arXiv subjects
Publications and source records attributed to Junsheng Zhang.
We show that on a compact Kähler manifold all real $(1,1)$-classes admitting solutions to the supercritical deformed Hermitian-Yang-Mills equation form a both open and closed subset of those which satisfy the numerical condition proposed by Collins-Jacob-Yau. More importantly, we show by examples that it can be a proper subset. This disproves a conjecture made by Collins-Jacob-Yau.
We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kähler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein.
We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact Kähler manifolds $(X,ω)$, where $X$ is the complement of a divisor in a compact Kähler manifold and we impose some conditions on the cohomology class and the asymptotic behaviour of the Kähler form $ω$. We introduce the notion of stability with respect to a pair of $(1,1)$-classes which generalizes the standard slope stability. We prove that this new stability condition is both sufficient and necessary for the existence of projectively Hermitian-Yang-Mills metrics in our setting.
Knowledge graphs (KGs) on COVID-19 have been constructed to accelerate the research process of COVID-19. However, KGs are always incomplete, especially the new constructed COVID-19 KGs. Link prediction task aims to predict missing entities for (e, r, t) or (h, r, e), where h and t are certain entities, e is an entity that needs to be predicted and r is a relation. This task also has the potential to solve COVID-19 related KGs' incomplete problem. Although various knowledge graph embedding (KGE) approaches have been proposed to the link prediction task, these existing methods suffer from the limitation of using a single scoring function, which fails to capture rich features of COVID-19 KGs. In this work, we propose the MDistMult model that leverages multiple scoring functions to extract more features from existing triples. We employ experiments on the CCKS2020 COVID-19 Antiviral Drugs Knowledge Graph (CADKG). The experimental results demonstrate that our MDistMult achieves state-of-the-art performance in link prediction task on the CADKG dataset
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of topological centrality (TC) reflecting the topological positions of nodes and edges in general networks, and proposes an approach to calculating the topological centrality. The proposed topological centrality is then used to discover communities and build the backbone network. Experiments and applications on research network show the significance of the proposed approach.