Results 11 to 20 of about 1,302,221 (298)
Metrics for Probabilistic Geometries [PDF]
CoRR, 2014 We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian ...
Tosi, Alessandra +3 more
openaire +5 more sources
Metric geometry tools for automatic structure phase map generation [PDF]
, 2023 Extracting a phase map that provides a hierarchical summary of high-throughput experiments is a long-standing bottleneck for the modern goal of achieving automation and acceleration in material discovery.
Lilo D, Pozzo, Karen, Li, Kiran, Vaddi
core +1 more source
Metric Algebraic Geometry [PDF]
Oberwolfach Seminar: Metric Algebraic Geometry 2322bOberwolfach Seminar: Metric Algebraic Geometry 2322bMetric algebraic geometry combines concepts from algebraic geometry and differential geometry.
Sturmfels, Bernd +2 more
core +3 more sources
Metric geometry of spaces of persistence diagrams. [PDF]
J Appl Comput TopolAbstractPersistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a family of functors $${\mathcal {D}}_p$$ D p
Che M +3 more
europepmc +5 more sources
Application of the Fisher-Rao metric to ellipse detection [PDF]
, 2007 The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is
Stephen J. Maybank, Maybank, Stephen J.
core +1 more source
Geometry of the Cassinian Metric and Its Inner Metric [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2015 12 ...
Ibragimov, Zair +3 more
openaire +2 more sources
A Fisher-Rao metric for paracatadioptric images of lines [PDF]
, 2012 In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but the image is severely distorted.
Maybank, Stephen J. +2 more
core +1 more source
Asymptotic Geometry of the Hitchin Metric [PDF]
Communications in Mathematical Physics, 2019 We study the asymptotics of the natural $L^2$ metric on the Hitchin moduli space with group $G = \mathrm{SU}(2)$. Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore \cite{gmn13}, is that on the regular part of the Hitchin system, this metric is well-approximated by the semiflat metric from \cite{gmn13 ...
Rafe Mazzeo +3 more
openaire +3 more sources
General teleparallel metrical geometries
International Journal of Geometric Methods in Modern Physics, 2023 In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity.
Adak, Muzaffer +3 more
openaire +8 more sources
Finslerian Viewpoint to the Rectifying, Normal and Osculating Curves [PDF]
, 2022 The theory of Finsler metric was introduced by Paul Finsler, in 1918. The author defines this metric using the Minkowski norm instead of the inner product. Therefore, this geometry is a more general metric and includes the Riemannian metric.
Ekmekci, F. Nejat +2 more
core +1 more source