Related papers: An Analytic Method for $S$-Expansion involving Res…
By means of a generalization of the Maurer-Cartan expansion method we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher order Maurer-Cartan equations for the case $\mathcal{G}=V_{0}\oplus V_{1}$ are…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
S-expansions of three-dimensional real Lie algebras are considered. It is shown that the expansion operation allows one to obtain a non-unimodular Lie algebra from a unimodular one. Nevertheless S-expansions define no ordering on the…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
We introduce a framework for expanding residual computational graphs using jets, operators that generalize truncated Taylor series. Our method provides a systematic approach to disentangle contributions of different computational paths to…
Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…
We tackle the task of Term Set Expansion (TSE): given a small seed set of example terms from a semantic class, finding more members of that class. The task is of great practical utility, and also of theoretical utility as it requires…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
The supermultiplet model, based on the reduction chain $\mathfrak{su}(4) \supset \mathfrak{su}(2) \times \mathfrak{su}(2)$, is revisited through the lens of commutants within universal enveloping algebras of Lie algebras. From this…
The transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first…
After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras.…
Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation…
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
A method of constructing finite $p$-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci-Sylvester (greedy) algorithm by iterating a $p$-adic division algorithm. The method extends to…
To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…
We explore the question concerning the number of distinct resonant algebras depending on the generator content, which consists of the Lorentz generator, translation, and new additional Lorentz-like and translation-like generators. Such…
Relation Extraction (RE) is a pivotal task in automatically extracting structured information from unstructured text. In this paper, we present a multi-faceted approach that integrates representative examples and through co-set expansion.…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…