Relative, local and global dimension in complex networks

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. To take into account locality, finiteness and discreteness, dynamical processes can be used to probe the space geometry and define its dimension. Here we show that each point in space can be assigned a relative dimension with respect to the source of a diffusive process, a concept that provides a scale-dependent definition for local and global dimension also applicable to networks. To showcase its application to physical systems, we demonstrate that the local dimension of structural protein graphs correlates with structural flexibility, and the relative dimension with respect to the active site uncovers regions involved in allosteric communication. In simple models of epidemics on networks, the relative dimension is predictive of the spreading capability of nodes, and identifies scales at which the graph structure is predictive of infectivity.

Uniform Pooling for Graph Networks

The graph convolution network has received a lot of attention because it extends the convolution to non-Euclidean domains. However, the graph pooling method is still less concerned, which can learn coarse graph embedding to facilitate graph classification. Previous pooling methods were based on assigning a score to each node and then pooling only the highest-scoring nodes, which might throw away whole neighbourhoods of nodes and therefore information. Here, we proposed a novel pooling method UGPool with a new point-of-view on selecting nodes. UGPool learns node scores based on node features and uniformly pools neighboring nodes instead of top nodes in the score-space, resulting in a uniformly coarsened graph. In multiple graph classification tasks, including the protein graphs, the biological graphs and the brain connectivity graphs, we demonstrated that UGPool outperforms other graph pooling methods while maintaining high efficiency. Moreover, we also show that UGPool can be integrated with multiple graph convolution networks to effectively improve performance compared to no pooling.

Drug–target affinity prediction using graph neural network and contact maps

Prediction of drug–target affinity by constructing both molecule and protein graphs.

3D Graphical Representation of Protein Sequences Based on Conformational Parameters of Amino Acids

Based on the helix and-sheet and the-turn conformational parameters, and and , of the 20 amino acids, we propose a new 3D graphical representation of protein sequence without circuit or degeneracy, which may reflect the innate structure of the protein sequence. Then the numerical characterizations of protein graphs, the leading eigenvalues of the L/L matrices associated with the graphical curves for protein sequences, was utilized as descriptors to analyze the similarity/dissimilarity of the nine ND5 protein sequences.