This study aims to unravel the resource allocation problem (RAP) by using a consensus-based distributed optimization algorithm under dynamic event-triggered (DET) strategies. Firstly, based on the multi-agent consensus approach, a novel one-to-all DET strategy is presented to solve the RAP. Secondly, the proposed one-to-all DET strategy is extended to a one-to-one DET strategy, where each agent transmits its state asynchronously to its neighbors. Furthermore, it is proven that the proposed two types of DET strategies do not have Zeno behavior. Finally, numerical simulations are provided to validate and illustrate the effectiveness of the theoretical results.

Background: Single-cell RNA sequencing is an advanced technology that makes it possible to unravel cellular heterogeneity and conduct single-cell analysis of gene expression. However, owing to technical defects, many dropout events occur during sequencing, bringing about adverse effects on downstream analysis. Methods: To solve the dropout events existing in single-cell RNA sequencing, we propose an imputation method scTSSR-D, which recovers gene expression by two-side self-representation and dropout information. scTSSR-D is the first global method that combines a partial imputation method to impute dropout values. In other words, we make full use of genes, cells, and dropout information when recovering the gene expression. objective: scTSSR-D is the first global method that combines a partial imputation method to impute dropout values. In other words, we make full use of genes, cells, and dropout information when recovering the gene expression. Results: The results show scTSSR-D outperforms other existing methods in the following experiments: capturing the Gini coefficient and gene-to-gene correlations observed in single-molecule RNA fluorescence in situ hybridization, down-sampling experiments, differential expression analysis, and the accuracy of cell clustering. Conclusion: scTSSR-D is a more stable and reliable method to recover gene expression. Meanwhile, our method improves even more dramatically on large datasets compared to the result of existing methods. result: The result shows that scTSSR-D outperforms other existing methods in the following experiments: capturing the Gini coefficient and gene-to-gene correlations observed in single-molecule RNA fluorescence in situ hybridization (FISH), down-sampling experiments, DE analysis, and the accuracy of cell clustering. other: We make full use of genes, cells, and dropout information when recovering the gene expression.