Related papers: On matrix Lax representations for (1+1)-dimensiona…

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…

I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group…

Tuning scientific and probabilistic machine learning models $-$ for example, partial differential equations, Gaussian processes, or Bayesian neural networks $-$ often relies on evaluating functions of matrices whose size grows with the data…

A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method of construction of exact solutions, based on a class of…

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…

Medical Lay Language Generation (MLLG) plays a vital role in improving the accessibility of complex scientific content for broader audiences. Recent literature to MLLG commonly employ parameter-efficient fine-tuning methods such as Low-Rank…

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are…

The Myrzakulov-Lakshmanan-II (ML-II) equation is one of a (2+1)-dimensional generalizations of the Heisenberg ferromagnetic equation. It is integrable and has a non-isospectral Lax representation. In this paper, the Darboux transformation…

This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction,…

A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.

In this article, we study Momentum Light Ray Transform (MLRT) on symmetric tensor fields. MLRT is an integral transform in time-space domain ($(t,x)\in \mathbb{R}^{1+n}$), which integrates a scalar function or a tensor field along the light…

Augmented generation techniques such as Retrieval-Augmented Generation (RAG) and Cache-Augmented Generation (CAG) have revolutionized the field by enhancing large language model (LLM) outputs with external knowledge and cached information.…

The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…

There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn…

Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroinformatics. However, the understanding of whether DR and…

In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of…