Related papers: Visually pleasing knot projections in R

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external…

Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore intriguing that no proper studies and tools have been…

This paper aims to develop a mathematical foundation to model knitting with graphs. We provide a precise definition for knit objects with a knot theoretic component and propose a simple undirected graph, a simple directed graph, and a…

In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…

Bootstrapping is a popular and computationally demanding resampling method used for measuring the accuracy of sample estimates and assisting with statistical inference. R is a freely available language and environment for statistical…

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al.…

CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows the user to formulate convex optimization problems in a natural mathematical syntax…

A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space…

RNA 3D architectures are stabilized by sophisticated networks of (non-canonical) base pair interactions, which can be conveniently encoded as multi-relational graphs and efficiently exploited by graph theoretical approaches and recent…

We present vivid, an R package for visualizing variable importance and variable interactions in machine learning models. The package provides a range of displays including heatmap and graph-based displays for viewing variable importance and…

We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks for transforming the unknot into other knots. We encode such a…

The simulator is an R package that streamlines the process of performing simulations by creating a common infrastructure that can be easily used and reused across projects. Methodological statisticians routinely write simulations to compare…

We propose the use of beamplots - which can be produced by using the R package BibPlots and WoS downloads - as a preferred alternative to h index values for assessing single researchers.

Let n be any integer greater than two. We prove that there exists a projection P having the following properties. (1) P is not the projection of any unknotted knot. (2) The singular point set of P consists of double points. (3) P is the…

R is a language and computing environment that has been developed for data manipulation, statistical computing, and scientific graphing. In the paper, we demonstrate its use analyzing data collected in a few experiments taken from an…

An \"{u}bercrossing diagram is a knot diagram with only one crossing that may involve more than two strands of the knot. Such a diagram without any nested loops is called a petal projection. Every knot has a petal projection from which the…

The mplot package provides an easy to use implementation of model stability and variable inclusion plots (M\"uller and Welsh 2010; Murray, Heritier, and M\"uller 2013) as well as the adaptive fence (Jiang, Rao, Gu, and Nguyen 2008; Jiang,…

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use…

This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.

The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially…