Related papers: A Survey on Dual-Quaternions
Deep learning is a research hot topic in the field of machine learning. Real-value neural networks (Real NNs), especially deep real networks (DRNs), have been widely used in many research fields. In recent years, the deep complex networks…
Quantum Computing (QC) refers to an emerging paradigm that inherits and builds with the concepts and phenomena of Quantum Mechanic (QM) with the significant potential to unlock a remarkable opportunity to solve complex and computationally…
Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
The development of deep learning algorithms has extensively empowered humanity's task automatization capacity. However, the huge improvement in the performance of these models is highly correlated with their increasing level of complexity,…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
The evolution of image halftoning, from its analog roots to contemporary digital methodologies, encapsulates a fascinating journey marked by technological advancements and creative innovations. Yet the theoretical understanding of…
As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by…
We consider general physical characteristics of doubly heavy baryons: the spectroscopy in the framework of potential approach and sum rules of QCD, mechanisms of production in various interactions on the basis of fragmentation model with…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
Quantum Transformers integrate the representational power of classical Transformers with the computational advantages of quantum computing. Since 2022, research in this area has rapidly expanded, giving rise to diverse technical paradigms…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
The world is witnessing the birth of a revolutionary computing paradigm that promises to have a profound effect on the way we interact with computers, devices, physical spaces, and other people. This new technology, called ubiquitous…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…