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Linear and quadratic optimization are crucial in numerous real-world applications, ranging from training machine learning models to solving integer linear programs. Recently, learning-to-optimize methods (L2O) for linear (LPs) or quadratic…

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…

Noether's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that…

Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error density is a scale mixture of multivariate…

This paper investigates the geometry of compact stellar objects via Noether symmetry strategy in the framework of curvature-matter coupled gravity. For this purpose, we assume the specific model of this theory to evaluate Noether equations,…

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

The universal principle obtained by Emmy Noether in 1918, asserts that the invariance of a variational problem with respect to a one-parameter family of symmetry transformations implies the existence of a conserved quantity along the…

The exterior differential system for constant mean curvature (CMC) surfaces in a 3-dimensional space form is an elliptic Monge-Ampere system defined on the unit tangent bundle. We determine the infinite sequence of higher-order symmetries…

The theorem of Noether dictates that for every continuous symmetry group of an Action the system must possess a conservation law. In this paper we discuss some subgroups of Arnold's labelling symmetry diffeomorphism related to…

With the increase of computing power, machine learning models in medical imaging have been introduced to help in rending medical diagnosis and inspection, like hemophilia, a rare disorder in which blood cannot clot normally. Often, one of…

The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…

In this paper, we explore and compare multiple solutions to the problem of data augmentation in image classification. Previous work has demonstrated the effectiveness of data augmentation through simple techniques, such as cropping,…

The success of deep learning depends heavily on the availability of large datasets, but in robotic manipulation there are many learning problems for which such datasets do not exist. Collecting these datasets is time-consuming and…

The aim of this paper is to present a new approach to construct constants of motion associated with scaling symmetries of dynamical systems. Scaling maps could be symmetries of the equations of motion but not of its associated Lagrangian…

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

Data augmentation is essential to achieve state-of-the-art performance in many deep learning applications. However, the most effective augmentation techniques become computationally prohibitive for even medium-sized datasets. To address…

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…

Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…