Related papers: Visually pleasing knot projections in R

This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing…

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian…

In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand…

Current state-of-the-art two-stage detectors generate oriented proposals through time-consuming schemes. This diminishes the detectors' speed, thereby becoming the computational bottleneck in advanced oriented object detection systems. This…

Early last century witnessed both the complete classification of 2-dimensional manifolds and a proof that classification of 4-dimensional manifolds is undecidable, setting up 3-dimensional manifolds as a central battleground of topology to…

In this paper we study rational real algebraic knots in $\R P^3$. We show that two real algebraic knots of degree $\leq5$ are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible…

We introduce a new combinatorial method to encode knots and links with applications to knot invariants. Clasp diagrams defined in this paper are combinatorial blueprints for building knot diagrams out of full twists on two strings rather…

Here I present the 'clifford' package for working with Clifford algebras in the R programming language. The algebra is described and package idiom is given.

A tutorial-style introduction to the R-package robFitConGraph is given. The latter provides a robust goodness-of-fit test for Gaussian graphical models. Its use is demonstrated at a data example on music performance anxiety, which also…

We explore free knot diagrams, which are projections of knots into the plane which don't record over/under data at crossings. We consider the combinatorial question of which free knot diagrams give which knots and with what probability.…

This paper studies knots in three dimensional projective space. Our technique is to associate a virtual link to a link in projective space so that equivalent projective links go to equivalent virtual links (modulo a special flype move). We…

The Rocker Project provides widely used Docker images for R across different application scenarios. This article surveys downstream projects that build upon the Rocker Project images and presents the current state of R packages for managing…

We introduce ICON, an R package that contains 1075 complex network datasets in a standard edgelist format. All provided datasets have associated citations and have been indexed by the Colorado Index of Complex Networks - also referred to as…

Monitoring the quality of statistical processes has been of great importance, mostly in industrial applications. Control charts are widely used for this purpose, but often lack the possibility to monitor survival outcomes. Recently,…

Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…

Celtic knots are an ancient art form often attributed to Celtic cultures, used to decorate monuments and manuscripts, and to symbolise eternity and interconnectedness. This paper describes the framework CelticGraph to draw graphs as Celtic…

Graph neural networks (GNNs) are increasingly applied to physical design tasks such as congestion prediction and wirelength estimation, yet progress is hindered by inconsistent circuit representations and the absence of controlled…

The R-package REPPlab is designed to explore multivariate data sets using one-dimensional unsupervised projection pursuit. It is useful in practice as a preprocessing step to find clusters or as an outlier detection tool for multivariate…

Monitoring progress on the United Nations Sustainable Development Goals (SDGs) is important for both academic and non-academic organizations. Existing approaches to monitoring SDGs have focused on specific data types; namely, publications…

We construct a map from knots to (abstract) 2-knots which can be extended to higher dimensions; this map is the natural "knot" counterpart for "braid" theory of groups $G_{n}^{k}$.