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
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 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:...
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...
Elastic and inelastic neutron scattering studies of Li(Ni$_{1-x}$Fe$_{x}$)PO$_4$ single crystals reveal anomalous spin-wave dispersions along the crystallographic direction parallel to the characteristic wave vector of the magnetic incommensurate p...
We set out an elementary approach to derive Visible Point Identities summed on lattice points of inverted triangle (2D), pyramid (3D), hyperpyramid (4D, 5D and so on) utilizing the greatest common divisor for the nD Visible Point Vectors. This enable...
The aim of this paper is to propose an application of mutual information-based ensemble methods to the analysis and classification of heart beats associated with different types of Arrhythmia. Models of multilayer perceptrons, support vector machines...
We characterize the range of the attenuated and non-attenuated $X$-ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert transform associated with the $A$-analytic functions à la Bukhgeim. As...
graphics editor for creating illustrations, as well as logos, icons, and other elements of graphic design. It is primarily focused on editing drawings in the
Augmented Reality (AR) is a powerful perceptual technology that can alter what users see, hear, feel, and experience throughout their daily lives. When combined with the speed and flexibility of context-aware generative AI, the power is greatly expan...
The elastic-input neuro tagger and hybrid tagger, combined with a neural network and Brill's error-driven learning, have already been proposed for the purpose of constructing a practical tagger using as little training data as possible. When a smal...
Jan 31, 2018 · 数学上通常是什么原因叫一件东西做「canonical」？ 研究神经网络时，有某个 vector embedding 我想叫它做 canonical，不知是否恰当？ 显示全部 关注者 210 被浏览
Stroking and filling are the two basic rendering operations on paths in vector graphics. The theory of filling a path is well-understood in terms of contour integrals and winding numbers, but when path rendering standards specify stroking, they resor...
Stroking a path is one of the two basic rendering operations in vector graphics standards (e.g., PostScript, PDF, SVG). We survey path stroking rendering results from real-world software implementations of path stroking for anecdotal evidence that su...
A correlation is a binary vector that encodes all possible positions of overlaps of two words, where an overlap for an ordered pair of words (u,v) occurs if a suffix of word u matches a prefix of word v. As multiple pairs can have the same correlatio...
GENtle is a free software under GPL license. GENtle is an equivalent to the proprietary Vector NTI, a tool for molecular biologists to analyze and edit
I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?