Related papers: Visually pleasing knot projections in R
Pre-compiled binary packages provide a convenient way of efficiently distributing software that has been adopted by most Linux package management systems. However, the heterogeneity of the Linux ecosystem, combined with the growing number…
Nowadays, Neural Networks are considered one of the most effective methods for various tasks such as anomaly detection, computer-aided disease detection, or natural language processing. However, these networks suffer from the ``black-box''…
Knot and link diagrams are projections of one or more 3-dimensional simple closed curves into $R^2$, such that no more than two points project to the same point in $R^2$. These diagrams are drawings of 4-regular plane multigraphs. Knots are…
stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to…
We describe the Rocker project, which provides a widely-used suite of Docker images with customized R environments for particular tasks. We discuss how this suite is organized, and how these tools can increase portability, scaling,…
Network science established itself as a prominent tool for modeling time series and complex systems. This modeling process consists of transforming a set or a single time series into a network. Nodes may represent complete time series,…
Effective visualisation of multidimensional data is crucial for generating insights. Glyph-based visualisations, which encode data dimensions onto multiple visual channels such as colour, shape, and size, provide an effective means of…
The R package cpr provides tools for selection of parsimonious B-spline regression models via algorithms coined `control polygon reduction' (CPR) and `control net reduction' (CNR). B-Splines are commonly used in regression models to smooth…
This paper complements "Writing R Extensions," the official guide for writing R extensions, for those interested in developing R packages using Rust. It highlights idiosyncrasies of R and Rust that must be addressed by any integration and…
We define a new kind of Gauss diagrams to describe knots in the solid torus with projections in the annulus. We see that it provides an efficient tool for showing that a knot diagram can be fully recovered from its decorated Gauss diagram,…
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…
We introduce the problem of knot-based inverse perceptual art. Given multiple target images and their corresponding viewing configurations, the objective is to find a 3D knot-based tubular structure whose appearance resembles the target…
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by…
A code package, BlurRing, is developed as a method to allow for multi-dimensional likelihood visualisation. From the BlurRing visualisation additional information about the likelihood can be extracted. The spread in any direction of the…
In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…
The R package innsight offers a general toolbox for revealing variable-wise interpretations of deep neural networks' predictions with so-called feature attribution methods. Aside from the unified and user-friendly framework, the package…
Networks or graphs are widely used across the sciences to represent relationships of many kinds. igraph (https://igraph.org) is a general-purpose software library for graph construction, analysis, and visualisation, combining fast and…
This paper visualizes a knot reduction algorithm
For a virtual knot $K$ and an integer $r$ with $r\geq2$, we introduce a method of constructing an $r$-component virtual link $L(K;r)$, which we call the $r$-multiplexing of $K$. Every invariant of $L(K;r)$ is an invariant of $K$. We give a…