Related papers: Visually pleasing knot projections in R
To harness the full benefit of new computing platforms, it is necessary to develop software with parallel computing capabilities. This is no less true for statisticians than for astrophysicists. The R programming language, which is perhaps…
The rise of the programmable web offers new opportunities for the empirically driven social sciences. The access, compilation and preparation of data from the programmable web for statistical analysis can, however, involve substantial…
We construct a graph G such that any embedding of G into R^{3} contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H…
Reductivity of knot projections refers to the minimum number of splices of double points needed to obtain reducible knot projections. Considering the type and method of splicing (Seifert type splice or non-Seifert type splice, recursively…
In this article, we present a problem of nonlinear constraint optimization with equality and inequality constraints. Objective functions are defined to be nonlinear and optimizers may have a lower and upper bound. We solve the optimization…
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…
This paper develops an R package rMultiNet to analyze multilayer network data. We provide two general frameworks from recent literature, e.g. mixture multilayer stochastic block model(MMSBM) and mixture multilayer latent space model(MMLSM)…
We introduce a graphical user interface for constructing arbitrary tensor networks and specifying common operations like contractions or splitting, denoted GuiTeNet. Tensors are represented as nodes with attached legs, corresponding to the…
Neural networks have excelled at regression and classification problems when the input space consists of scalar variables. As a result of this proficiency, several popular packages have been developed that allow users to easily fit these…
The kendallknight package introduces an efficient implementation of Kendall's correlation coefficient computation, significantly improving the processing time for large datasets without sacrificing accuracy. The kendallknight package,…
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…
New presentations of a link and a virtual link are introduced and algebraic systems on links and virtual links are constructed respectively. Based on the algebraic systems, Reduction Crossing Algorithms for them are proposed which are used…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
Graph Neural Networks (GNNs) have achieved significant success across various applications. However, their complex structures and inner workings can be challenging for non-AI experts to understand. To address this issue, this study presents…
In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least four, and height at least…
This paper introduces the R package FKSUM, which offers fast and exact evaluation of univariate kernel smoothers. The main kernel computations are implemented in C++, and are wrapped in simple, intuitive and versatile R functions. The fast…
For a virtual knot $K$ and an integer $r\geq 0$, the $r$-covering $K^{(r)}$ is defined by using the indices of chords on a Gauss diagram of $K$. In this paper, we prove that for any finite set of virtual knots $J_0,J_2,J_3,\dots,J_m$, there…
Calendars are broadly used in society to display temporal information, and events. This paper describes a new R package with functionality to organize and display temporal data, collected on sub-daily resolution, into a calendar layout. The…
In this work we present a visualization tool specifically tailored to deal with skewed data. The technique is based upon the use of two types of notched boxplots (the usual one, and one which is tuned for the skewness of the data), the…
In this short article I introduce the mvp package, which provides some functionality for handling multivariate polynomials. The package uses the C++ Standard Template Library's map class to store and retrieve elements; it conforms to…