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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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2 results for “hyperballs”

Explicit Formulae to Interchangeably use Hyperplanes and Hyperballs using Inversive Geometrycs.LG

The paper shows how to use hyperplanes and hyperballs interchangeably using inversive geometry.

problem Tackles the interchangeability of hyperplanes and hyperballs in discriminative boundaries.

method Applies inversive geometry to transform Euclidean data into spherical data and back, providing explicit formulae.

result Shows a duality between hyperspherical caps and hyperballs, providing explicit formulae to map between them.

inversive geometry hyperplanes hyperballs spherical data machine learning

2024-05-28abs ↗pdf ↗

Existence and nonexistence results for eigenfunctions of the Laplacian in unbounded domains of H^nmath.DG

We investigate, for the Laplacian operator, the existence and nonexistence of eigenfunctions of eigenvalue between zero and the first eigenvalue of the hyperbolic space H^n, for unbounded domains of H^n. If a domain is contained in a horoball, we prove that there is no positive bounded eigenfunction that vanishes on th…

2013-10-11abs ↗pdf ↗