameter tractable (FPT) with parameter k by obtaining a kernel with at most 7k vertices. In this paper, we extend the study to any fixed c by giving both a linear-vertex and a linear-edge kernel. In the particular case of $$c=2$$ , we obtain a kernel with less than 4k vertices and less than $$6k+(3+\sqrt{2})\sqrt{k}+4$$ edges. These results imply that for any fixed $$c\ge 2$$ , c-Load Coloring is FPT and the optimization version of c-Load Coloring (where k is to be maximized) has an approximation algorithm with a constant ratio.