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Recently, the connectionist temporal classification (CTC) model coupled with recurrent (RNN) or convolutional neural networks (CNN), made it easier to train speech recognition systems in an end-to-end fashion. However in real-valued models,…
A general representation of the quaternion gradients presented in the literature is proposed, and an universal update equation for QLMS-like algorithms is obtained. The general update law is used to study the convergence of widely linear…
We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexes using $C-$ and $E-$ Weyl group orbit functions. For these cases we present the convolution theorem. We provide an example of application of…
A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…
We develop an interpretable and learnable Wigner-Ville distribution that produces a super-resolved quadratic signal representation for time-series analysis. Our approach has two main hallmarks. First, it interpolates between known…
The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…
The field of neural networks has seen significant advances in recent years with the development of deep and convolutional neural networks. Although many of the current works address real-valued models, recent studies reveal that neural…
Recently learned image compression (LIC) has achieved great progress and even outperformed the traditional approach using DCT or discrete wavelet transform (DWT). However, LIC mainly reduces spatial redundancy in the autoencoder networks…
This work is devoted to the development of the octonion linear canonical transform (OLCT) theory proposed by Gao and Li in 2021 that has been designated as an emerging tool in the scenario of signal processing. The purpose of this work is…
Transformers are popular neural network models that use layers of self-attention and fully-connected nodes with embedded tokens. Vision Transformers (ViT) adapt transformers for image recognition tasks. In order to do this, the images are…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
Linear canonical transforms (LCTs) are of importance in many areas of science and engineering with many applications. Therefore a satisfactory discrete implementation is of considerable interest. Although there are methods that link the…
The main purpose of this work is to identify invariant quadratic operators associated with Linear Canonical Transformations (LCTs) which could play important roles in physics. LCTs are considered in many fields. In quantum theory, they can…
We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak…
Dense pixelwise prediction such as semantic segmentation is an up-to-date challenge for deep convolutional neural networks (CNNs). Many state-of-the-art approaches either tackle the loss of high-resolution information due to pooling in the…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…
Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and…