Related papers: RNA Folding and Large N Matrix Theory
An entanglement Renyi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Renyi entropy is computed in 4D conformal N=4…
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…
RNA's diverse biological functions stem from its structural versatility, yet accurately predicting and designing RNA sequences given a 3D conformation (inverse folding) remains a challenge. Here, I introduce a deep learning framework that…
We propose a new deterministic methodology to predict RNA sequence and protein folding. Is stem enough for structure prediction? The main idea is to consider all possible stem formation in the given sequence. With the stem loop energy and…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
RNA co-transcriptional folding has long been suspected to play an active role in helping proper native folding of ribozymes and structured regulatory motifs in mRNA untranslated regions. Yet, the underlying mechanisms and coding…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…
Integrative biomolecular modeling of RNA relies on structural refined collections and accurate experimental data that reflect binding and folding behavior. However, the prediction of such collections remains challenging due to the rugged…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Cutting and packing problems arise in a large variety of industrial applications, where there is a need to cut pieces from a large object, or placing them inside a containers, without overlap. When the pieces or the containers have…
The general formalism for calculating the Newtonian potential in fine-tuned or critical Randall-Sundrum braneworlds is outlined. It is based on using the full tensor structure of the graviton propagator. This approach avoids the…
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…
We consider entanglement through permeable junctions of $N$ $(1+1)$-dimensional free boson and free fermion conformal field theories. In the folded picture we constrain the form of the general boundary state. We calculate replicated…
Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper,…
An RNA sequence is a string composed of four types of nucleotides, $A, C, G$, and $U$. The goal of the RNA folding problem is to find a maximum cardinality set of crossing-free pairs of the form $\{A,U\}$ or $\{C,G\}$ in a given RNA…
We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…
We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where…
The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar…
We introduce a model of thermalized conformations in space of RNA -or single stranded DNA- molecules, which includes the possibility of hairpin formation. This model contains the usual secondary structure information, but extends it to the…
Despite nearly two scores of research on RNA secondary structure and RNA-RNA interaction prediction, the accuracy of the state-of-the-art algorithms are still far from satisfactory. Researchers have proposed increasingly complex energy…