Related papers: The Haar measure in solid mechanics
In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part.…
We define a general notion of a smooth invariant (central) ergodic measure on the space of paths of an $N$-graded graph (Bratteli diagram). It is based on the notion of standardness of the tail filtration in the space of paths, and the…
We use the Bellman function method to give an elementary proof of a sharp weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the weight and in the complexity of the shift. Together with the representation of a…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
This paper discusses the role of the Skorokhod space and the convergence of probability measures on it in some recent studies of the foundations of quantum mechanics, both in the conventional setting over the real number field and in the…
Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
Human Activity Recognition (HAR) using wearable inertial measurement unit (IMU) sensors can revolutionize healthcare by enabling continual health monitoring, disease prediction, and routine recognition. Despite the high accuracy of Deep…
A QCD fit analysis to the combined HERA inclusive deep inelastic cross sections measured by the H1 and ZEUS collaborations for $e^\pm p$ scattering to extract HERAPDF sets is presented. The results are used for predictions of $ p\bar{p}$…
Full 3D inversion of time-domain Airborne ElectroMagnetic (AEM) data requires specialists' expertise and a tremendous amount of computational resources, not readily available to everyone. Consequently, quasi-2D/3D inversion methods are…
This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
With the rapid development of the internet of things (IoT) and artificial intelligence (AI) technologies, human activity recognition (HAR) has been applied in a variety of domains such as security and surveillance, human-robot interaction,…
The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense,…
The statistical model of hadronization succeeds in reproducing particle abundances and transverse momentum spectra in high energy collisions of elementary particles as well as of heavy ions. Despite its apparent success, the interpretation…
Humans have the remarkable ability to use held objects as tools to interact with their environment. For this to occur, humans internally estimate how hand movements affect the object's movement. We wish to endow robots with this capability.…
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…
We introduce a novel application of the Hartmann sensor, traditionally designed for wavefront sensing, to measure the coherence properties of optical signals. By drawing an analogy between the coherence matrix and the density matrix of a…