Identifying critical higher-order interactions in complex networks.

Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Proximity-Based Compression for Network Embedding.

Network embedding that encodes structural information of graphs into a low-dimensional vector space has been proven to be essential for network analysis applications, including node classification and community detection. Although recent methods show promising performance for various applications, graph embedding still has some challenges; either the huge size of graphs may hinder a direct application of the existing network embedding method to them, or they suffer compromises in accuracy from locality and noise. In this paper, we propose a novel Network Embedding method, NECL, to generate embedding more efficiently or effectively. Our goal is to answer the following two questions: 1) Does the network Compression significantly boost Learning? 2) Does network compression improve the quality of the representation? For these goals, first, we propose a novel graph compression method based on the neighborhood similarity that compresses the input graph to a smaller graph with incorporating local proximity of its vertices into super-nodes; second, we employ the compressed graph for network embedding instead of the original large graph to bring down the embedding cost and also to capture the global structure of the original graph; third, we refine the embeddings from the compressed graph to the original graph. NECL is a general meta-strategy that improves the efficiency and effectiveness of many state-of-the-art graph embedding algorithms based on node proximity, including DeepWalk, Node2vec, and LINE. Extensive experiments validate the efficiency and effectiveness of our method, which decreases embedding time and improves classification accuracy as evaluated on single and multi-label classification tasks with large real-world graphs.

Differential transcriptional regulation by alternatively designed mechanisms: A mathematical modeling approach.

Cells maintain cellular homeostasis employing different regulatory mechanisms to respond external stimuli. We study two groups of signal-dependent transcriptional regulatory mechanisms. In the first group, we assume that repressor and activator proteins compete for binding to the same regulatory site on DNA (competitive mechanisms). In the second group, they can bind to different regulatory regions in a noncompetitive fashion (noncompetitive mechanisms). For both competitive and noncompetitive mechanisms, we studied the gene expression dynamics by increasing the repressor or decreasing the activator abundance (inhibition mechanisms), or by decreasing the repressor or increasing the activator abundance (activation mechanisms). We employed delay differential equation models. Our simulation results show that the competitive and noncompetitive inhibition mechanisms exhibit comparable repression effectiveness. However, response time is fastest in the noncompetitive inhibition mechanism due to increased repressor abundance, and slowest in the competitive inhibition mechanism by increased repressor level. The competitive and noncompetitive inhibition mechanisms through decreased activator abundance show comparable and moderate response times, while the competitive and noncompetitive activation mechanisms by increased activator protein level display more effective and faster response. Our study exemplifies the importance of mathematical modeling and computer simulation in the analysis of gene expression dynamics.