Signals as submanifolds, and configurations of points

2024/08/27 by Tatyana Barron, Barron, Tatyana, Spencer Kelly +3 · 2 citations
Business, Management and Accounting · Engineering · Physics and Astronomy · #Advanced Optical Imaging Technologies #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optical and Acousto-Optic Technologies #Optics and Image Analysis

paper · pdf · doi:10.48550/arxiv.2408.15375

openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the purposes of abstract theory of signal propagation, a signal is a submanifold of a Riemannian manifold. We obtain energy inequalities, or upper bounds, lower bounds on energy in a number of specific cases, including parameter spaces of Gaussians and spaces of configurations of points. We discuss the role of time as well as graph embeddings.

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