Search for: All records

The ability to detect and count certain substructures in graphs is important for solving many tasks on graph-structured data, especially in the contexts of computa- tional chemistry and biology as well as social network analysis. Inspired by this, we propose to study the expressive power of graph neural networks (GNNs) via their ability to count attributed graph substructures, extending recent works that examine their power in graph isomorphism testing and function approximation. We distinguish between two types of substructure counting: induced-subgraph-count and subgraph-count, and establish both positive and negative answers for popular GNN architectures. Specifically, we prove that Message Passing Neural Networks (MPNNs), 2-Weisfeiler-Lehman (2-WL) and 2-Invariant Graph Networks (2-IGNs) cannot perform induced-subgraph-count of any connected substructure consisting of 3 or more nodes, while they can perform subgraph-count of star-shaped sub- structures. As an intermediary step, we prove that 2-WL and 2-IGNs are equivalent in distinguishing non-isomorphic graphs, partly answering an open problem raised in [38]. We also prove positive results for k-WL and k-IGNs as well as negative results for k-WL with a finite number of iterations. We then conduct experiments that support the theoretical results for MPNNs and 2-IGNs. Moreover, motivated by substructure counting and inspired by [45], we propose the Local Relational Pooling model and demonstrate that it is not only effective for substructure counting but also able to achieve competitive performance on molecular prediction tasks. 

Split thickness skin grafts (STSGs) are one of the standard treatments available for full thickness wound repair when full thickness grafts (FTGs) are not viable, such as in the case of wounds with large surface areas. The donor sites of STSGs may be harvested repeatedly, but STSG transplants are still limited by insufficient blood supply at the early stages of wound healing. Prevascularized human mesenchymal stem cell (hMSC) sheets may accelerate wound healing and improve regeneration by providing pre-formed vessel structures and angiogenic factors to overcome this limitation. This book chapter provides the protocol of co-culturing hMSCs and endothelial cells to attain a prevascularized hMSC cell sheet (PHCS). The protocols for implantation of the prevascularized stem cell sheet for full thickness skin wound repair in a rat autologous skin graft model as well as the evaluation of the wound healing effects are also provided.