Related papers: Methods for Analyzing RNA Pseudoknots via Chord Di…
RNA design aims to identify RNA sequences that fold into a target secondary structure. This task is challenging in terms of computational efficiency. Most existing methods focus on either minimum free energy (MFE)-based or ensemble-based…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial…
The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced…
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\sf T}_{k,\sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the…
Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as…
DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum stack-length. We show that the numbers of $k$-noncrossing structures without isolated base pairs are significantly smaller than the number of all…
RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main…
We consider a certain abstract of RNA secondary structures, which is closely related to RNA shapes. The generating function counting the number of the abstract structures is obtained by means of Narayana numbers and 2-Motzkin paths, through…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge \sigma$ and in which there…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
Three-dimensional volumetric imaging of cells allows for in situ visualization, thus preserving contextual insights into cellular processes. Despite recent advances in machine learning methods, morphological analysis of sub-nuclear…
RNA 3D motifs are recurrent substructures, modelled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and…
Circular RNAs (circRNAs) are important components of the non-coding RNA regulatory network. Previous circRNA identification primarily relies on high-throughput RNA sequencing (RNA-seq) data combined with alignment-based algorithms that…
The identification of disease-gene associations is instrumental in understanding the mechanisms of diseases and developing novel treatments. Besides identifying genes from RNA-Seq datasets, it is often necessary to identify gene clusters…
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…
Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base…