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Table representation of search results timeline featuring number of search results per year.

Year Number of Results
1988 1
1990 1
1995 1
1996 1
1999 1
2001 1
2002 1
2005 2
2010 1
2012 1
2013 2
2014 2
2015 4
2016 1
2017 2
2018 2
2019 2
2020 7
2021 7
2022 8
2023 2
2024 1

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48 results

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Page 1
What geometric visual hallucinations tell us about the visual cortex.
Bressloff PC, Cowan JD, Golubitsky M, Thomas PJ, Wiener MC. Bressloff PC, et al. Neural Comput. 2002 Mar;14(3):473-91. doi: 10.1162/089976602317250861. Neural Comput. 2002. PMID: 11860679
Here, we summarize a theory of their origin in visual cortex (area V1), based on the assumption that the form of the retino-cortical map and the architecture of V1 determine their geometry. (A much longer and more detailed mathematical version has been published in Philoso …
Here, we summarize a theory of their origin in visual cortex (area V1), based on the assumption that the form of the retino-cortical map and …
Geodesic motion in Euclidean Schwarzschild geometry.
Battista E, Esposito G. Battista E, et al. Eur Phys J C Part Fields. 2022;82(12):1088. doi: 10.1140/epjc/s10052-022-11070-w. Epub 2022 Dec 2. Eur Phys J C Part Fields. 2022. PMID: 36474711 Free PMC article.
This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the equatorial plane. The explicit form of geodesic motion is obtained in terms of incomplete elliptic integrals of first, second and th …
This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the …
Arrangements of Approaching Pseudo-Lines.
Felsner S, Pilz A, Schnider P. Felsner S, et al. Discrete Comput Geom. 2022;67(2):380-402. doi: 10.1007/s00454-021-00361-w. Epub 2022 Jan 22. Discrete Comput Geom. 2022. PMID: 35221404 Free PMC article.

We consider arrangements of n pseudo-lines in the Euclidean plane where each pseudo-line i is represented by a bi-infinite connected x-monotone curve fi(x) , x R , such that for any two pseudo-lines i and j with i < j , the function x fj(x) - fi(x) is monotonical

…
We consider arrangements of n pseudo-lines in the Euclidean plane where each pseudo-line i is represented by a bi-infinite con …
Topological Hyperbolic Lattices.
Yu S, Piao X, Park N. Yu S, et al. Phys Rev Lett. 2020 Jul 31;125(5):053901. doi: 10.1103/PhysRevLett.125.053901. Phys Rev Lett. 2020. PMID: 32794858
Notably, an infinite number of regular tessellations in hyperbolic geometry-hyperbolic lattices-are expected to extend Euclidean Bravais lattices and the consequent wave phenomena to non-Euclidean geometry. ...We demonstrate that the proposed platforms …
Notably, an infinite number of regular tessellations in hyperbolic geometry-hyperbolic lattices-are expected to extend Euclidean …
Solving olympiad geometry without human demonstrations.
Trinh TH, Wu Y, Le QV, He H, Luong T. Trinh TH, et al. Nature. 2024 Jan;625(7995):476-482. doi: 10.1038/s41586-023-06747-5. Epub 2024 Jan 17. Nature. 2024. PMID: 38233616 Free PMC article.
We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. ...Notably, AlphaGeometry produces human-readable p …
We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstration …
Origins of Hyperbolicity in Color Perception.
Prencipe N, Garcin V, Provenzi E. Prencipe N, et al. J Imaging. 2020 Jun 4;6(6):42. doi: 10.3390/jimaging6060042. J Imaging. 2020. PMID: 34460588 Free PMC article.
Secondly, we show that, within Yilmaz's model, the color space can be coherently endowed with the Minkowski metric only by imposing the Euclidean metric on the hue-chroma plane. This fact motivates the need of further investigation about both the proper definition a …
Secondly, we show that, within Yilmaz's model, the color space can be coherently endowed with the Minkowski metric only by imposing the E …
Spectral multidimensional scaling.
Aflalo Y, Kimmel R. Aflalo Y, et al. Proc Natl Acad Sci U S A. 2013 Nov 5;110(45):18052-7. doi: 10.1073/pnas.1308708110. Epub 2013 Oct 9. Proc Natl Acad Sci U S A. 2013. PMID: 24108352 Free PMC article.
The idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its Laplace-Beltrami operator. There, embedding into a small dimensional Euclidean space is accomplished while optimizing for a small number of coefficients. …
The idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its Laplace-Beltrami oper …
Emergent quasiparticles in Euclidean tilings.
Crasto de Lima F, Fazzio A. Crasto de Lima F, et al. Nanoscale. 2021 Mar 18;13(10):5270-5274. doi: 10.1039/d0nr08908g. Nanoscale. 2021. PMID: 33662069
Given this correlation between structure and properties, exploring new geometries can lead to unexplored states and phenomena. Kepler is the pioneer of the mathematical tiling theory, describing ways of filling the Euclidean plane with geometric forms in his …
Given this correlation between structure and properties, exploring new geometries can lead to unexplored states and phenomena. Kepler …
Modeling and concepts of the Malingue plasty compared to Z-plasty.
Albert T, Meersseman L, Raimbeau G, Saint-Cast Y, Bigorre N. Albert T, et al. Hand Surg Rehabil. 2023 Apr;42(2):154-159. doi: 10.1016/j.hansur.2022.12.005. Epub 2023 Jan 7. Hand Surg Rehabil. 2023. PMID: 36627021
The second step was based on inert models (latex gloves) and cadaveric models, to study the mechanical behavior of the flaps. Differences in gains in length were analyzed by Euclidean and non-Euclidean geometry. The Malingue plasty flaps showed greater vascul …
The second step was based on inert models (latex gloves) and cadaveric models, to study the mechanical behavior of the flaps. Differences in …
Local groups in Delone sets in the Euclidean space.
Dolbilin N, Shtogrin M. Dolbilin N, et al. Acta Crystallogr A Found Adv. 2022 Sep 1;78(Pt 5):452-458. doi: 10.1107/S2053273322007549. Epub 2022 Aug 30. Acta Crystallogr A Found Adv. 2022. PMID: 36047402
A few conjectures and theorems on the local groups for arbitrary Delone sets in the Euclidean plane and 3D space are discussed. Some of these statements significantly refine and generalize the famous Bravais theorem on the impossibility of fifth-order axes in 2D and …
A few conjectures and theorems on the local groups for arbitrary Delone sets in the Euclidean plane and 3D space are discussed …
48 results