Related papers: Methods for Analyzing RNA Pseudoknots via Chord Di…

RNA structure prediction is a challenging problem, especially with pseudoknots. Recently, there has been a shift from the classical minimum free energy-based methods (MFE) to partition function-based ones that assemble structures using…

Pseudodiagrams are knot or link diagrams where some of the crossing information is missing. Pseudoknots are equivalence classes of pseudodiagrams, where equivalence is generated by a natural set of Reidemeister moves. In this paper, we…

In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set,…

Structural prediction has long been considered critical in RNA research, especially following the success of AlphaFold2 in protein studies, which has drawn significant attention to the field. While recent advances in machine learning and…

In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…

Graphs can be used to effectively represent complex data structures. Learning these irregular data in graphs is challenging and still suffers from shallow learning. Applying deep learning on graphs has recently showed good performance in…

RNA-Seq technology offers new high-throughput ways for transcript identification and quantification based on short reads, and has recently attracted great interest. The problem is usually modeled by a weighted splicing graph whose nodes…

The problem of estimating the structure of a graph from observed data is of growing interest in the context of high-throughput genomic data, and single-cell RNA sequencing in particular. These, however, are challenging applications, since…

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous…

Secondary structure plays an important role in determining the function of non-coding RNAs. Hence, identifying RNA secondary structures is of great value to research. Computational prediction is a mainstream approach for predicting RNA…

In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be…

It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from…

Despite great interest in solving RNA secondary structures due to their impact on function, it remains an open problem to determine structure from sequence. Among experimental approaches, a promising candidate is the "chemical modification…

The measurement of the similarity of RNA secondary structures, and in general of contact structures, of a fixed length has several specific applications. For instance, it is used in the analysis of the ensemble of suboptimal secondary…

Clustering analysis is fundamental in single-cell RNA sequencing (scRNA-seq) data analysis for elucidating cellular heterogeneity and diversity. Recent graph-based scRNA-seq clustering methods, particularly graph neural networks (GNNs),…

Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…

Accurate prediction of RNA properties, such as stability and interactions, is crucial for advancing our understanding of biological processes and developing RNA-based therapeutics. RNA structures can be represented as 1D sequences, 2D…

We introduce a computational topology-based approach with unsupervised machine-learning algorithms to estimate the database size and content of RNA-like graph topologies. Specifically, we apply graph theory enumeration to generate all…

Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output.…

A pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by R. Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots.…