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Mathematics & Statistics

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Displaying 76 - 100 of 473

Improving quantum state detection with adaptive sequential observations

May 13, 2022
Author(s)
Emanuel Knill, Scott Glancy, Daniel Cole, Shawn Geller
For many quantum systems intended for information processing, one detects the logical state of a qubit by integrating a continuously observed quantity over time. For example, ion and atom qubits are typically measured by driving a cycling transition and

ON RANKS OF QUADRATIC TWISTS OF A MORDELL CURVE

May 13, 2022
Author(s)
Abhishek Juyal, Dustin Moody, Bidisha Roy
In this article, we consider the quadratic twists of the Mordell curve $E:y^2=x^3-1$. For a square-free integer $k$, the quadratic twist of $E$ is given by $E_k:y^2=x^3-k^3.$ We prove that there exist infinitely many $k$ for which the rank of $E_k$ is 0

Grassmannian Shape Representations for Aerodynamic Applications

February 28, 2022
Author(s)
Olga Doronina, Zachary J. Grey, Andrew Glaws
Airfoil shape design is a classical problem in engineering and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach

Graph Convolutional Neural Network Applied to the Prediction of Normal Boiling Point

February 4, 2022
Author(s)
Chen Qu, Anthony J. Kearsley, Barry I. Schneider, Walid Keyrouz, Thomas C. Allison
In this article, we describe training and validation of a machine learning model for the prediction of organic compound normal boiling points. Data are drawn from the experimental literature as captured in the NIST Thermodynamics Research Center (TRC)

Characterizing Frequency Stability Measurements having Multiple Data Gaps

February 2, 2022
Author(s)
David A. Howe, Noah Schlossberger
Time series measurements with data gaps (dead times) prevent accurate computations of frequency variances such as the Allan variance (AVAR) and its square-root ADEV. To extract frequency distributions, data must be sequentially ordered and equally spaced

Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography

January 20, 2022
Author(s)
Zhen Guo, Jungki Song, George Barbastathis, Michael Glinsky, Courtenay Vaughan, Kurt Larson, Bradley Alpert, Zachary H. Levine
Limited-angle X-ray tomography reconstruction is an ill-posed inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as

Time-series Imputation Algorithm

November 5, 2021
Author(s)
David A. Howe, Chloe Champagne
Statistical imputation is a field of study that attempts to fill missing data. It is commonly applied to population statistics whose data have no correlation with running time. For a time series, data is typically analyzed using the autocorrelation, the

Theory of Curvature and Grooving Effects in DIGM - II: the Mathematics

October 12, 2021
Author(s)
O Penrose, John W. Cahn
We examine and solve the mathematical problems that arise when diffusion induced grain boundary motion is formulated as a free boundary problem, i.e. as a system of partial differential equations on a moving curved interface with surface grooving as a

On Computing Elastic Shape Distances between Curves in d-dimensional Space

June 21, 2021
Author(s)
Javier Bernal, James F. Lawrence, Gunay Dogan, Robert Hagwood
The computation of the elastic registration of two simple curves in higher dimensions and therefore of the elastic shape distance between them has been investigated by Srivastava et al. Assuming the first curve has one or more starting points, and the

Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind

May 20, 2021
Author(s)
Howard Cohl, Hans Volkmer, Justin Park
We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second

Vectorizing Green's Identities

May 5, 2021
Author(s)
Alex Yuffa
Green's theorem and Green's identities are well-known and their uses span almost every branch of science and mathematics. In this paper, we derive a vector analogue of Green's three scalar identities and consider some of their uses. We also offer a number
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