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...
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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...
This paper presents a computationally efficient machine-learned method for natural language response suggestion. Feed-forward neural networks using n-gram embedding features encode messages into vectors which are optimized to give message-response pa...
As a fundamental communicative service, email is playing an important role in both individual and corporate communications, which also makes it one of the most frequently attack vectors. An email's authenticity is based on an authentication chain inv...
In this paper we provide nearly linear time algorithms for several problems closely associated with the classic Perron-Frobenius theorem, including computing Perron vectors, i.e. entrywise non-negative eigenvectors of non-negative matrices, and solvi...
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...
The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed. However, this me...
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...
Network embedding is a method to learn low-dimensional representation vectors for nodes in complex networks. In real networks, nodes may have multiple tags but existing methods ignore the abundant semantic and hierarchical information of tags. This i...
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