Can Non‐Euclidean Distances Improve Spatial Interpolation of Precipitation in Mountainous Regions?
Sign Up to like & getrecommendations! Published in 2025 at "International Journal of Climatology"
DOI: 10.1002/joc.70071
Abstract: Mountainous regions have complex terrain that affects precipitation distribution. However, conventional Euclidean distances account only for horizontal separation and neglect vertical variations in such terrain. The non‐Euclidean distance metrics, presented herein, aim to better represent… read more here.
Keywords: euclidean distance; non euclidean; precipitation; mountainous regions ... See more keywords
Cohomology of Fuchsian groups and non-Euclidean crystallographic groups
Sign Up to like & getrecommendations! Published in 2022 at "manuscripta mathematica"
DOI: 10.1007/s00229-022-01369-z
Abstract: For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology. read more here.
Keywords: group; cohomology fuchsian; euclidean crystallographic; cohomology ... See more keywords
The sphere packing problem into bounded containers in three-dimension non-Euclidean space
Sign Up to like & getrecommendations! Published in 2018 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2018.11.450
Abstract: Abstract This paper deals with the problem of optimal packing a given number of equal spheres into different closed sets. We consider the problem both in three-dimensional Euclidean and non-Euclidean spaces. The special algorithm based… read more here.
Keywords: space; problem bounded; non euclidean; problem ... See more keywords
Computing the signatures of subgroups of non-Euclidean crystallographic groups
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2017.01.017
Abstract: Abstract A (planar and cocompact) non-Euclidean crystallographic (NEC) group Δ is a subgroup of the group of, conformal and anti-conformal, isometries of the hyperbolic plane H 2 such that H 2 / Δ is compact.… read more here.
Keywords: subgroups non; computing signatures; euclidean crystallographic; crystallographic groups ... See more keywords
Generalised rigid body motions in non-Euclidean planes with applications to global rigidity
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2022.126259
Abstract: A bar-joint framework (G, p) in a (non-Euclidean) real normed plane X is the combination of a finite, simple graph G and a placement p of the vertices in X . A framework (G, p)… read more here.
Keywords: non euclidean; global rigidity; rigidity; rigid body ... See more keywords
Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures
Sign Up to like & getrecommendations! Published in 2024 at "Machine Learning"
DOI: 10.1088/2632-2153/adf375
Abstract: The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently… read more here.
Keywords: geometric topological; machine learning; non euclidean; modern machine ... See more keywords
Topological Hyperbolic Lattices.
Sign Up to like & getrecommendations! Published in 2020 at "Physical review letters"
DOI: 10.1103/physrevlett.125.053901
Abstract: Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general theory of relativity. Notably, an infinite… read more here.
Keywords: non euclidean; geometry; topological hyperbolic; hyperbolic lattices ... See more keywords
Fractional Excitations in Non-Euclidean Elastic Plates.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review letters"
DOI: 10.1103/physrevlett.127.098001
Abstract: We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of charge-1/2 solitons… read more here.
Keywords: euclidean elastic; non euclidean; fractional excitations; elastic plates ... See more keywords
Observation of Topological p-Orbital Disclination States in Non-Euclidean Acoustic Metamaterials.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review letters"
DOI: 10.1103/physrevlett.129.154301
Abstract: Disclinations-topological defects ubiquitously existing in various materials-can reveal the intrinsic band topology of the hosting material through the bulk-disclination correspondence. In low-dimensional materials and nanostructure such as graphene and fullerenes, disclinations yield curved surfaces and… read more here.
Keywords: topology; disclination; physics; acoustic metamaterials ... See more keywords
Deep Wavelet Neural Process: Modeling Stochastic Variation of Non-Euclidean Functional Data for Manufacturing Quality Inference
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Transactions on Industrial Informatics"
DOI: 10.1109/tii.2023.3331094
Abstract: Modeling and inferring the intricate stochastic variations of the manufacturing quality still remain a significant challenge, especially when dealing with non-Euclidean functional data, which emerge ubiquitous in manufacturing processes. To address this issue, this study… read more here.
Keywords: manufacturing quality; euclidean functional; non euclidean; wavelet ... See more keywords
A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2018.2870353
Abstract: We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity, as well as practical faster convergence. Under mild… read more here.
Keywords: non euclidean; matrix; framework non; non convex ... See more keywords