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We present a numerical study of the ultrametric properties of the set of RNA secondary structures with the maximum number of base pairs (energetically degenerate minima) within the maximum matching model (Nussinov algorithm). Using 18…
The problem of estimating the structure of a graph from observed data is of growing interest in the context of high-throughput genomic data, and single-cell RNA sequencing in particular. These, however, are challenging applications, since…
This paper proposes a novel model for predicting subgraphs in dynamic graphs, an extension of traditional link prediction. This proposed end-to-end model learns a mapping from the subgraph structures in the current snapshot to the subgraph…
Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical…
We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the…
Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
RNA design aims to identify RNA sequences that fold into a target secondary structure. This task is challenging in terms of computational efficiency. Most existing methods focus on either minimum free energy (MFE)-based or ensemble-based…
Biomolecular graph analysis has recently gained much attention in the emerging field of geometric deep learning. Here we focus on organizing biomolecular graphs in ways that expose meaningful relations and variations between them. We…
A polynomial is presented that models a topological knot in a unique manner. It distinguishes all types of knots including the orientation and has a group theory interpretation. The topologies may be labeled via a number, which upon a base…
This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module…
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
The complexity and non-Euclidean structure of graph data hinder the development of data augmentation methods similar to those in computer vision. In this paper, we propose a feature augmentation method for graph nodes based on topological…
Understanding the base pairing of an RNA sequence provides insight into its molecular structure.By mining suboptimal sampling data, RNAprofiling 1.0 identifies the dominant helices in low-energy secondary structures as features, organizes…
RNA-KG is a recently developed knowledge graph that integrates the interactions involving coding and non-coding RNA molecules extracted from public data sources. It can be used to support the classification of new molecules, identify new…
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…
Graph neural networks (GNNs) have achieved impressive performance in graph domain adaptation. However, extensive source graphs could be unavailable in real-world scenarios due to privacy and storage concerns. To this end, we investigate an…
Non-coding RNA (ncRNA) are RNA sequences which don't code for a gene but instead carry important biological functions. The task of ncRNA classification consists in classifying a given ncRNA sequence into its family. While it has been shown…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…