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On 3D fixed-angle chains that are locked, equilateral, equiangular, and obtuse

  • For most classes of chains, it is known if these contain locks, but especially for fixed-angle equilateral equiangular obtuse open polygonal chains in 3D, which can be used to model protein backbones, this is unknown. Fixed-angle equilateral equiangular obtuse closed and open polygonal chains can be used to model polymers. For these, it is clear, that locks based on knots exist, but not which chains are generally locked. We therefore examine both open and closed fixed-angle equilateral equiangular obtuse chains. For this purpose, those chains are divided into various subgroups and, depending on the subgroup, other aspects are investigated to show locks. Techniques from knot theory, graph theory, and specifically robot arm reachability and motion planning are combined. Algorithms are developed to create chains in desired configurations and to study them. It is shown why all fixed-angle equilateral equiangular obtuse closed chains are expected to be locked or in rare cases rigid and non-locked, but never non-locked and non-rigid. For fixed-angle equilateral equiangular obtuse open chains it is shown why it is expected that there are open chains that are locked and that the smallest locked open chain has 𝑛=7.

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Metadaten
Verfasserangaben:Jonas Lummerzheim
URN:urn:nbn:de:hbz:832-epub4-19524
DOI:https://doi.org/10.57683/EPUB-1952
Gutachter*in:Hubert Randerath, Dieter Rosenthal
Dokumentart:Masterarbeit/Diplomarbeit
Sprache:Englisch
Veröffentlichende Institution:Hochschulbibliothek der Technischen Hochschule Köln
Titel verleihende Institution:Technische Hochschule Köln
Datum der Veröffentlichung:18.03.2022
Datum der Freigabe:19.04.2022
GND-Schlagwort:Knoten; Konfigurationsraum; Polygonzug; Proteine; Torus
Freies Schlagwort / Tag:3D; Equiangular; Equilateral; Fixed-Angle; Polygonal Chain
Seitenzahl:64
Fakultäten und Zentrale Einrichtungen:Informations-, Medien- und Elektrotechnik (F07) / Fakultät 07 / Institut für Nachrichtentechnik
CCS-Klassifikation:G. Mathematics of Computing
A. General Literature / A.0 GENERAL
D. Software / D.1 PROGRAMMING TECHNIQUES (E)
F. Theory of Computation / F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY (B.6-7, F.1.3)
I. Computing Methodologies / I.6 SIMULATION AND MODELING (G.3)
J. Computer Applications / J.2 PHYSICAL SCIENCES AND ENGINEERING
J. Computer Applications / J.3 LIFE AND MEDICAL SCIENCES
DDC-Sachgruppen:000 Allgemeines, Informatik, Informationswissenschaft / 000 Allgemeines, Wissenschaft
500 Naturwissenschaften und Mathematik / 510 Mathematik
500 Naturwissenschaften und Mathematik / 530 Physik
500 Naturwissenschaften und Mathematik / 540 Chemie
500 Naturwissenschaften und Mathematik / 570 Biowissenschaften, Biologie
JEL-Klassifikation:C Mathematical and Quantitative Methods / C6 Mathematical Methods and Programming
C Mathematical and Quantitative Methods / C8 Data Collection and Data Estimation Methodology; Computer Programs
C Mathematical and Quantitative Methods / C9 Design of Experiments
Open Access:Open Access
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International