Polynomial Invariants for Cactuses

Iersel, Leo van; Moulton, Vincent; Murakami, Yukihiro

doi:10.2139/ssrn.4233802

Cited by 2 publications

(3 citation statements)

References 16 publications

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“…In order to study secondary structures with pseudoknots using polynomial-based methods, we can represent the secondary structures by directed acyclic graphs (DAGs). Recent studies have introduced complete polynomial invariants for some classes of DAGs in studying phylogenetic networks [10, 20, 30]. There remains a considerable scope to modify the definitions of the polynomials and the rooted tree representations to capture more information about RNA secondary structures, for example, the order of stems and groups of unpaired nucleotides around a multiloop or the opening region.…”

Section: Discussionmentioning

confidence: 99%

“…Recent studies have introduced complete polynomial invariants for some classes of DAGs in studying phylogenetic networks [10,20,31]. In future work we aim to modify the definitions of the polynomials and the rooted tree representations to capture more information about RNA secondary structures, for example, the order of stems and groups of unpaired nucleotides around a multiloop or the opening region.…”

Section: Discussionmentioning

confidence: 99%

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Analyzing the link between RNA secondary structures and R-loop formation with tree polynomials

Liu,

Lusk,

Jonoska

et al. 2023

Preprint

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R-loops are a class of non-canonical nucleic acid structures that typically form during transcription, when the nascent RNA hybridizes with the DNA template strand, leaving the DNA coding strand unpaired. Co-transcriptional R-loops are abundant in nature and biologically relevant. Recent research shows that DNA sequence and topology affect R-loops, and yet it remains unclear how these and other factors drive R-loop formation. In this work, we investigate the link between the secondary structure of the nascent RNA and the probability of R-loop formation. We introduce tree-polynomial representations, a mathematical object that enables accurate and efficient data analysis of RNA secondary structures. With tree-polynomial representations, we establish a strong correlation between the secondary structure of the RNA transcript and the probability of R-loop formation. We identify that branches with short stems separated by multiple bubbles in the RNA secondary structure drive the strong correlation and potentially promote R-loop formation.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Analyzing the link between RNA secondary structures and R-loop formation with tree polynomials

Liu,

Lusk,

Jonoska

et al. 2023

Preprint

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“…This builds an one-to-one correspondence between unlabeled trees and a class of bivariate polynomials, that is, two unlabeled trees are isomorphic if and only if they have the same polynomial. This tree distinguishing polynomial has been applied to study phylogenetic trees and pathogen evolution (P. Liu et al, 2022) and generalized to represent some classes of phylogenetic networks (Janssen and Liu, 2021;Pons et al, 2022;van Iersel et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Quantifying syntax similarity with a polynomial representation of dependency trees

Liu¹,

Feng²,

Liu³

2022

Glottometrics

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We introduce a graph polynomial that distinguishes tree structures to represent dependency grammar and a measure based on the polynomial representation to quantify syntax similarity. The polynomial encodes accurate and comprehensive information about the dependency structure and dependency relations of words in a sentence, which enables in-depth analysis of dependency trees with data analysis tools. We apply the polynomial-based methods to analyze sentences in the ParallelUniversal Dependencies treebanks. Specifically, we compare the syntax of sentences and their translations in different languages, and we perform a syntactic typology study of available languages in the Parallel Universal Dependencies treebanks. We also demonstrate and discuss the potential of the methods in measuring syntax diversity of corpora.

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Polynomial Invariants for Cactuses

Cited by 2 publications

References 16 publications

Analyzing the link between RNA secondary structures and R-loop formation with tree polynomials

Analyzing the link between RNA secondary structures and R-loop formation with tree polynomials

Quantifying syntax similarity with a polynomial representation of dependency trees

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