Related papers: The KnotMosaics Package for SageMath
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
The scientific computing landscape has evolved dramatically in the past few years, with new schemes for organizing and storing data that reflect the growth in size and complexity of astronomical data sets. In response to this changing…
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically…
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…
A GraphMaps is a system that visualizes a graph using zoom levels, which is similar to a geographic map visualization. GraphMaps reveals the structural properties of the graph and enables users to explore the graph in a natural way by using…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
A knot mosaic is a grid of pictorial tiles representing a tame knot or link. Recently, two groups independently introduced a new set of tiles. We call mosaics made with these new tiles corner mosaics. The (corner) tile number is the minimum…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
Lomonaco and Kauffman introduced a knot mosaic system to give a definition of a quantum knot system which can be viewed as a blueprint for the construction of an actual physical quantum system. A knot $n$-mosaic is an $n \times n$ matrix of…
We introduce MOSAIC, a Python program for machine learning models. Our framework is developed with in mind accelerating machine learning studies through making implementing and testing arbitrary network architectures and data sets simpler,…
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by…
Knots and links represent a fundamental motif of non-local connectivity that permeates the physical sciences from string theory to protein folds. While spectral braiding has been explored in two-band non-Hermitian models across various…
We introduce pygrank, an open source Python package to define, run and evaluate node ranking algorithms. We provide object-oriented and extensively unit-tested algorithm components, such as graph filters, post-processors, measures,…
We propose KnotGym, an interactive environment for complex, spatial reasoning and manipulation. KnotGym includes goal-oriented rope manipulation tasks with varying levels of complexity, all requiring acting from pure image observations.…
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…
This article describes a software named "KnotPortal" for visualization of branched covers of knots based on an idea by Bill Thurston to view a knot as a portal to other universes. Our implementation allows users to explore these knotted…
We describe a new method of producing equations for the canonical component of representation variety of a knot group into $PSL_2(\mathbb{C})$. Unlike known methods, this one does not involve any polyhedral decomposition or triangulation of…
The coil in transcranial magnetic stimulation (TMS) determines the spatial shape of the electromagnetic field in the head, which structures are concurrently activated, and how focal stimulation is. Most of the readily available coils have…
Grid diagrams are a combinatorial version of classical link diagrams, widely used in theoretical, computational and applied knot theory. Motivated by questions from (bio)-physical knot theory, we introduce GridPyM, a Sage compatible Python…