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Multiple x-ray beams generated by interference processes in perfect crystals were imaged with a resolution of about 100nm using tele-ptychography in the diffraction direction. These multiple wave-fields, also known as x-ray diffraction…
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…
Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is still a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of…
We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
We study the orientation dependence of the reconstructed deceleration parameter as a function of redshift. We use the Union 2 and Loss datasets, by using the well known preferred axis discussed in the literature, finding the best fit…
Magnetic Resonance Imaging (MRI) is a powerful medical imaging modality, but unfortunately suffers from long scan times which, aside from increasing operational costs, can lead to image artifacts due to patient motion. Motion during the…
It is proposed to create materials with a desired refraction coefficient in a bounded domain $D\subset \R^3$ by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit…
Experimental results on hadronic soft and hard diffractive processes are reviewed with emphasis on aspects of the data that point to the underlying QCD mechanism for diffraction. Diffractive differential cross sections are shown to be…
Reconfigurable intelligent surface (RIS) has been explored as a supportive technology for wireless communication since around 2019. While the literature highlights the potential of RIS in different modern applications, two key issues have…
Reflected diffusions in convex polyhedral domains arise in a variety of applications, including interacting particle systems, queueing networks, biochemical reaction networks and mathematical finance. Under suitable conditions on the data,…
This review explores particle resuspension from surfaces due to fluid flows. The objective of this review is to provide a general framework and terminology for particle resuspension while highlighting the future developments needed to…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
In this manuscript we demonstrate a method to reconstruct the wavefront of focused beams from a measured diffraction pattern behind a diffracting mask in real-time. The phase problem is solved by means of a neural network, which is trained…
Neural Radiance Fields (NeRF) have constituted a remarkable breakthrough in image-based 3D reconstruction. However, their implicit volumetric representations differ significantly from the widely-adopted polygonal meshes and lack support…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…
In this article we study the spherical mean Radon transform in $\mathbf R^3$ with detectors centered on a plane. We use the consistency method suggested by the author of this article for the inversion of the transform in 3D. A new iterative…
Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport…