Related papers: GRLite and GRTensorJ: Graphical user interfaces to…
We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2), su(3), and g(2). This leads to an efficient practical method to reduce tensor…
As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful…
Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package…
We present TNRKit, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit, it provides a…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
ImageJ is a graphical user interface (GUI) driven, public domain, Java-based, software package for general image processing traditionally used mainly in life sciences fields. The image processing capabilities of ImageJ are useful and…
Spectral line observations are an indispensable tool to remotely probe the physical and chemical conditions throughout the universe. Modelling their behaviour is a computational challenge that requires dedicated software. In this paper, we…
Graph data have become increasingly common. Visualizing them helps people better understand relations among entities. Unfortunately, existing graph visualization tools are primarily designed for single-person desktop use, offering limited…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
Neutrino telescopes, an extension of traditional multiwavelength astronomy, provide a complementary view of the universe using neutrinos. Differences in detector geometry and detection medium mean that improvements to reconstruction…
We give graphical presentations for the two quantum subgroups of type $G_2$. To do this we use a method of extending a tensor category by embedding the planar algebra of a $\otimes$-generating object into the graph planar algebra of this…
It is shown that for a large class of non-holonomic quantum mechanical systems one can make the computation of BRST charge fully algorithmic. Two computer algebra programs written in the language of {\tt REDUCE} are described. They are able…
ImageJ is a graphical user interface (GUI) driven, public domain, Java-based, software package for general image processing traditionally used mainly in life sciences fields. The image processing capabilities of ImageJ are useful and…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor…
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on…
Developing autonomous agents that effectively interact with Graphic User Interfaces (GUIs) remains a challenging open problem, especially for small on-device models. In this paper, we present Ferret-UI Lite, a compact, end-to-end GUI agent…
We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…