Related papers: Metamorphism as a covariant transform for the SSR …
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…
Metamorphic testing is a testing method for problems without test oracles. Integration testing allows for detecting errors in complex systems that may not be found during the testing of their components. In this paper, we propose a novel…