Related papers: Posets and spaces of $k$-noncrossing RNA Structure…
The three-dimensional conformations of non-coding RNAs underpin their biochemical functions but have largely eluded experimental characterization. Here, we report that integrating a classic mutation/rescue strategy with high-throughput…
DNA plays a special role in polymer science not just because of the highly selective recognition of complementary single DNA strands but also because bacteria can express DNA chains that are very long yet perfectly monodisperse. The latter…
A series of coarse-grained models have been developed for the study of the molecular dynamics of RNA nanostructures. The models in the series have one to three beads per nucleotide and include different amounts of detailed structural…
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The…
The two strands of a DNA molecule with a repetitive sequence can pair into many different basepairing patterns. For perfectly periodic sequences, early bulk experiments of Poerschke indicate the existence of a sliding process, permitting…
Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…
Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as planar, 3-regular graphs with facets…
Mapping between sequence and structure is currently an open problem in structural biology. Despite many experimental and computational efforts it is not clear yet how the structure is encoded in the sequence. Answering this question may…
A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev,…
We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by…
Accurate RNA secondary structure prediction is vital for understanding cellular regulation and disease mechanisms. Deep learning (DL) methods have surpassed traditional algorithms by predicting complex features like pseudoknots and…
In this paper we study $k$-noncrossing matchings. A $k$-noncrossing matching is a labeled graph with vertex set $\{1,...,2n\}$ arranged in increasing order in a horizontal line and vertex-degree 1. The $n$ arcs are drawn in the upper…
Predicting the secondary structure of RNA is a core challenge in computational biology, essential for understanding molecular function and designing novel therapeutics. The field has evolved from foundational but accuracy-limited…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
An $k$-noncrossing RNA structure can be identified with an $k$-noncrossing diagram over $[n]$, which in turn corresponds to a vacillating tableaux having at most $(k-1)$ rows. In this paper we derive the limit distribution of irreducible…
The three dimensional structure of DNA in the nucleus (chromatin) plays an important role in many cellular processes. Recent experimental advances have led to high-throughput methods of capturing information about chromatin conformation on…
Single-cell RNA sequencing (scRNA-seq) is powerful technology that allows researchers to understand gene expression patterns at the single-cell level. However, analysing scRNA-seq data is challenging due to issues and biases in data…
Let $S_{g}$ denote the genus $g$ closed orientable surface. For $k\in \mathbb{N}$, a $k$-system is a collection of pairwise non-homotopic simple closed curves such that no two intersect more than $k$ times. Juvan-Malni\v{c}-Mohar…
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 the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…