Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-015-0596-z
Abstract: Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for… read more here.
Keywords: valued orthogonal; clifford; clifford algebra; orthogonal polynomials ... See more keywords
General Steerable Two-sided Clifford Fourier Transform, Convolution and Mustard Convolution
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-016-0687-5
Abstract: In this paper we use the general steerable two-sided Clifford Fourier transform (CFT), and relate the classical convolution of Clifford algebra-valued signals over $${\mathbb{R}^{p,q}}$$Rp,q with the (equally steerable) Mustard convolution. A Mustard convolution can be… read more here.
Keywords: mustard convolution; convolution; clifford; general steerable ... See more keywords
Division Algebras, Clifford Algebras, Periodicity
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-018-0820-8
Abstract: The dimensions 2, 8 and 24 play significant roles in lattice theory. In Clifford algebra theory there are well-known periodicities of the first two of these dimensions. Using novel representations of the purely Euclidean Clifford… read more here.
Keywords: periodicity; clifford; clifford algebras; division algebras ... See more keywords
Blood vessel segmentation of retinal image using Clifford matched filter and Clifford convolution
Sign Up to like & getrecommendations! Published in 2019 at "Multimedia Tools and Applications"
DOI: 10.1007/s11042-019-08111-0
Abstract: The appearance and structure of blood vessels in retinal fundus image is a fundamental part of diagnosing different issues related with such as diabetes and hypertension. The proposed blood vessel segmentation in fundus image using… read more here.
Keywords: vessel segmentation; image; clifford; blood vessel ... See more keywords
Dynamics behavior for second-order neutral Clifford differential equations: inertial neural networks with mixed delays
Sign Up to like & getrecommendations! Published in 2020 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-020-01148-0
Abstract: In this paper, Clifford-valued inertial neutral neural networks with time-varying delays and infinite distributed delay are investigated. With the help of the pseudo almost periodic function theory, Banach’s fixed point theorem, and the differential inequality… read more here.
Keywords: mixed delays; neural networks; networks mixed; clifford ... See more keywords
On the Plemelj–Privalov theorem in Clifford analysis involving higher order Lipschitz classes
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123411
Abstract: Abstract The main purpose of this work is to prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator which arise naturally in polymonogenic Clifford algebra valued function… read more here.
Keywords: lipschitz classes; clifford; higher order; order lipschitz ... See more keywords
Unbiased simulation of near-Clifford quantum circuits
Sign Up to like & getrecommendations! Published in 2017 at "Physical Review A"
DOI: 10.1103/physreva.95.062337
Abstract: Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We present a method… read more here.
Keywords: simulation near; quantum circuits; clifford; simulation ... See more keywords
Direct Randomized Benchmarking for Multiqubit Devices.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review letters"
DOI: 10.1103/physrevlett.123.030503
Abstract: Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single… read more here.
Keywords: error rate; clifford; randomized benchmarking; direct randomized ... See more keywords
Globally Asymptotic Almost Automorphic Synchronization of Clifford-Valued RNNs With Delays
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Access"
DOI: 10.1109/access.2019.2912838
Abstract: In this paper, we consider a class of Clifford-valued recurrent neural networks (RNNs) with discrete and infinitely distributed delays. In order to overcome the non-commutativity of the multiplication of Clifford numbers, we first transform the… read more here.
Keywords: clifford; almost automorphic; valued rnns; globally asymptotic ... See more keywords
Finite-Time Synchronization of Clifford-Valued Neural Networks With Infinite Distributed Delays and Impulses
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Access"
DOI: 10.1109/access.2021.3102585
Abstract: We study the issue of finite-time synchronization pertaining to a class of Clifford-valued neural networks with discrete and infinite distributed delays and impulse phenomena. Since multiplication of Clifford numbers is of non-commutativity, we decompose the… read more here.
Keywords: finite time; clifford; time synchronization; clifford valued ... See more keywords
Polarization of Quantum Channels Using Clifford-Based Channel Combining
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2021.3063093
Abstract: We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate randomly… read more here.
Keywords: clifford; channel combining; polarization quantum; qubit ... See more keywords