相关论文: An Algorithmic Approach to Classify Knots
The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how…
Understanding topological features in networks is crucial for unravelling complex phenomena across fields such as neuroscience, condensed matter, and high-energy physics. However, identifying higher-order topological structures -- such as…
This work proposes PatchNet, an automated tool based on hierarchical deep learning for classifying patches by extracting features from commit messages and code changes. PatchNet contains a deep hierarchical structure that mirrors the…
Community detection and link prediction are both of great significance in network analysis, which provide very valuable insights into topological structures of the network from different perspectives. In this paper, we propose a novel…
We give a recipe for constructing families of distinct knots that have identical Khovanov homology and give examples of pairs of prime knots, as well as infinite families, with this property.
The most tight conformations of prime knots are found with the use of the SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry of the knots is analysed. Connections with the physics of polymers are discussed.
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
It is proposed a new code for contours of plane images. This code was applied for optical character recognition of printed and handwritten characters. One can apply it to recognition of any visual images.
We give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid.
In this paper we constructed new model of plastic deformation. The knot theory was used to classify the plastic state.
A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…
We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar…
We explore the possibility of applying the framework of frequent pattern mining to a class of continuous objects appearing in nature, namely knots. We introduce the frequent knot mining problem and present a solution. The key observation is…
In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
This project explores the mathematical study of knots and links in topology, focusing on differentiating between the two-component Unlink and the Hopf Link using a computational tool named LINKAGE. LINKAGE employs the linking number,…
Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…
These notes present two normal surface theory algorithms to detect the unknot and use the split-link algorithm to prove that the figure-eight knot is knotted.
Generalizing Howie and Greene's characterization of alternating knots, we give a topological characterization of almost alternating knots.
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.