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Penrose Tilings Encode Golden Ratio via ℚ(√5), Forcing Aperiodic 5-Fold Symmetry — E8 Intelligence Research

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FINDING: Penrose tilings encode quadratic irrationality (golden ratio) as the algebraic number field ℚ(√5), forcing aperiodicity via 5-fold rotational symmetry forbidden in periodic lattices. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618034; its algebraic conjugate φ' = (1-√5)/2 ≈ -0.618034; field ℚ(√5); inflation factor φ; substitution rules on rhombi ...
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TissueViewer: a web-based multiplexed image viewer. [PDF]

open access: yesBioinformatics
van IJzendoorn DGP   +3 more
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Reproducible lung protective effects of a TGFβR1/ALK5 inhibitor in a bleomycin-induced and spirometry-confirmed model of IPF in male mice. [PDF]

open access: yesPhysiol Rep
Petersen AG   +14 more
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Air pollution exposure, respiratory consequences, and perceptions among urban African children living in poor conditions - A case study in Abidjan, Côte d'Ivoire. [PDF]

open access: yesPLOS Glob Public Health
Pajot A   +13 more
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