Related papers: Physical Knot Classification Beyond Accuracy: A Be…

We propose a novel, good-quality, and less demanding method for detecting knots on the surface of wooden logs using multimodal data fusion. Knots are a primary factor affecting the quality of sawn timber, making their detection fundamental…

Topological materials discovery has emerged as an important frontier in condensed matter physics. While theoretical classification frameworks have been used to identify thousands of candidate topological materials, experimental…

Protein contacts provide key information for the understanding of protein structure and function, and therefore contact prediction from sequences is an important problem. Recent research shows that some correctly predicted long-range…

Knots across various length scales, from micro to macro-scales, such as polymers, DNA, shoelaces, and surgery, serving their unique mechanical properties. The shape of ideal knots has been extensively studied in the context of knot theory,…

Topology Bench is a comprehensive topology dataset designed to accelerate benchmarking studies in optical networks. The dataset, focusing on core optical networks, comprises publicly accessible and ready-to-use topologies, including (a) 105…

Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields. In order to characterize their…

The computer artificial intelligence system AlphaFold has recently predicted previously unknown three-dimensional structures of thousands of proteins. Focusing on the subset with high-confidence scores, we algorithmically analyze these…

We compose the table of knots in the thickened torus T x I having diagrams with at most 4 crossings. The knots are constructed by the three-step process. First we list regular graphs of degree 4 with at most 4 vertices, then for each graph…

Biological network alignment (NA) aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for transfer of functional knowledge between the aligned nodes. However, current NA…

In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using…

Predictive uncertainty-a model's self awareness regarding its accuracy on an input-is key for both building robust models via training interventions and for test-time applications such as selective classification. We propose a novel…

This paper discusses some geometric ideas associated with knots in real projective 3-space $\mathbb{R}P^3$. These ideas are borrowed from classical knot theory. Since knots in $\mathbb{R}P^3$ are classified into three disjoint classes, -…

High quality object proposals are crucial in visual tracking algorithms that utilize region proposal network (RPN). Refinement of these proposals, typically by box regression and classification in parallel, has been popularly adopted to…

Convolutional neural networks typically encode an input image into a series of intermediate features with decreasing resolutions. While this structure is suited to classification tasks, it does not perform well for tasks requiring…

Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…

Recently there had been a great deal of activity associated with various schemes of designing both analytical and experimental methods describing knotted structures in electrodynamics and in hydrodynamics.The majority of works in…

RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…

We show that multiple machine learning algorithms can match human performance in classifying transient imaging data from the Sloan Digital Sky Survey (SDSS) supernova survey into real objects and artefacts. This is a first step in any…

Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks…

We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number,…