Related papers: The Willing Kingdon Clifford Algebra Library
In this paper we introduce GP+, an open-source library for kernel-based learning via Gaussian processes (GPs) which are powerful statistical models that are completely characterized by their parametric covariance and mean functions. GP+ is…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
PyGOD is an open-source Python library for detecting outliers in graph data. As the first comprehensive library of its kind, PyGOD supports a wide array of leading graph-based methods for outlier detection under an easy-to-use,…
Any cutting-edge scientific research project requires a myriad of computational tools for data generation, management, analysis and visualization. Python is a flexible and extensible scientific programming platform that offered the perfect…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…
The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
We introduce TurboGP, a Genetic Programming (GP) library fully written in Python and specifically designed for machine learning tasks. TurboGP implements modern features not available in other GP implementations, such as island and cellular…
Despite the prevalence of symmetry in scientific linear systems, these structural properties are often underutilized by standard computational software. This paper introduces PySymmetry, an open-source Sage/Python framework that implements…
The last two decades, since the seminal work of Selig, has seen projective geometric algebra (PGA) gain popularity as a modern coordinate-free framework for doing classical Euclidean geometry and other Cayley-Klein geometries. This…
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into…
Organizations have realized the importance of data analysis and its benefits. This in combination with Machine Learning algorithms has allowed to solve problems more easily, making these processes less time-consuming. Neural networks are…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
This paper presents $\mu\text{KG}$, an open-source Python library for representation learning over knowledge graphs. $\mu\text{KG}$ supports joint representation learning over multi-source knowledge graphs (and also a single knowledge…
Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support…
We show that main results of rational trigonometry (as developed by NJ Wildberger, "Divine Proportions", 2005) can be succinctly expressed using projective geometric algebra (PGA). In fact, the PGA representation exhibits distinct…