Researchers have solved a long-standing problem in topology by helping classify four-dimensional shapes (4-manifolds) that ...

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, ...

I've long been fascinated by the fundamental mystery of our universe's origin. In my work, I explore an alternative to the ...

Maggie Miller, University of Texas at Austin I study three-manifolds, or spaces that look like 3D Euclidean space when you zoom in but that have more structure when you zoom out. An analogy would ...

ABSTRACT: In this paper, a class of Choquard equation with Hardy potential in the whole space ℝ N will be considered, where the parameters p , q and α in the convolution-nonlinearity term are under a ...

Abstract: Graph neural networks (GNNs), grounded in spatial or spectral domains, have achieved remarkable success in learning graph representations in Euclidean space. Recent advances in spatial GNNs ...

Theoretical physicists James Hartle and Stephen Hawking, for example, proposed that rather than having a strict beginning as ...

Additionally, Euclidean space is inadequate for capturing the hierarchical structure, which limits the performance of the model on complex data. To address these issues, we propose a Structural-Aware ...

Although the telescope is just getting started on its mission, it has already delivered some impressive snapshots of the dark ...

But that may as well have been the prelude to the role that would enable his early retirement — setting up the publishing ...