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1. On fast reconstruction of periodic structures with partial scattering data

   https://doi.org/10.3934/era.2024303  

   Daugherty, John; Kaduk, Nate; Morgan, Elena; Nguyen, Dinh-Liem; Snidanko, Peyton; Truong, Trung (January 2024, Electronic Research Archive)

   This paper presents a numerical method for solving the inverse problem of reconstructing the shape of periodic structures from scattering data. This inverse problem is motivated by applications in the nondestructive evaluation of photonic crystals. The numerical method belongs to the class of sampling methods that aim to construct an imaging function for the shape of the periodic structure using scattering data. By extending the results of Nguyen, Stahl, and Truong [Inverse Problems, 39:065013, 2023], we studied a simple imaging function that uses half the data required by the numerical method in the cited paper. Additionally, this imaging function is fast, simple to implement, and very robust against noise in the data. Both isotropic and anisotropic cases were investigated, and numerical examples were presented to demonstrate the performance of the numerical method. 

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2. Single-scattering properties of ellipsoidal dust aerosols constrained by measured dust shape distributions

   https://doi.org/10.5194/acp-23-2557-2023  

   Huang, Yue; Kok, Jasper F; Saito, Masanori; Muñoz, Olga (January 2023, Atmospheric Chemistry and Physics)

   Abstract. Most global aerosol models approximate dust as sphericalparticles, whereas most remote sensing retrieval algorithms approximate dust as spheroidal particles with a shape distribution that conflicts withmeasurements. These inconsistent and inaccurate shape assumptions generatebiases in dust single-scattering properties. Here, we obtain dustsingle-scattering properties by approximating dust as triaxial ellipsoidalparticles with observationally constrained shape distributions. We findthat, relative to the ellipsoidal dust optics obtained here, the sphericaldust optics used in most aerosol models underestimate dust single-scattering albedo, mass extinction efficiency, and asymmetry parameter for almost all dust sizes in both the shortwave and longwave spectra. We further find that the ellipsoidal dust optics are in substantially better agreement with observations of the scattering matrix and linear depolarization ratio than the spheroidal dust optics used in most retrieval algorithms. However, relative to observations, the ellipsoidal dust optics overestimate the lidar ratio by underestimating the backscattering intensity by a factor of ∼2. This occurs largely because the computational method used to simulate ellipsoidal dust optics (i.e., the improved geometric optics method) underestimates the backscattering intensity by a factor of ∼2 relative to other computational methods (e.g., the physical geometric optics method). We conclude that the ellipsoidal dust optics with observationally constrained shape distributions can help improve global aerosol models and possibly remote sensing retrieval algorithms that do not use the backscattering signal. 

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3. Prediction of Effective Elastic Properties of Carbon/UHMWPE Nanocomposites by Combination of Numerical and Analytical Modeling

   https://doi.org/10.12783/asc38/36636  

   BUKLOVSKYI, STANISLAV; MIROSHNICHENKO, KATERYNA; TSUKROV, IGOR; THOMSON, REBECCA J.; SOLBERG, PEDER C.; CITTERS, DOUGLAS W.; Miroshnichenko, Kateryna; Tsukrov, Igor; Thomson, Rebecca J.; Solberg, Peder C.; et al (September 2023, Destech Publications, Inc.)

   In this paper, we investigate ultra-high-molecular-weight-polyethylene (UHMWPE) doped with conductive carbon black (CCB) nanoparticles. This nanocomposite is considered a candidate for biomedical applications such as orthopedics. Micro-computed tomography (μCT) and scanning electron microscopy studies show that the composite has a complex microstructure consisting of larger particles of UHMWPE surrounded by a thin layer containing a high concentration of CCB nano inclusions. The overall mechanical properties of these composites depend on the volume fraction of CCB and the manufacturing procedures e.g., compression molding or equal channel angular extrusion. To predict the effective elastic properties of the CCB/UHMWPE nanocomposite, we propose a multiscale modeling framework based on a combined analytical-numerical approach. μCT images are processed to extract the size, shape, and orientation distributions of UHMWPE particles as well as the volume fractions and spatial distribution of CCB containing layer. These distributions are used to develop multiscale numerical models of the composite including finite element analysis of representative volume elements on the mesoscale, and micromechanical predictions of CCB containing layer on the microscale. The predictive ability of the models is confirmed by comparison with the experimental measurements obtained by dynamic mechanical analysis. 

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4. An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

   https://doi.org/10.3390/pharmaceutics13010042  

   Yamada, Walter M.; Neely, Michael N.; Bartroff, Jay; Bayard, David S.; Burke, James V.; van Guilder, Mike; Jelliffe, Roger W.; Kryshchenko, Alona; Leary, Robert; Tatarinova, Tatiana; et al (January 2021, Pharmaceutics)

   Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing. 

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5. One-Bit Normalized Scatter Matrix Estimation For Complex Elliptically Symmetric Distributions

   https://doi.org/10.1109/ICASSP40776.2020.9053956  

   Liu, Chun-Lin; Vaidyanathan, P. P. (May 2020, Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc)

   null (Ed.)

   One-bit quantization has attracted attention in massive MIMO, radar, and array processing, due to its simplicity, low cost, and capability of parameter estimation. Specifically, the shape of the covariance of the unquantized data can be estimated from the arcsine law and onebit data, if the unquantized data is Gaussian. However, in practice, the Gaussian assumption is not satisfied due to outliers. It is known from the literature that outliers can be modeled by complex elliptically symmetric (CES) distributions with heavy tails. This paper shows that the arcsine law remains applicable to CES distributions. Therefore, the normalized scatter matrix of the unquantized data can be readily estimated from one-bit samples derived from CES distributions. The proposed estimator is not only computationally fast but also robust to CES distributions with heavy tails. These attributes will be demonstrated through numerical examples, in terms of computational time and the estimation error. An application in DOA estimation with MUSIC spectrum is also presented. 

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