相关论文: Vortex metrology using circular and elliptical Lag…
Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
Vortex beams are a type of structured light characterized by phase rotation around the propagation axis, resulting in orbital angular momentum. Their properties make them useful in various applications such as high-resolution microscopy,…
In this article, we construct traveling-rotating helical vortices with small cross-section to the 3D incompressible Euler equations in an infinite pipe, which tend asymptotically to singular helical vortex filament evolved by the binormal…
The behavior of a dilute two-component superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de…
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1)…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
The presence of outliers can significantly degrade the performance of ellipse fitting methods. We develop an ellipse fitting method that is robust to outliers based on the maximum correntropy criterion with variable center (MCC-VC), where a…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over…
The transverse structure of light is recognized as a resource that can be used to encode information onto photons and has been shown to be useful to enhance communication capacity as well as resolve point sources in superresolution imaging.…
Rapid identification, characterization, and localization of gravitational waves from binary compact object mergers can enable well-informed follow-on multimessenger observations. In this work, we investigate a small modification to the RIFT…
A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…
We deduce a set of circularly polarized Gaussian laser beam modes via a separation-of-variables solution to the Helmholtz wave equation in oblate spheriodal coordinates. On transforming to cylindrical coordinates these become the well-known…
Propagation of coherent light in a Kerr nonlinear medium can be mapped onto a flow of an equivalent fluid. Here we use this mapping to model the conditions in the vicinity of a rotating black hole as a Laguerre-Gauss vortex beam. We…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
The generation and measurement of optical vortex (OV) are the basis for a variety of related applications. However, the special case of high-order OVs has not been sufficient addressed yet. Herein, a generation and measurement method of…
The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass…
The rapid developments in orbital-angular-momentum-carrying Laguerre-Gaussian (LG0 l) modes in recent years have facilitated progresses in optical communication, micromanipulation and quantum information. However, it is still challenging to…