Related papers: RNA substructure as a random matrix ensemble
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
We introduce a powerful analytic method to study the statistics of the number $\mathcal{N}_{\textbf{A}}(\gamma)$ of eigenvalues inside any contour $\gamma \in \mathbb{C}$ for infinitely large non-Hermitian random matrices ${\textbf A}$. Our…
Structured RNA plays many functionally relevant roles in molecular life. Structural information, while required to understand the functional cycles in detail, is challenging to gather. Computational methods promise to complement…
A growing number of RNA sequences are now known to have distributions of multiple stable sequences. Recent algorithms use the list of nucleotides in a sequence and auxiliary experimental data to predict such distributions. Although the…
We describe quantitatively a RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the…
The secondary structure of ribonucleic acid (RNA) is more stable and accessible in the cell than its tertiary structure, making it essential for functional prediction. Although deep learning has shown promising results in this field,…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
Existing state-of-the-art methods that take a single RNA sequence and predict the corresponding RNA secondary-structure are thermodynamic methods. These predict the most stable RNA structure, but do not consider the process of structure…
Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction…
Consider the network of all secondary structures of a given RNA sequence, where nodes are connected when the corresponding structures have base pair distance one. The expected degree of the network is the average number of neighbors, where…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
We consider random non-hermitean matrices in the large $N$ limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this…
RNA folding prediction remains challenging, but can be also studied using a topological mathematical approach. In the present paper, the mathematical method to compute the topological classification of RNA structures and based on matrix…
Dual graphs have been applied to model RNA secondary structures. The purpose of the paper is two-fold: we present new graph-theoretic properties of dual graphs to validate the further analysis and classification of RNAs using these…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…