Band subset selection (BSS) is one of the ways to implement band selection (BS) for a hyperspectral image (HSI). Different from conventional BS methods, which select bands one by one, BSS selects a band subset each time and preserves the best one fro...
Wigner’s little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathe...
In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and...
It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive...
In this paper, we propose using quiver representations as a tool for understanding artificial neural network algorithms. Specifically, we construct these algorithms by utilizing the group algebra of a finite cyclic group as vertices and convolution t...
We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representat...
This paper proposes a method called Grouped Contrastive Learning of self-supervised Sentence Representation (GCLSR), which can learn an effective and meaningful representation of sentences. Previous works maximize the similarity between two vectors t...
An abstract sampling theory associated with a unitary representation of a countable discrete non abelian group G, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples, the use of...
In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space...
27 September 2022
Urinary incontinence (UI) is a major public health problem. Although trivialized, it affects nearly 9% of the world’s population and its prevalence increases with age. It affects many people living in nursing homes. In the literature, there is...
Restricted by technical and budget constraints, hyperspectral images (HSIs) are usually obtained with low spatial resolution. In order to improve the spatial resolution of a given hyperspectral image, a new spatial and spectral image fusion approach...
Hyperspectral image (HSI) super-resolution is a vital technique that generates high spatial-resolution HSI (HR-HSI) by integrating information from low spatial-resolution HSI with high spatial-resolution multispectral image (MSI). However, existing s...
11 May 2023
Symptoms resulting from childhood trauma can negatively impact socioemotional well-being and school performance during early adolescence unless positive changes in attachment security and mental representations of significant relationships occur. A s...
Spectral-spatial classification has been widely applied for remote sensing applications, especially for hyperspectral imagery. Traditional methods mainly focus on local spatial similarity and neglect nonlocal spatial similarity. Recently, nonlocal se...
Infrared (IR) Image preprocessing is aimed at image denoising and enhancement to help with small target detection. According to the sparse representation theory, the IR original image is low rank, and the coefficient shows a sparse character. The low...
We geometrically derive the explicit form of the unitary representation of the Poincaré group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton–Baylis photon...
Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a sui...
Permutations on a set, endowed with function composition, build a group called a symmetric group. In addition to their algebraic structure, symmetric groups have two metrics that are of particular interest to us here: the Cayley distance and the Kend...
Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two...
We study a projective unitary representation of the product G=G˜×G, where G is a locally compact Abelian group and G^ is its dual consisting of characters on G. It is proven that the representation is irreducible, which allows us to defin...
In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of...
In this paper, we study Spin*(8)-Higgs bundles over compact Riemann surfaces, extending the work of Bradlow, García-Prada, and Gothen on SO*(8). The group Spin*(8) is exceptional among classical real forms, as its complexification Spin(8,C) ad...
The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we f...
Langlands duality is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now has seemed unrelated to the Langlands program. That is the topic of inv...
We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is,...
All ethnic/racial terminology may be seen as a form of representation, whereby meanings are generated by a range of social categorizers in settings of popular culture, political discourse, and statistical governmentality. This paper investigates thes...
A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it...
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...
We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group B 6 to obtain a totally l...
A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian methods play...
An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In Wigner’s view, the rest mass and the spin of a free elementary particle in flat space-time are...
This is mainly a review of an intense 15-year long collaboration between the authors on explicit realisations of compact Lie groups and their applications. Starting with an elementary example, we will illustrate the main idea at the foundation of the...
Just as Gauss’s interpretation of complex numbers as points in a number plane in the form of a suitably formulated axiom found its way into the vector representation of Fourier transforms, this is the case with Euler’s formula and Riemann...
Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies in LS-GDM suffer from challenges. In the current research, a proportional hesitant f...
We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the hidden symm...
Let k be an algebraically closed field of prime characteristic and let G be a semisimple, simply connected, linear algebraic group. It is an open problem to find the cohomology of line bundles on the flag variety G / B , where B is a Borel sub...
Beltrami equations L¯t(g)=μ(·,t)Lt(g) on S3 (where Lt, |t|<1, are the Rossi operators i.e., Lt spans the globally nonembeddable CR structure H(t) on S3 discovered by H. Rossi) are derived such that to describe quasiconformal mapping...
Discriminative feature learning is the key to remote sensing scene classification. Previous research has found that most of the existing convolutional neural networks (CNN) focus on the global semantic features and ignore shallower features (low-leve...
Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy s...
Representations of braid group Bn on n≥2 strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group VBn on n≥2 strands is an ex...
Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be suffic...
Motivated by a ternary generalization of the Pauli exclusion principle proposed by R. Kerner, we propose a notion of a Z3-skew-symmetric covariant SO(3)-tensor of the third order, consider it as a 3-dimensional matrix, and study the geometry of the 1...
A data center with a large number of servers, large storage, and many network devices requires power for cooling to reduce heat generation, air conditioning, and emergency power generation facilities, in addition to power for operation internally con...
Surface crack detection and temporal evolution analysis are fundamental tasks in remote sensing and photogrammetry, providing critical information for slope stability assessment, infrastructure safety inspection, and long-term geohazard monitoring. H...
The momentum-independent Casimir operators of the homogeneous spin-Lorentz group are employed in the construction of covariant projector operators, which can decompose anyone of its reducible finite-dimensional representation spaces into irreducible...
Achieving high-quality reconstructions of images is the focus of research in image compressed sensing. Group sparse representation improves the quality of reconstructed images by exploiting the non-local similarity of images; however, block-matching...
The notion of matched pair (F,G,▹,◃) of finite groups was introduced by Takeuchi in 1981, which is equivalent to a factorization of the group F⋈G. We find in this paper some sufficient conditions when equations νm(F⋈G)=ν...
Although emotions occupy an important place in Alevism, their representation in Alevi history and the present has not yet been sufficiently researched. This study addresses this desideratum and discusses the representation and codification of emotion...
In this paper, we propose a boosting synthetic aperture radar (SAR) image despeckling method based on non-local weighted group low-rank representation (WGLRR). The spatial structure information of SAR images leads to the similarity of the patches. Fu...
Group activity recognition that infers the activity of a group of people is a challenging task and has received a great deal of interest in recent years. Different from individual action recognition, group activity recognition needs to model not only...
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