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In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…

Crystal Structure Prediction (CSP) of molecular crystals plays a central role in applications, such as pharmaceuticals and organic electronics. CSP is challenging and computationally expensive due to the need to explore a large search space…

Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…

Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…

The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…

Optical spectrometers have propelled scientific and technological advancements in a wide range of fields. While sophisticated systems with excellent performance metrics are serving well in controlled laboratory environments, many…

This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is…

This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…

This paper explores the point set representation for tubular structure extraction tasks. Compared with the traditional mask representation, the point set representation enjoys its flexibility and representation ability, which would not be…

Revealing the structure of complex biological macromolecules, such as proteins, is an essential step for understanding the chemical mechanisms that determine the diversity of their functions. Synchrotron based x-ray crystallography and…

In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…

Periodically time-varying media, known as photonic time crystals (PTCs), provide a promising platform for observing unconventional wave phenomena. We analyze the scattering of electromagnetic waves from spatially finite PTCs using the…

This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…

Fast and accurate prediction of optimal crystal structure, topology, and microstructures is important for accelerating the design and discovery of new materials. A challenge lies in the exorbitantly large structural and compositional space…

We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of…

The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…

Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by…