Results 1 to 10 of about 5,189 (241)

Using Parametric Mathematical Modeling to Develop a Geometric and Topological Intuition for Molecular Knots

Applied Mathematics, 2020
Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics
Tahmineh Azizi, Jacob Pichelmeyer
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An outlined tour of geometry and topology as perceived through physics and mathematics emphasizing geometrization, elliptization, uniformization, and projectivization for Thruston's 8-geometries covering Riemann over Teichmuller spaces

, 2022
<p>Equivalence, duality, and invariance are the pin-points of unification in modern theoretical physics that got the twist of topologies when going beyond the notions of differential and conformal domains to geometries to the symplectic norm of topologies with the pillars being the algebraic geometry taking the counting of specified states ...
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Information-Geometric and Topological Features of AI Behavioral Signatures: A 14-Module Mathematical Framework

Description of a 14-module mathematical pipeline spanning information theory, algebraic topology, dynamical systems, differential geometry, gauge theory, and category theory. Produces 272-dimensional feature vectors expanded to 1,543 dimensions. Achieves 0.958 AUC (GPT-4) on LLM behavioral drift detection.
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Mathematical and Physical Analysis of Geometric Genesis: Complete Technical Formalism on Mass Hierarchy, Topology and Geometry

Este informe presenta un análisis exhaustivo del formalismo matemático y físico que fundamenta la teoría de Génesis Geométrica, con enfoque particular en la derivación cuantitativa de la jerarquía de masas y propiedades de partículas elementales. Como cuarto componente de un ecosistema teórico coherente, este trabajo provee el rigor matemático técnico ...
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The Unified Force Topology: Purely geometric derivation of the mathematical constants for all four fundamental forces, proving they are all born from the Golden Ratio interacting with the dimensionality of the superfluid lattice.

A primary objective of theoretical physics has been the Grand Unification of the four fundamental forces—Electromagnetism, the Strong Nuclear Force, the Weak Nuclear Force, and Gravity. Standard models treat the coupling strengths of these forces as independent, empirically derived parameters.
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Gravitational and Planck Constants as Mathematical Necessities: First Derivation of G and ℏ from Geometric, Topological, and Information-Theoretic Structure

We present the first complete explanation of why the gravitational constant G and the Planck constant ℏ must have the values they do. Instead of treating them as arbitrary inputs to physics, we show that they arise naturally from the geometry, topology, and information structure of spacetime itself.
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** The Polynomial-Time Computation Engine ** A Mathematics Architecture via Geometric Topology Icosahedral Spectral Isomorphism

𝖳𝗁𝗂𝗌 𝗉𝖺𝗉𝖾𝗋 𝗌𝗂𝗍𝗎𝖺𝗍𝖾𝗌 𝗂𝗍𝗌𝖾𝗅𝖿 𝖺𝗍 𝗍𝗁𝖾 𝗂𝗇𝗍𝖾𝗋𝗌𝖾𝖼𝗍𝗂𝗈𝗇 𝗈𝖿 𝖼𝗈𝗆𝗉𝗎𝗍𝖺𝗍𝗂𝗈𝗇𝖺𝗅 𝖼𝗈𝗆𝗉𝗅𝖾𝗑𝗂𝗍𝗒 𝗍𝗁𝖾𝗈𝗋𝗒 𝖺𝗇𝖽 𝖽𝗂𝗌𝖼𝗋𝖾𝗍𝖾 𝗌𝗉𝖾𝖼𝗍𝗋𝖺𝗅 𝗀𝖾𝗈𝗆𝖾𝗍𝗋𝗒. 𝖶𝗁𝗂𝗅𝖾 𝗍𝗁𝖾 𝖠𝖪𝖲 𝖺𝗅𝗀𝗈𝗋𝗂𝗍𝗁𝗆 (𝟤𝟢𝟢𝟤) 𝖽𝖾𝖿𝗂𝗇𝗂𝗍𝗂𝗏𝖾𝗅𝗒 𝖾𝗌𝗍𝖺𝖻𝗅𝗂𝗌𝗁𝖾𝖽 𝗍𝗁𝖺𝗍 𝗉𝗋𝗂𝗆𝖺𝗅𝗂𝗍𝗒 𝗏𝖾𝗋𝗂𝖿𝗂𝖼𝖺𝗍𝗂𝗈𝗇 𝗋𝖾𝗌𝗂𝖽𝖾𝗌 𝗐𝗂𝗍𝗁𝗂𝗇 𝗍𝗁𝖾 𝖼𝗈𝗆𝗉𝗅𝖾𝗑𝗂𝗍𝗒 𝖼𝗅𝖺𝗌𝗌 𝖯, 𝗂𝗍𝗌 𝗉𝗈𝗅𝗒𝗇𝗈𝗆𝗂𝖺𝗅 𝖻𝗈𝗎𝗇𝖽 𝗋𝖾𝗆𝖺𝗂𝗇𝗌 𝖼𝗈𝗆𝗉𝗎𝗍𝖺𝗍𝗂𝗈𝗇𝖺𝗅𝗅𝗒 𝗉𝗋𝗈𝗁𝗂𝖻𝗂𝗍𝗂𝗏𝖾 𝖿𝗈𝗋 𝗁𝗂𝗀𝗁-𝗏𝖾𝗅𝗈𝖼𝗂𝗍𝗒 𝖼𝗋𝗒𝗉𝗍𝗈𝗀𝗋𝖺𝗉𝗁𝗂𝖼 𝗌𝖼𝖺𝗅𝗂𝗇𝗀.
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An effective deep learning algorithm for medical image registration. [PDF]

PLOS Digit Health
Deng J, Chen K, Li M, Zuo Z, Frangi AF, Zhang J.   +5 more
europepmc   +1 more source