Related papers: Fast matrix representation for Clifford algebras
In this work the algorithms of fast multiplication of matrices are considered. To any algorithm there associated a certain group of automorphisms. These automorphism groups are found for some well-known algorithms, including algorithms of…
Irreducible representations of both Leavitt and Cohn path algebras of an arbitrary digraph with coefficients in a commutative field is classified. They are constructed in several ways using both infinite paths on the right as well as direct…
Ram and Rammage have introduced an automorphism and Clifford theory on affine Hecke algebras. Here we will extend them to cyclotomic Hecke algebras and rational Cherednik algebras.
We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the…
This paper initiates a systematic study of the cyclotomic KLR algebras of affine types $A$ and $C$. We start by introducing a graded deformation of these algebras and the constructing all of the irreducible representations of the deformed…
The modular composite representation (MCR) is a computing model that represents information with high-dimensional integer vectors using modular arithmetic. Originally proposed as a generalization of the binary spatter code model, it aims to…
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…
When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier…
This paper revisits the little-known Gibbs-Rodrigues representation of rotations in a three-dimensional space and demonstrates a set of algorithms for handling it. In this representation the rotation is itself represented as a…
Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that…
A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
Given a large unlabeled set of images, how to efficiently and effectively group them into clusters based on extracted visual representations remains a challenging problem. To address this problem, we propose a convolutional neural network…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…
We describe the representation theory of C*-crossed-products of a unital C*-algebra A by the cyclic group of order 2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…