Related papers: ReLie: a Reduce program for Lie group analysis of …

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the…

This study will explicitly demonstrate by example that an unrestricted infinite and forward recursive hierarchy of differential equations must be identified as an unclosed system of equations, despite the fact that to each unknown function…

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…

In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…

The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to…

This paper proposed a new regression model called $l_1$-regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a…

Large language models (LLMs) achieve high performance on mathematical reasoning, but these results can be inflated by training data leakage or superficial pattern matching rather than genuine reasoning. To this end, an adversarial…

Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization.…

Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for…

Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…

Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

This study uses Lie's theory of symmetries to compute the symmetry group of a class of partial differential equations parameterized by four constants: $u_{t}=-\left((a-bx)u_{x}+(d-ey)u_{y}+\frac{x}{2}u_{xx}+\frac{y}{2}u_{yy}\right)$; under…

The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had succesful applications in both mathematics and theoretical physics. This work deals with generalizations of the…

A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points of view. The classifications of Lie reduction operators and…

We present in this paper a routine which construct the ideal generated by a list of elements in a matrix Lie algebra at any particular characteristic. We have used this algorithm to analyze the problem of the simplicity of some Lie…

Large language models (LLMs) are increasingly used to solve complex tasks where they must retrieve and compose many pieces of in-context information in long reasoning chains. For many real-world tasks it is hard to accurately gauge how…