Related papers: The Momentum Light Ray Transform
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are examined using…
Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents…
We propose a novel multilinear dynamical system (MLDS) in a transform domain, named $\mathcal{L}$-MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal…
The DEtection TRansformer (DETR) opened new possibilities for object detection by modeling it as a translation task: converting image features into object-level representations. Previous works typically add expensive modules to DETR to…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
The energy-momentum tensor (EMT) is the conserved current corresponding to space-time translation symmetry. Its applications are remarkably diverse, ranging from the thermodynamics to the calculation of transport coefficients. While the EMT…
In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens…
This paper proves a novel analytical inversion formula for the so-called modulo Radon transform (MRT), which models a recently proposed approach to one-shot high dynamic range tomography. It is based on the solution of a Poisson problem…
The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large, the corresponding weight matrices can be enormous,…
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…
In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy-momentum tensor in this context and…
A momentum conservation approach is introduced to manipulate light at distance using metasurfaces. Given a specified field existing on one side of the metasurface and specified desired field transmitted from the opposite side, a general…
According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise…
Learning a good distance measure for distance-based classification in time series leads to significant performance improvement in many tasks. Specifically, it is critical to effectively deal with variations and temporal dependencies in time…
Magnetic resonance imaging (MRI) can present multi-contrast images of the same anatomical structures, enabling multi-contrast super-resolution (SR) techniques. Compared with SR reconstruction using a single-contrast, multi-contrast SR…
In exploring the light-induced dynamics within the linear response regime, this study investigates the induced orbital angular momentum on a wide variety of electronic structures. We derive a general expression for the torque induced by…
In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the…
In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the…
Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…
A logarithm transformation over the matter overdensity field $\delta$ brings information from the bispectrum and higher-order n-point functions to the power spectrum. We calculate the power spectrum for the log-transformed field $A$ at one,…