Related papers: New alphabet-dependent morphological transition in…
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…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
The vertex-cover problem is studied for random graphs $G_{N,cN}$ having $N$ vertices and $cN$ edges. Exact numerical results are obtained by a branch-and-bound algorithm. It is found that a transition in the coverability at a $c$-dependent…
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…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
A k-noncrossing RNA pseudoknot structure is a graph over $\{1,...,n\}$ without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing…
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
We extend recent methods for parametric sequence alignment to the parameter space for scoring RNA folds. This involves the construction of an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common…
We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number,…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large…
A new statistical method of alignment of two heteropolymers which can form hierarchical cloverleaf-like secondary structures is proposed. This offers a new constructive algorithm for quantitative determination of binding free energy of two…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Formation of base pairs between the nucleotides of an RNA sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching --…
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological…
Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is…
We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via…
Packing transitions in the lowest energy structures of Li clusters as a function of size have been identified via simulated annealing. For N>21, the large $p$ character of Li leads to unexpected ionic structures. At N~25, a packing pattern…
A linear external perturbation is introduced in the action of the partition function of the random matrix model of RNA [G. Vernizzi, H. Orland and A. Zee, Phys. Rev. Lett. 94, 168103 (2005)]. It is seen that (i). the perturbation…