In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881-1884. This original document is preserved in the Dibner Library of the History of Sc...
In this paper we consider so-called Google matrices and show that all eigenvalues ($λ$) of them have a fundamental property $|λ|\leq 1$. The stochastic eigenvector corresponding to $λ=1$ called the PageRank vector plays a central role in the Googl...
The steel industry has great impacts on the economy and the environment of both developed and underdeveloped countries. The importance of this industry and these impacts have led many researchers to investigate the relationship between a country's st...
A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived....
mod: Modulo Operator Description Modulo operator. Usage mod(n, m) modq(a, b, k) Value a numeric (integer) value or vector/matrix, resp. an integer number
Bidirectional encoder representations from transformers (BERT) is a language model introduced in October 2018 by researchers at Google. [1][2] It learns to represent text as a sequence of vectors …
Bidirectional encoder representations from transformers (BERT) is a language model introduced in October 2018 by researchers at Google. [1][2] It learns to represent text as a sequence of vectors …
The Systematic Normal Form (SysNF) is a canonical form of lattices introduced in [Eldar,Shor '16], in which the basis entries satisfy a certain co-primality condition. Using a "smooth" analysis of lattices by SysNF lattices we design a quantum algori...
Download design elements for free: icons, photos, vector illustrations, and music for your videos. All the assets made by designers → consistent quality ⚡️.
We provide with criteria for a family of sequences of operators to share a frequently universal vector. These criteria are variants of the classical Frequent Hypercyclicity Criterion and of a recent criterion due to Grivaux, Matheron and Menet where...
differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon denoted by ( X
Deep learning currently dominates the benchmarks for various NLP tasks and, at the basis of such systems, words are frequently represented as embeddings --vectors in a low dimensional space-- learned from large text corpora and various algorithms hav...
We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures: the Linearly...
The boosted Taub-NUT metric with zero ADM mass is shown to possess a dual momentum in the direction of the boost giving credit to the existence of another 4-vector K_μin linearized gravity associated to the NUT charge and dual to the usual P_μ. T...
A nut graph is a nontrivial simple graph whose adjacency matrix contains a one-dimensional null space spanned by a vector without zero entries. Moreover, an $\ell$-circulant graph is a graph that admits a cyclic group of automorphisms having $\ell$ v...
A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which non-trivial kernel vectors do not contain a zero. Chemical graphs are connected, with maximum degree at most three. We present a new algorithm for the ex...
A nut graph is a simple graph whose kernel is spanned by a single full vector (i.e. the adjacency matrix has a single zero eigenvalue and all non-zero kernel eigenvectors have no zero entry). We classify generalisations of nut graphs to nut digraphs:...
Soit F la catégories des foncteurs entre espaces vectoriels sur le corps à deux éléments. À l'aide des catégories de foncteurs en grassmanniennes, nous avons émis dans [Dja06a] une conjecture décrivant la filtration de Krull de la catégori...
In this paper, we introduce a MusIc conditioned 3D Dance GEneraTion model, named MIDGET based on Dance motion Vector Quantised Variational AutoEncoder (VQ-VAE) model and Motion Generative Pre-Training (GPT) model to generate vibrant and highquality d...
In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time, quantum co...