Related papers: Shapes of topological RNA structures
One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching…
We present a new method for exploring cancer gene expression data based on tools from algebraic topology. Our method selects a small relevant subset from tens of thousands of genes while simultaneously identifying nontrivial higher order…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
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…
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…
Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous co-assembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively…
We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different…
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays…
Graph neural networks (GNNs) are increasingly used to model biological systems, yet the reliability of post-hoc explanation methods for recovering meaningful molecular mechanisms remains unclear. Here, we systematically evaluate four widely…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…
In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all $k$-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate…
In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases…
DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
In this paper we present a combinatorial proof of a relation between the generating functions of unicellular and bicellular maps. This relation is a consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it can be…
RNA molecules are single-stranded analogues of DNA that can fold into various structures which influence their biological function within the cell. RNA structures can be modelled combinatorially in terms of a certain type of graph called an…
In this paper we study canonical $\gamma$-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $\gamma$-structure is composed by specific building…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…