Related papers: Visually pleasing knot projections in R
We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian…
Researchers in the humanities are among the many who are now exploring the world of big data. They have begun to use programming languages like Python or R and their corresponding libraries to manipulate large data sets and discover brand…
Contouring is an indispensable step in Radiotherapy (RT) treatment planning. However, today's contouring software is constrained to only work with a 2D display, which is less intuitive and requires high task loads. Virtual Reality (VR) has…
In this short article I introduce the "jordan" package which provides functionality for working with different types of Jordan algebra. I give some numerical verification of the Jordan identity for the five types of Jordan algebras. The…
Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via…
Software is increasingly produced in the form of ecosystems, collections of interdependent components maintained by a distributed community. These ecosystems act as network organizations, not markets, and thus often lack actionable…
This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction…
Motivation: Revealing structural variations across sequences of closely related individuals or species is crucial for understanding their diversification mechanisms and roles. Results: We developed PatchWorkPlot, a tool for visualization of…
Parcellations are fundamental tools in neuroanatomy, allowing researchers to place functional imaging and molecular data within a structural context in the brain. Visualizing these parcellations is critical to guide biological understanding…
We present a certified algorithm that takes a smooth algebraic curve in $\mathbb{R}^n$ and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}^2$. Our algorithm is designed for curves given implicitly…
Book covers are intentionally designed and provide an introduction to a book. However, they typically require professional skills to design and produce the cover images. Thus, we propose a generative neural network that can produce book…
We study a quantum version of the $n$-dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in particular, can be used to construct the Jones polynomial…
Summary: R and Matlab are two high-level scientific programming languages which are frequently applied in computational biology. To extend the wide variety of available and approved implementations, we present the Rcall interface which runs…
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link…
This paper explores the interactions between knot theory and quantum computing. On one side, knot theory has been used to create models of quantum computing, and on the other, it is a source of computational problems. Knot theory is often…
In this paper, we introduce a package for semi-supervised learning research in the R programming language called RSSL. We cover the purpose of the package, the methods it includes and comment on their use and implementation. We then show,…
360{\deg} images are usually represented in either equirectangular projection (ERP) or multiple perspective projections. Different from the flat 2D images, the detection task is challenging for 360{\deg} images due to the distortion of ERP…
We show that for every m in N, there exists an n in N such that every embedding of the complete graph K_n in R^3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r in N such that every…
A plane curve is a knot diagram in which each crossing is replaced by a 4-valent vertex, and so are dual to a subset of planar quadrangulations. The aim of this paper is to introduce a new tool for sampling diagrams via sampling of plane…
Objects in the {\tt stl map} class of {\tt C++} associate a value to each of a set of keys. Accessing values or keys of such an object is problematic in the R programming language because the value-key pairs are not stored in a well-defined…