This paper investigates the average controllability of Laplacian dynamical networks characterized by an exponential degree distribution. We introduce a novel configuration network model with an exponential degree distribution, incorporating a degree distribution parameter to adjust the heterogeneity of the distribution. We thoroughly examine the impact of degree distribution and degree correlation on average controllability. Our results reveal that increased heterogeneity in degree distribution tends to enhance average controllability, particularly when edges connect nodes with higher degrees. Moreover, networks with high assortativity exhibit improved average controllability. Building on these findings, we propose two effective strategies for optimizing average controllability. These strategies offer valuable guidance for the design of optimal complex networks in practical settings.

The vigorous development of the digital economy brings new opportunities for enterprise digital transformation. This article proposes a knowledge-sharing-based digital consulting capacity platform, focusing on important digital transformation concerns in the consulting profession. By sorting out the practical problems and challenges, the optimization path of constructing the digital consulting capability-sharing platform for the intelligent city field is explored. Seven business centers are built to gather digital resources such as policies, industry trends, and market information. Knowledge precipitation is more convenient and comprehensive, and business management is more scientific. This paper analyzes the framework of the digital consulting capability platform in detail. Furthermore, this paper carries out the actual deployment and verifies the effectiveness of the digital consulting capability platform scheme based on knowledge sharing.

MOTIVATION: Automated function prediction (AFP) of proteins is a large-scale multi-label classification problem. Two limitations of most network-based methods for AFP are (i) a single model must be trained for each species and (ii) protein sequence information is totally ignored. These limitations cause weaker performance than sequence-based methods. Thus, the challenge is how to develop a powerful network-based method for AFP to overcome these limitations. RESULTS: We propose DeepGraphGO, an end-to-end, multispecies graph neural network-based method for AFP, which makes the most of both protein sequence and high-order protein network information. Our multispecies strategy allows one single model to be trained for all species, indicating a larger number of training samples than existing methods. Extensive experiments with a large-scale dataset show that DeepGraphGO outperforms a number of competing state-of-the-art methods significantly, including DeepGOPlus and three representative network-based methods: GeneMANIA, deepNF and clusDCA. We further confirm the effectiveness of our multispecies strategy and the advantage of DeepGraphGO over so-called difficult proteins. Finally, we integrate DeepGraphGO into the state-of-the-art ensemble method, NetGO, as a component and achieve a further performance improvement. AVAILABILITY AND IMPLEMENTATION: https://github.com/yourh/DeepGraphGO. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.