Related papers: Shapes of topological RNA structures
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…
Heterogeneous graphs are present in various domains, such as social networks, recommendation systems, and biological networks. Unlike homogeneous graphs, heterogeneous graphs consist of multiple types of nodes and edges, each representing…
Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive…
Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of…
Orthologous genes, which arise through speciation, play a key role in comparative genomics and functional inference. In particular, graph-based methods allow for the inference of orthology estimates without prior knowledge of the underlying…
In many industries, as well as in academic research, information is primarily transmitted in the form of unstructured documents (this article, for example). Hierarchically-related data is rendered as tables, and extracting information from…
Spatial arrangement of cells of various types, such as tumor infiltrating lymphocytes and the advancing edge of a tumor, are important features for detecting and characterizing cancers. However, convolutional neural networks (CNNs) do not…
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…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…