Related papers: ReLie: a Reduce program for Lie group analysis of …
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
In recent years, there has been a growing interest in low-light image enhancement (LLIE) due to its importance for critical downstream tasks. Current Retinex-based methods and learning-based approaches have shown significant LLIE…
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study…
This paper presents EASE (Effortless Algorithmic Solution Evolution), an open-source and fully modular framework for iterative algorithmic solution generation leveraging large language models (LLMs). EASE integrates generation, testing,…
We investigate a class of Lie algebras which we call {\it generalized reductive Lie algebras}. These are generalizations of semi-simple, reductive, and affine Kac-Moody Lie algebras. A generalized reductive Lie algebra which has an…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.
The current technology landscape lacks a foundational AI model for solving process engineering calculations. In this work, we introduce a novel autonomous agent framework leveraging Retrieval-Augmented Instruction-Tuning (RAIT) to enhance…
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…
We propose regular expression inference (REI) as a challenge for code/language modelling, and the wider machine learning community. REI is a supervised machine learning (ML) and program optimisation task, and poses the problem of finding…
An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of…
Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities.…
We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of…
We present the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra branching of…
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and…
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…
We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.
We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…