Related papers: Pseudoknot RNA Structures with Arc-Length $\ge 3$

In post-transcriptional regulation, an mRNA molecule is bound by many proteins and/or miRNAs to modulate its function. To enable combinatorial gene regulation, these binding partners of an RNA must communicate with each other, exhibiting…

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…

We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The…

Let c(K;F) denote the surface crossing number of a knot K with respect to a closed connected surface F in S^3. We relate c(K;F) to the tunnel number t(K) and to the Heegaard deficiency delta(F)=g(M_1;F)+g(M_2;F)-g(F), where S^3=M_1 union_F…

One of the unifying concepts in the iron-pnictide superconductors, both for the mechanism of magnetic ordering and of unconventional order parameter character, has been the electron and hole Fermi surfaces that are approximately nested.…

Linear upper bounds may be derived by imposing specific structural conditions on a generating set, such as additional constraints on ranks, eigenvalues, or the degree of the minimal polynomial of the generating matrices. This paper…

Two-dimensional arsenic allotropes have been grown on metallic surfaces, while topological properties have been theoretically described on strained structures. Here we experimentally grow arsenene by molecular beam epitaxy over the…

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r(H, K_n^{(3)})$ of a fixed $3$-uniform hypergraph $H$ versus the complete $3$-uniform hypergraph with $n$ vertices. We study this…

We show that the folding rates (k_F) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free energy barriers separating the folded and the unfolded states is Gaussian, which follows from central…

Counterterms that are not reducible to $\zeta_{n}$ are generated by ${}_3F_2$ hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the…

Superconductors with non-trivial band topology are emerging as one of the best avenues to study quantum anomalies and experimental realization of Majorana Fermions. This article reports the successful crystal growth of superconducting SnAs,…

An extensive study of $\alpha$-decay half-lives for various decay chains of isotopes of $Z$ = 120 is performed within the axially deformed relativistic mean-field (RMF) formalism by employing the NL3, NL3$^*$, and DD-ME2 parameter set. The…

A cross-bifix-free code of length $n$ over $\mathbb{Z}_q$ is defined as a non-empty subset of $\mathbb{Z}_q^n$ satisfying that the prefix set of each codeword is disjoint from the suffix set of every codeword. Cross-bifix-free codes have…

The iron-pnictide superconductors have a layered structureformed by stacks of FeAs planes from which the superconductivity originates. Given the multiband and quasi three-dimensional \cite{3D_SC} (3D) electronic structure of these…

A collection of $k$ sets is said to form a $k$-sunflower, or $\Delta$-system, if the intersection of any two sets from the collection is the same, and we call a family of sets $\mathcal{F}$ sunflower-free if it contains no sunflowers.…

We present a general setting for structure-sequence comparison in a large class of RNA structures that unifies and generalizes a number of recent works on specific families on structures. Our approach is based on tree decomposition of…

We construct a just infinite fractal 3-generated Lie superalgebra $\mathbf Q$ over arbitrary field, which gives rise to an associative hull $\mathbf A$, a Poisson superalgebra $\mathbf P$, and two Jordan superalgebras $\mathbf J$, $\mathbf…

In cond-mat/9907125 the low-temperature behavior of a model for RNA secondary structure was studied. It is claimed that the model exhibits a breaking of the replica symmetry, since the width of the distribution P(q) of overlaps may converge…

For a 3-uniform hypergraph (3-graph) $F$, let $r(F,n)$ be the smallest $N$ such that any $N$-vertex $F$-free 3-graph has an independent set of size $n$. We construct a $3$-graph $H_2$ with six vertices and five edges such that…

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…