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With the development of graph neural network, researchers begin to use bipartite graph to model user-item interactions for recommendation. It is worth noting that most of graph recommendation models represent users and items in the real-valued space, which ignore the rich representational capacity of the non-real space. Besides, the simplicity and symmetry of the inner product make it ineffectively capture the intricate antisymmetric relations between users and items in interaction modeling. In this paper, based on the framework of graph neural network, we propose Graph Collaborative Filtering for recommendation in Complex and Quaternion space (GCFC and GCFQ respectively). Specifically, we first use complex embeddings or quaternion embeddings to initialize users and items. Then, the Hermitian product (for GCFC) or Hamilton product (for GCFQ) and embedding propagation layers are used to further enrich the embeddings of users and items. As such, we can obtain both latent inter-dependencies and intra-dependencies between components of users and items. Finally, we aggregate the embeddings of different propagation layers and use the Hermitian or Hamilton product with inner product to obtain the intricate antisymmetric relations between users and items. We have carried out extensive experiments on four real-world datasets to verify the effectiveness of GCFC and GCFQ. [ABSTRACT FROM AUTHOR]

Mucus secretion and its composition are vital in the maintenance of airway health, among which hypoxia-inducible factors (HIFs) are thought to be involved in the regulation of mucin synthesis and regulation. Nasal mucus composition difference between healthy individuals and chronic rhinosinusitis (CRS) patients may contribute to the pathology of chronic nasal diseases, but so far, their role has yet to be completely understood. Nasal biopsy specimens were obtained from 24 healthy subjects and 99 patients with CRS without (CRSsNP, n=36) or with (CRSwNP, n=63) nasal polyps. Immunohistochemical (IHC) and immunofluorescent (IF) staining, quantitative real-time PCR, and western blot were performed to compare the nasal mucus composition between the subjects. Areas of the serous gland and mucous gland were both significantly increased in CRSsNP patients. In CRSwNP patients, a decrease in submucosal gland density and a marked increase in goblet cells were observed. The major gel-forming mucins in the sinonasal mucosa of CRSsNP and CRSwNP are MUC5B and MUC5AC respectively. Mucous cells are found in a higher proportion in both CRSsNP and CRSwNP. The proportion of MUC5AC-positive goblet cells was increased in CRSwNP. The mRNA level of HIF-2α was significantly increased in CRS, and both HIF-1α and HIF-2α were expressed in serous cell but not mucous cell. Over secretion and altered composition of mucus are observed in sinonasal mucosa of CRS, which was mainly associated with glandular hyperplasia in CRSsNP and goblet cell hyperplasia in CRSwNP. Mucus abnormality compromised both non-specific and specific antimicrobial capabilities in the sinonasal mucosa. HIF expression may contribute to differences in mucin synthesis and serous gland regulation, which needs further investigation to understand the pathology of CRS. [ABSTRACT FROM AUTHOR]