Related papers: RNA-LEGO: Combinatorial Design of Pseudoknot RNA
In this paper we prove a duality between $k$-noncrossing partitions over $[n]=\{1,...,n\}$ and $k$-noncrossing braids over $[n-1]$. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
Much current network analysis is predicated on the assumption that important biological networks will either possess scale free or exponential statistics which are independent of network size allowing unconstrained network growth over time.…
Negami found an upper bound on the stick number $s(K)$ of a nontrivial knot $K$ in terms of the minimal crossing number $c(K)$ of the knot which is $s(K) \leq 2 c(K)$. Furthermore McCabe proved $s(K) \leq c(K) + 3$ for a $2$-bridge knot or…
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
Let $\crs(K_n)$ be the minimum number of crossings over all rectilinear drawings of the complete graph on $n$ vertices on the plane. In this paper we prove that $\crs(K_n) < 0.380473\binom{n}{4}+\Theta(n^3)$; improving thus on the previous…
Motivation: Non-coding RNAs (ncRNAs) express their functions by adopting molecular structures. Specifically, RNA secondary structures serve as a relatively stable intermediate step before tertiary structures, offering a reliable signature…
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…
RNA-RNA binding is an important phenomenon observed for many classes of non-coding RNAs and plays a crucial role in a number of regulatory processes. Recently several MFE folding algorithms for predicting the joint structure of two…
We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…
The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical…
Long non-coding RNA, microRNA, and messenger RNA enable key regulations of various biological processes through a variety of diverse interaction mechanisms. Identifying the interactions and cross-talk between these heterogeneous RNA classes…
We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices.…
In this paper, we develop new algorithms for the basic RNA folding problem. Given an RNA sequence that contains $n$ nucleotides, the goal of the problem is to compute a pseudoknot-free secondary structure that maximizes the number of base…
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…
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 present computational results about quasi-alternating knots and links and odd homology obtained by looking at link families in the Conway notation. More precisely, we list quasi-alternating links up to 12 crossings and the first examples…
Models for RNA secondary structures (the topology of folded RNA) without pseudo knots are disordered systems with a complex state-space below a critical temperature. Hence, a complex dynamical (glassy) behavior can be expected, when…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…