Related papers: Weighted distance transforms generalized to module…

We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…

We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we prove that if the size of the working finite field is large compared to the degree of the code, the low weight…

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…

In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) cubic lattices. We prove that…

Let G be a connected reductive group. To any irreducible G-variety one assigns the lattice generated by all weights of B-semiinvariant rational functions on X, where B$ is a Borel subgroup of G. This lattice is called the weight lattice of…

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new…

We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…

We investigate approaches to regularisation during fine-tuning of deep neural networks. First we provide a neural network generalisation bound based on Rademacher complexity that uses the distance the weights have moved from their initial…

We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…

Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…

We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…

Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…

Approximating distance is one of the key challenge in a facility location problem. Several algorithms have been proposed, however, none of them focused on estimating distance between two concave regions. In this work, we present an…

In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance…

This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a…

We explore the application of volumetric reconstruction from structured-light sensors in cognitive neuroscience, specifically in the quantification of the size-weight illusion, whereby humans tend to systematically perceive smaller objects…

Chamfer Distance (CD) is a widely adopted metric in 3D point cloud learning due to its simplicity and efficiency. However, it suffers from a fundamental limitation: it relies solely on Euclidean distances, which often fail to capture the…

In recent study in Ref.[7] (arXiv: 2401.12525), we have introduced a method aimed at calculating the weak-field asymptotic deflection angle. This method offers an efficient computational approach that avoids the complexities of integration…