U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Mathematics & Statistics

Search Publications

Search Title, Abstract, Conference, Citation, Keyword or Author
  • Published Date
Displaying 51 - 75 of 473

Separable Shape Tensors for Aerodynamic Design

January 31, 2023
Author(s)
Zachary J. Grey, Andrew Glaws, Olga Doronina
Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and

Restricted Domain Compressive Sensing for Antenna Metrology

November 21, 2022
Author(s)
Marc Valdez, Alex Yuffa, Michael Wakin
In this paper, we prove a compressive sensing guarantee for restricted measurement domains in spherical near-field to far-field transformations for antenna metrology. We achieve this by first defining Slepian functions on a measurement sub-domain $R$ of

Extracting Mathematical Concepts from Text

October 12, 2022
Author(s)
Jacob Collard, Valeria de Paiva, Brendan Fong, Eswaran Subrahmanian
We investigate some different systems for extracting mathematical entities from texts in the mathematical field of category theory, as a first step for constructing a mathematical knowledge graph. We consider four different term extractors and compare

A characterization of the Centers of Chordal Graphs

September 30, 2022
Author(s)
James Shook, Bing Wei
A graph is $k$-chordal if it does not have an induced cycle with length greater than $k$. We call a graph chordal if it is $3$-chordal. Let $G$ be a graph. The distance between the vertices $x$ and $y$, denoted by $d_G}(x,y)$, is the length of a shortest

Provably efficient machine learning for quantum many-body problems

September 23, 2022
Author(s)
Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor Albert, John Preskill
Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems that arise in physics and chemistry, but the advantages of ML over more traditional classical methods have not been firmly

A Study of Error Floor Behavior in QC-MDPC Codes

August 17, 2022
Author(s)
Sarah Arpin, Tyler Billingsley, Daniel Hast, Jun Bo Lao, Ray Perlner, Angela Robinson
We present experimental findings on the decoding failure rate (DFR) of BIKE, a third-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level. We select parameters according to BIKE design principles and conduct a

Recommendation for Key Derivation Using Pseudorandom Functions

August 17, 2022
Author(s)
Lily Chen
This Recommendation specifies techniques for the derivation of additional keying material from a secret key—either established through a key-establishment scheme or shared through some other manner—using pseudorandom functions: HMAC, CMAC, and KMAC.

Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process

July 5, 2022
Author(s)
Gorjan Alagic, David Cooper, Quynh Dang, Thinh Dang, John M. Kelsey, Jacob Lichtinger, Yi-Kai Liu, Carl A. Miller, Dustin Moody, Rene Peralta, Ray Perlner, Angela Robinson, Daniel Smith-Tone, Daniel Apon
The National Institute of Standards and Technology is in the process of selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signature, public

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
Was this page helpful?