Related papers: Geometrical Representation for Number-theoretic Tr…
In differential geometry, geometric structures can often be encoded by differential forms satisfying algebraic and differential constraints. This is in particular the case for spinorial G-structures, where the defining tensors are…
Mulmuley and Sohoni (GCT1 in SICOMP 2001, GCT2 in SICOMP 2008) proposed to view the permanent versus determinant problem as a specific orbit closure problem and to attack it by methods from geometric invariant and representation theory. We…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…
We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
In this chapter we give a geometric representation of $H_{n}(B;\mathbb{L})$ classes, where $\mathbb{L}$ is the $4$-periodic surgery spectrum, by establishing a relationship between the normal cobordism classes…
For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the…
This paper studies the geometry of binary hyperdimensional computing (HDC), a computational scheme in which data are encoded using high-dimensional binary vectors. We establish a result about the similarity structure induced by the HDC…
The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as…
We introduce partial duality of hypermaps, which include the classical Euler-Poincar\'e duality as a particular case. Combinatorially, hypermaps may be described in one of three ways: as three involutions on the set of flags (bi-rotation…
In this paper, we propose a new representation for multiview image sets. Our approach relies on graphs to describe geometry information in a compact and controllable way. The links of the graph connect pixels in different images and…
We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…
Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…