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We consider the problem of recovering the initial value, from the trace on the light cone, of the solution of an initial value problem for the wave equation. When the space is odd dimensional, we show that the map from the initial value to…
Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\,…
New techniques for imaging electromagnetic near-fields in nanostructures drive advancements in nanotechnology, optoelectronics, materials science, and biochemistry. Most existing techniques probe near-fields along surfaces, lacking the…
Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional…
We propose an approach to far-field optical imaging beyond the diffraction limit. The proposed system allows image magnification, is robust with respect to material losses and can be fabricated by adapting existing metamaterial technologies…
The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…
We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$.
Let $G_{n,r}(\bbK)$ be the Grassmannian manifold of $k$-dimensional $\bbK$-subspaces in $\bbK^n$ where $\bbK=\mathbb R, \mathbb C, \mathbb H$ is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine…
Realizing active metasurfaces with substantial tunability is important for many applications but remains challenging due to difficulties in dynamically tuning light-matter interactions at subwavelength scales. Here, we introduce reversible…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a…
Highly directional radiation from photonic structures is important for many applications, including high power photonic crystal surface emitting lasers, grating couplers, and light detection and ranging devices. However, previous…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's…
Kernel-phase is a recently developed paradigm that tackles the classical problem of image deconvolution, based on an interferometric point of view of image formation. Kernel-phase inherits and borrows from the notion of closure-phase,…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the…
The electronic properties of graphene are unique and are attracting increased attention to this novel 2-dimensional system. Its photonic properties are not less impressive. For example, this single atomic layer absorbs through direct…
Photonic computing has emerged as a promising substrate for accelerating the dense linear-algebra operations at the heart of AI, yet adoption for large Transformer models remains in its infancy. We identify two bottlenecks: (1) costly…
We compute the radiation of dileptons and photons using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most…