It is shown how solutions to the Tzitzéica equation can be used to construct a family of (pseudo) hyper-complex metrics in four dimensions.
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4 results for “Hyper-complex”
QGNN uses Quaternion space for better graph and node classification.
problem Existing GNN methods struggle with Euclidean vector space limitations.
method Proposes QGNN to learn graph representations in Quaternion space.
result Obtains state-of-the-art results on graph and node classification benchmarks.
In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument principle to establish a natural link between the fundamental solutions of …
In recent years, hyper-complex deep networks (such as complex-valued and quaternion-valued neural networks) have received a renewed interest in the literature. They find applications in multiple fields, ranging from image reconstruction to 3D audio processing. Similar to their real-valued counterparts, quaternion neura…