Meta-Learning on Graph with Curvature-Based Analysis (Student Abstract)

Learning latent representations in graphs is finding a mapping that embeds nodes or edges as data points in a low-dimensional vector space. This paper introduces a flexible framework to enhance existing methodologies that have difficulty capturing local proximity and global relationships at the same time. Our approach generates a virtual edge between non-adjacent nodes based on the Forman-Ricci curvature in network. By analyzing the network using topological information, global relationships structurally similar can easily be detected and successfully integrated with previous works.

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The genus of graphs associated with vector spaces

Journal of Algebra and Its Applications ◽

10.1142/s0219498820500863 ◽

2019 ◽

Vol 19 (05) ◽

pp. 2050086 ◽

Cited By ~ 1

Author(s):

T. Tamizh Chelvam ◽

K. Prabha Ananthi

Keyword(s):

Finite Field ◽

Vector Space ◽

Undirected Graph ◽

Vector Spaces ◽

Dimensional Vector ◽

Vertex Connectivity ◽

Dimensional Vector Space ◽

Nonzero Component ◽

Vertex Set ◽

Component Graph

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

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Linear Transformations in n-Dimensional Vector Space. An Introduction to the Theory of Hilbert Space

The Mathematical Gazette ◽

10.2307/3608979 ◽

1953 ◽

Vol 37 (320) ◽

pp. 156

Author(s):

J. L. B. Copper ◽

H. L. Hamburger ◽

M. E. Grimshaw

Keyword(s):

Hilbert Space ◽

Vector Space ◽

Dimensional Vector ◽

Linear Transformations ◽

Dimensional Vector Space

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Algebraically nonequivalent constructivization for infinite-dimensional vector space

Algebra and Logic ◽

10.1007/bf01978555 ◽

1990 ◽

Vol 29 (6) ◽

pp. 430-440 ◽

Cited By ~ 2

Author(s):

D. V. Lytkina

Keyword(s):

Vector Space ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Infinite Dimensional

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THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

Bulletin of the Australian Mathematical Society ◽

10.1017/s000497271100253x ◽

2011 ◽

Vol 85 (1) ◽

pp. 19-25

Author(s):

YIN CHEN

Keyword(s):

Finite Field ◽

Projective Space ◽

Vector Space ◽

Orthogonal Group ◽

Homogeneous Polynomial ◽

Classical Group ◽

Projective Group ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Projective Linear Group

AbstractLet Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

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Identities Generalizing the Theorems of Pappus and Desargues

Symmetry ◽

10.3390/sym13081382 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1382

Author(s):

Roger D. Maddux

Keyword(s):

Projective Plane ◽

Vector Space ◽

Invariant Theory ◽

Lattice Theory ◽

Three Dimensional ◽

Dimensional Vector ◽

Dimensional Vector Space

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

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The study of one-factor regression models with parameters in the form of linear operators MATRICES of two-dimensional vector space

Information Technology and Mathematical Modeling in the Management of Complex Systems ◽

10.26731/2658-3704.2020.2(7).1-13 ◽

2020 ◽

pp. 1-13

Author(s):

Mikhail Pavlovich Bazilevskiy

Keyword(s):

Vector Space ◽

Regression Models ◽

Linear Operators ◽

Two Dimensional ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Factor Regression

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Sets of idempotents that generate the semigroup of singular endomorphisms of a finite-dimensional vector space

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500016618 ◽

1982 ◽

Vol 25 (2) ◽

pp. 133-139 ◽

Cited By ~ 5

Author(s):

R. J. H. Dawlings

Keyword(s):

Vector Space ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Finite Dimensional Vector Space ◽

Finite Dimensional ◽

Mathematical System

IfMis a mathematical system and EndMis the set of singular endomorphisms ofM, then EndMforms a semigroup under composition of mappings. A number of papers have been written to determine the subsemigroupSMof EndMgenerated by the idempotentsEMof EndMfor different systemsM. The first of these was by J. M. Howie [4]; here the case ofMbeing an unstructured setXwas considered. Howie showed that ifXis finite, then EndX=Sx.

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