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On the Loop Homology of a Certain Complex of RNA Structures
- Source :
- Mathematics, Vol 9, Iss 1749, p 1749 (2021), Mathematics, Volume 9, Issue 15
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure and that the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex.
- Subjects :
- topology
General Mathematics
MathematicsofComputing_GENERAL
0102 computer and information sciences
Mayer–Vietoris sequence
Homology (mathematics)
01 natural sciences
Combinatorics
symbols.namesake
Simplicial complex
Euler characteristic
Computer Science (miscellaneous)
QA1-939
Rank (graph theory)
0101 mathematics
Engineering (miscellaneous)
GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries)
Protein secondary structure
Physics
010102 general mathematics
homology
secondary structure
algebra_number_theory
Loop (topology)
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
010201 computation theory & mathematics
symbols
simplicial complex
RNA
Mathematics
Singular homology
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Mathematics, Vol 9, Iss 1749, p 1749 (2021), Mathematics, Volume 9, Issue 15
- Accession number :
- edsair.doi.dedup.....01fb1967b53d3ea93d4fc883fbdb02ad