相关论文: Combinatorics Of RNA Structures With Pseudoknots

The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…

Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as…

We introduce pseudoconformal structures on 4--dimensional manifolds and study their properties. Such structures are arising from two different complex operators which agree in a 2--dimensional subbundle of the tangent bundle; this subbundle…

In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…

We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which…

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…

A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…

Superregular matrices, i.e., matrices where all square submatrices are non-singular, have a wide range of applications in communications. A superregular block matrix is a broader concept where all full block submatrices, with the…

Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…

Small regulatory RNAs (sRNAs) are short non-coding RNAs in bacteria capable of post-transcriptional regulation. sRNAs have recently gained attention as tools in basic and applied sciences for example to fine-tune genetic circuits or…

Networks of silicon nanowires possess intriguing electronic properties surpassing the predictions based on quantum confinement of individual nanowires. Employing large-scale atomistic pseudopotential computations, as yet unexplored branched…

Let Sn denote the network of all RNA secondary structures of length n, in which undirected edges exist between structures s, t such that t is obtained from s by the addition, removal or shift of a single base pair. Using context-free…

We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…

In a DNA sequence, we have the celebrated Watson-Crick complement $\overline{T}=A$, $\overline{A}=T$, $\overline{C}=G$, and $\overline{G}=C$. Given an integer $m\ge 2$, a secondary structure in a DNA sequence refers to the existence of two…

In this paper we compute the bivariate generating function of $\gamma$-matchings over two backbones, filtered by the number of arcs and the topological genus. $\gamma$-matchings over two backbones are chord-diagrams, obtained via…

Given the importance of non-coding RNAs to cellular regulatory functions and rapid growth of RNA transcripts, computational prediction of RNA tertiary structure remains highly demanded yet significantly challenging. Even for a short RNA…

We introduce a novel fully convolutional neural network (FCN) architecture for predicting the secondary structure of ribonucleic acid (RNA) molecules. Interpreting RNA structures as weighted graphs, we employ deep learning to estimate the…

DNA strand displacement systems have proven themselves to be fertile substrates for the design of programmable molecular machinery and circuitry. Domain-level reaction enumerators provide the foundations for molecular programming languages…

Knotted molecules occur naturally and are designed by scientists to gain special biological and material properties. Understanding and utilizing knotting require efficient methods to recognize and generate knotted structures, which are…

An avoidance pattern where the letters within an occurrence of which are required to be adjacent is referred to as a subword. In this paper, we enumerate members of the set NC_n of non-crossing partitions of length n according to the number…