Related papers: Convolution and correlation theorems for the windo…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
The graph linear canonical transform (GLCT) is presented as an extension of the graph Fourier transform (GFT) and the graph fractional Fourier transform (GFrFT), offering more flexibility as an effective tool for graph signal processing. In…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for…
Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a…
We give a geometrical characterization of the ideal of quadrics containing a canonical curve with an involution. This implies to study involutions of rational normal scrolls and Veronese surfaces.
We show that there exists, in quantum theory, a close relationship between the weak value and the correlation function, which sheds new lights on the concept of the weak value.
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the orthonormalization constants for these…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
We characterize point transformations in quantum mechanics from the mathematical viewpoint. To conclude that the canonical variables given by each point transformation in quantum mechanics correctly describe the extended point…
We propose a novel algorithm for computing the Walsh-Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. We prove that the algorithm, which we call the Cascading Haar Wavelet (CHW) algorithm, shares precisely the…
There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
The determinants of modular Collatz graphs and the modular Conway amusical permutation graph are determined, and some interesting number theoretic properties are described.
We present a convolutional neural network for the classification of correlation responses obtained by correlation filters. The proposed approach can improve the accuracy of classification, as well as achieve invariance to the image classes…
Every right adjoint functor between presentable $\infty$-categories is shown to decompose canonically as a coreflection, followed by, possibly transfinitely many, monadic functors. Furthermore, the coreflection part is given a presentation…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on…