This note defines a flag vector for $i$-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author's "On quantum topology...
4 days ago · With Vector Search, you can create two types of indexes, depending on how you plan to update them with your data. You can create an index designed for batch updates, or an index …
Our main result states that whenever we have a non-Euclidean norm $\|\cdot\|$ on a two-dimensional vector space $X$, there exists some $x\neq 0$ such that for every $λ\neq 1, λ>0$, there exist $y, z\in X$ verifying that $\|y\|=λ\|x\|$, $z\neq 0$,...
We address the problem of self-supervised learning on discrete event sequences generated by real-world users. Self-supervised learning incorporates complex information from the raw data in low-dimensional fixed-length vector representations that coul...
We propose a novel convolutional method for the detection and identification of vertebrae in whole spine MRIs. This involves using a learnt vector field to group detected vertebrae corners together into individual vertebral bodies and convolutional i...
num Systems. The idea behind the condition involves solving an n n system of equations Ax = b, where x is an n 1 (\column vector") of unknowns, b is a given n 1 (the \constants" of the equation or \system …
This report documents, describes, and evaluates new 2024 English GloVe (Global Vectors for Word Representation) models. While the original GloVe models built in 2014 have been widely used and found useful, languages and the world continue to evolve a...
The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface or a cur...
This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and polytopes, i...
This contribution proposes a recursive, computationally efficient, ready-to-use, online method for the ellipsoidal state characterization for linear discrete-time models with additive unknown disturbances vectors (bounded by known possibly degenerate...
We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing....
The purpose of this paper is to investigate applications the covariant derivatives, killing vector fields and to calculate the components of the curvature tensor CGR of the Cheeger-Gromoll metric with respect to adapted frames in a the Riemannian man...
The main purpose of present paper is to study the affine connection induced from the horizontal lift on the cross-section determined by a vector field in Mn with respect to the adapte frame of ....
Braid Floer homology is an invariant of proper relative braid classes. Closed integral curves of 1-periodic Hamiltonian vector fields on the 2-disc may be regarded as braids. If the Braid Floer homology of associated proper relative braid classes is...
Knowledge graph embedding (KGE) has been shown to be a powerful tool for predicting missing links of a knowledge graph. However, existing methods mainly focus on modeling relation patterns, while simply embed entities to vector spaces, such as real f...
projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various
We present a geometric construction of central extensions of covering groups of the group of volume preserving diffeomorphisms, integrating central extensions of the Lie algebra of divergence free vector fields defined by Lichnerowicz cocycles. Certa...
We generalize the prequantization central extension of a group of diffeomorphisms preserving a closed 2-form ω(ω-invariant diffeomorphisms) to an abelian extension of a group of diffeomorphisms preserving a closed vector valued 2-form ω, up to a l...
objects related to a vector space. Tensor may also refer to: Tensor (intrinsic definition) Tensor field Tensor product Tensor (obsolete), the norm used on the
two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense