Related papers: Physical Knot Classification Beyond Accuracy: A Be…
Classifying the topology of closed curves is a central problem in low dimensional topology with applications beyond mathematics spanning protein folding, polymer physics and even magnetohydrodynamics. The central problem is how to determine…
RetinaNet proposed Focal Loss for classification task and improved one-stage detectors greatly. However, there is still a gap between it and two-stage detectors. We analyze the prediction of RetinaNet and find that the misalignment of…
In this study, we consider the problem of detecting cracks from the image of a concrete surface for automated inspection of infrastructure, such as bridges. Its overall accuracy is determined by how accurately thin cracks with sub-pixel…
In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.
Numerical preprocessing remains an important component of tabular deep learning, where the representation of continuous features can strongly affect downstream performance. Although its importance is well established for classical…
In this paper, we approach the challenging problem of motion planning for knot tying. We propose a hierarchical approach in which the top layer produces a topological plan and the bottom layer translates this plan into continuous robot…
I briefly discuss a method of obtaining distinct classes of topologically equivalent knots by developing appropriate computer programs.
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in…
Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…
A powerful way to study groups is via their actions on suitable spaces. Classifying spaces for families of subgroups are a type of these spaces, obtained by imposing some strict conditions on the fixed-point sets. We show how in the…
Action Quality Assessment (AQA) requires fine-grained understanding of human motion and precise evaluation of pose similarity. This paper proposes a topology-aware Graph Convolutional Network (GCN) framework, termed GCN-PSN, which models…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular…
Pith detection in tree cross-sections is essential for forestry and wood quality analysis but remains a manual, error-prone task. This study evaluates deep learning models -- YOLOv9, U-Net, Swin Transformer, DeepLabV3, and Mask R-CNN -- to…
In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological…
Recent researches attempt to improve the detection performance by adopting the idea of cascade for single-stage detectors. In this paper, we analyze and discover that inconsistency is the major factor limiting the performance. The refined…
In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to…
Knots are entangled structures that cannot be untangled without a cut. Topological stability of knots is one of the many examples of their important properties that can be used in information storage and transfer. Knot dynamics is important…
Automatically determining knot number and positions is a fundamental and challenging problem in B-spline approximation. In this paper, the knot placement is abstracted as a mapping from initial knots to the optimal knots. We innovatively…
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.…