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Mathematics & Statistics

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Displaying 76 - 100 of 871

Physics-assisted Generative Adversarial Network for X-Ray Tomography

June 10, 2022
Author(s)
Zhen Guo, Jungki Song, George Barbastathis, Michael Glinsky, Courtenay Vaughan, Kurt Larson, Bradley Alpert, Zachary H. Levine
X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials study, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned

Pairs of Heron and right triangles with a common area and a common perimeter

May 23, 2022
Author(s)
Abhishek Juyal, Dustin Moody
A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common

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