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Hyperbolic geometry is a type of non-Euclidean geometry that arose historically when mathematicians tried to simplify the axioms of Euclidean geometry, and instead discovered unexpectedly that changing one of the axioms to its negation actually produced a consistent theory.
Hace 4 días · In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.
Hace 1 día · In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
Hace 1 día · A Riemannian metric makes it possible to define many geometric notions, including angles, lengths of curves, areas of surfaces, higher-dimensional analogues of area ( volumes, etc.), extrinsic curvature of submanifolds, and the intrinsic curvature of the manifold itself.
Hace 5 días · Our study also offers atlas options for constructing more sophisticated hierarchical networks and explains the association between key brain regions and NDD. Conclusion: MHNet leverages multi-view feature learning from both Euclidean and non-Euclidean spaces, incorporating high-order information from BFNs to enhance NDD classification performance.
Hace 3 días · By the late 19th century the hegemony of Euclidean geometry had been challenged by non-Euclidean geometry and projective geometry. The first notable attempt to reorganize the study of geometry was made by the German mathematician Felix Klein and published at Erlangen in 1872.
Hace 2 días · Graph Neural Networks (GNNs) have revolutionized the way we handle non-Euclidean structured data. From social networks to chemical compound analysis, GNNs are becoming an indispensable tool for data scientists and researchers. PyTorch Geometric (PyG) is a library built upon PyTorch, specifically designed to write and train GNNs efficiently and ...
