Related papers: Physical Knot Classification Beyond Accuracy: A Be…
Effective crack detection is pivotal for the structural health monitoring and inspection of buildings. This task presents a formidable challenge to computer vision techniques due to the inherently subtle nature of cracks, which often…
Frequently, knots are enumerated by their crossing number. However, the number of knots with crossing number $c$ grows exponentially with $c$, and to date computer-assisted proofs can only classify diagrams up to around twenty crossings.…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if…
Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides…
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The…
Anomaly Detection involves identifying deviations from normal data distributions and is critical in fields such as medical diagnostics and industrial defect detection. Traditional AD methods typically require the availability of normal…
Needle positioning is essential for various medical applications such as epidural anaesthesia. Physicians rely on their instincts while navigating the needle in epidural spaces. Thereby, identifying the tissue structures may be helpful to…
Motivation: Accurate classification of mitotic figures into normal and atypical types is crucial for tumor prognostication in digital pathology. However, developing robust deep learning models for this task is challenging due to the subtle…
Twisting a given knot $K$ about an unknotted circle $c$ a full $n \in \mathbb{N}$ times, we obtain a "twist family" of knots $\{ K_n \}$. Work of Kouno-Motegi-Shibuya implies that for a non-trivial twist family the crossing numbers…
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
We analyze different aspects of neural network predictions of knot invariants. First, we investigate the impact of different knot representations on the prediction of invariants and find that braid representations work in general the best.…
We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an…
Deep networks should be robust to rare events if they are to be successfully deployed in high-stakes real-world applications (e.g., self-driving cars). Here we study the capability of deep networks to recognize objects in unusual poses. We…
Performance of convolutional neural networks (CNNs) in image analysis tasks is often marred in the presence of acquisition-related distribution shifts between training and test images. Recently, it has been proposed to tackle this problem…
We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in…
In recent years, the focus on anomaly detection and localization in industrial inspection tasks has intensified. While existing studies have demonstrated impressive outcomes, they often rely heavily on extensive training datasets or robust…