Related papers: Knotted Portals in Virtual Reality
Acupuncture is a widely adopted medical practice that involves inserting thin needles into specific points on the body to alleviate pain and treat various health conditions. Current learning practices heavily rely on 2D atlases and practice…
Haptic sensations that align with virtual reality (VR) experiences have a profound impact on presence and enjoyment. There is potential to explore the dynamic capabilities of pneumatic inflatables to offer immersive sensations in virtual…
Over the years, several Bridges papers have delved into the concept of danceability of a knot diagram. Inspired by dancing on non-orientable surfaces, in this paper, we expand danceability to twisted virtual knot diagrams. This paper is…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
The notion of a virtual knot introduced by L. Kauffman induces the notion of a virtual braid. It is closely related with a welded braid of R. Fenn, R. Rimanyi and C. Rourke. Alexander's and Markov's theorems for virtual knots and braids are…
Virtual reality (VR) enables data visualization in an immersive and engaging manner, and it can be used for creating ways to explore scientific data. Here, we use VR for visualization of 3D histology data, creating a novel interface for…
We study virtualized Delta, sharp, and pass moves for oriented virtual links, and give necessary and sufficient conditions for two oriented virtual links to be related by the local moves. In particular, they are unknotting operations for…
This paper studies an algebraic invariant of virtual knots called the biquandle. The biquandle generalizes the fundamental group and the quandle of virtual knots. The approach taken in this paper to the biquandle emphasizes understanding…
While Virtual Reality (VR) systems have become increasingly immersive, they still rely predominantly on visual input, which can constrain perceptual performance when visual information is limited. Incorporating additional sensory…
The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of…
We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and…
We define new notions of groups of virtual and welded knots (or links) and we study their relations with other invariants, in particular the Kauffman group of a virtual knot.
We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that…
In this paper, we introduce invariants of virtual knotoids based on biquandles and biquandle virtual brackets. We show that one of these invariants, namely biquandle virtual bracket matrix, is a proper enhancement of the other invariants…
In this paper, we propose a new interface for virtual reality headset: a touchpad in front of the headset. To demonstrate the feasibility of the front touch interface, we built a prototype device, explored VR UI design space expansion, and…
A virtual knot, which is one of generalizations of knots in $\mathbb{R}^{3}$ (or $S^{3}$), is, roughly speaking, an embedded circle in thickened surface $S_{g} \times I$. In this paper we will discuss about knots in 3 dimensional $S_{g}…
We present ATLASrift - a Virtual Reality application that provides an interactive, immersive visit to ATLAS experiment. We envision it being used in two different ways: first as an educational and outreach tool - for schools, universities,…
This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial.…
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…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…