相关论文: Combinatorics Of RNA Structures With Pseudoknots
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…
Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the…
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…
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…
RNA secondary structure is an important computational model to understand how genetic variation maps into phenotypic (structural) variation. Evolutionary innovation in RNA structures is facilitated by neutral networks, large connected sets…
In this paper we compute the loop homology of bi-secondary structures. Bi-secondary structures were introduced by Haslinger and Stadler and are pairs of RNA secondary structures, i.e. diagrams having non-crossing arcs in the upper…
We compute the lowest moments of the nucleon's structure functions using quenched overlap fermions at two different lattice spacings. The renormalisation is done nonperturbatively in the RI'-MOM-scheme.
Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes…
The present paper is devoted to the study of the combinatorics of 216 maximal $C^3$ circular codes --- a particular type of structure arising in the analysis of genomic sequences. Their circularity property is believed to be intimately…
Functional or non-coding RNAs are attracting more attention as they are now potentially considered valuable resources in the development of new drugs intended to cure several human diseases. The identification of drugs targeting the…
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…
The tertiary structures of functional RNA molecules remain difficult to decipher. A new generation of automated RNA structure prediction methods may help address these challenges but have not yet been experimentally validated. Here we apply…
Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…
Pseudo links have two crossing types: classical crossings and indeterminate crossings. They were first introduced by Ryo Hanaki as a possible tool for analyzing images produced by electron microscopy of DNA. A normalized bracket polynomial…
Enumerative studies of RNA secondary structures were initiated four decades ago by Waterman and his coworkers. Since then, RNA secondary structures have been explored according to many different structural characteristics, for instance,…
In this paper we present a novel framework for sequence to shape maps. These combinatorial maps realize exponentially many shapes, and have preimages which contain extended connected subgraphs of diameter n (neutral networks). We prove that…
In this paper, we introduce polynomial time algorithms that generate random $k$-noncrossing partitions and 2-regular, $k$-noncrossing partitions with uniform probability. A $k$-noncrossing partition does not contain any $k$ mutually…
It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2} \cdot 2.618034^n$. Motivated by the kinetics of RNA secondary structure formation, we are interested in…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus $g$, for arbitrary $g>0$. Furthermore…