Pseudo-Riemannian geometry encodes information geometry in optimal transport. [PDF]
Inf Geom, 2022 Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from ...
Wong TL, Yang J.
europepmc +2 more sources
Geometry without topology as a new conception of geometry [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points).
Yuri A. Rylov
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Decoding Multi-Class Motor Imagery and Motor Execution Tasks Using Riemannian Geometry Algorithms on Large EEG Datasets [PDF]
Sensors, 2023 The use of Riemannian geometry decoding algorithms in classifying electroencephalography-based motor-imagery brain–computer interfaces (BCIs) trials is relatively new and promises to outperform the current state-of-the-art methods by overcoming the noise
Zaid Shuqfa +2 more
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Motor Imagery EEG Classification Based on Decision Tree Framework and Riemannian Geometry. [PDF]
Comput Intell Neurosci, 2019 This paper proposes a novel classification framework and a novel data reduction method to distinguish multiclass motor imagery (MI) electroencephalography (EEG) for brain computer interface (BCI) based on the manifold of covariance matrices in a ...
Guan S, Zhao K, Yang S.
europepmc +2 more sources
A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception [PDF]
Vision, 2018 We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size⁻distance relationship of retinal images associated with the optics of the human eye.
Peter D. Neilson +2 more
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Non-Riemannian geometry of M-theory [PDF]
Journal of High Energy Physics, 2019 We construct a background for M-theory that is moduli free. This background is then shown to be related to a topological phase of the E8(8) exceptional field theory (ExFT).
David S. Berman +2 more
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Dynamic graphs, community detection, and Riemannian geometry [PDF]
Applied Network Science, 2018 A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network.
Craig Bakker +2 more
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Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry [PDF]
Neural Information Processing Systems, 2023 Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach involves deriving the
Yong-Hyun Park +4 more
semanticscholar +1 more source
On the geometry of the tangent bundle with gradient Sasaki metric [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita
Lakehal Belarbi, Hichem Elhendi
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Excitonic topology and quantum geometry in organic semiconductors [PDF]
Nature CommunicationsExcitons drive the optoelectronic properties of organic semiconductors which underpin devices including solar cells and light-emitting diodes. Here we show that excitons can exhibit topologically non-trivial states protected by inversion symmetry and ...
Wojciech J. Jankowski +3 more
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