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Mathematics & Statistics

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Displaying 1 - 25 of 473

87 Years of Mathematical Functions at NIST

September 23, 2025
Author(s)
Ronald Boisvert
We survey the role that the National Institute of Standards and Technology has played in the development and use of the special functions of applied mathematics from the construction of tables of function values in the 1930s to the provision of online

Topological Initialization for Multidimensional Scaling

September 16, 2025
Author(s)
Melinda Kleczynski, Anthony Kearsley
Multidimensional scaling is a popular technique for visualizing dissimilarities between objects in complex datasets. For a single dataset, different initial configurations for multidimensional scaling may produce representations with qualitatively

Topology and Kinetic Pathways of Colloidosome Assembly and Disassembly

September 4, 2025
Author(s)
Raymond Adkins, Joanna Robaszewski, Seungwoo Shin, Fridtjof Brauns, Leroy Jia, Ayantika Khanra, Prerna Sharma, Robert Pelcovits, Thomas Powers, Zvonimir Dogic
Liquid shells, such as lipid vesicles, emulsions, and soap bubbles, are ubiquitous throughout biology, engineered matter, and everyday life. Their creation or disintegration is defined by a singularity separating topologically distinct one-boundary

Evaluating the Impact of Changes to the Internal Publication Review Policy at NIST

August 21, 2025
Author(s)
Juan Fung, Michael Hall, Jennifer Helgeson, Alden Dima, Anne Andrews, Jennifer Benkstein
This report presents the design and methodology of a survey conducted to evaluate the impact of changes to the organizational publication review policy at the National Institute for Standards and Technology (NIST). The purpose of the survey is to collect

Elongated particles in flow: commentary on small-angle scattering investigations

May 23, 2025
Author(s)
Guan-Rong Huang, Lionel Porcar, Ryan Murphy, Yuya Shinohara, Yangyang Wang, Jan-Michael Carrillo, Bobby G. Sumpter, Chi-Huan Tung, Lijie Ding, Changwoo Do, Wei-Ren Chen
This work thoroughly examines several analytical tools, each possessing a different level of mathematical intricacy, for the purpose of characterizing the orientation distribution function of elongated objects under flow. Our investigation places an

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

March 11, 2025
Author(s)
Gorjan Alagic, Maxime Bros, Pierre Ciadoux, David Cooper, Quynh Dang, Thinh Dang, John Kelsey, Jacob Lichtinger, Yi-Kai Liu, Carl Miller, Dustin Moody, Rene Peralta, Ray Perlner, Angela Robinson, Hamilton Silberg, Daniel Smith-Tone, Noah Waller
The National Institute of Standards and Technology is selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signatures, public-key encryption, and

Error Floor Prediction with Markov Models for QC-MDPC Codes

February 1, 2025
Author(s)
Sarah Arpin, Jun Bo Lau, Ray Perlner, Angela Robinson, Valentin Vasseur, Jean-Pierre Tillich
Quasi-cyclic moderate-density parity check (QC-MDPC) code-based encryption schemes under iterative decoders offer highly-competitive performance in the quantum-resistant space of cryptography, but the decoding-failure rate (DFR) of these algorithms are not

WLAN Protocols Identification Using Machine Learning and Ensemble Models

January 7, 2025
Author(s)
Akimun Jannat Alvina, Yao Ma, Mark Golkowski
The growing demand for wireless communications has caused significant spectrum congestion, requiring multiple WLAN protocols to share limited spectrum resources. To address this, further research is necessary to optimize spectrum sharing and improve

Workshop on Compositional Structures in Systems Engineering and Design

December 20, 2024
Author(s)
Spencer Breiner, Eswaran Subrahmanian, Joseph Moeller, Priyaa Varshinee Srinivasan
The focus of this workshop is to foster the development of applications of category theory to systems engineering and design. We are interested in bringing together experts from engineering and applied category theory, and those involved in software tools

Two tests of variance homogeneity for clustered data where group size is informative

December 3, 2024
Author(s)
Mary Gregg, Adam Creuziger, Somnath Datta, Douglas Lorenz
To evaluate variance homogeneity among groups for clustered data, Iachine et al. (Robust tests for the equality of variances for clustered data. J Stat Comput Simul 2010;80(4):365–377) introduced an extension of the well-known Levene test. However, this

Status Report on the First Round of the Additional Digital Signature Schemes for the NIST Post-Quantum Cryptography Standardization Process

October 24, 2024
Author(s)
Gorjan Alagic, Maxime Bros, Pierre Ciadoux, David Cooper, Quynh Dang, Thinh Dang, John M. Kelsey, Jacob Lichtinger, Carl A. Miller, Dustin Moody, Rene Peralta, Ray Perlner, Angela Robinson, Hamilton Silberg, Daniel Smith-Tone, Noah Waller, Yi-Kai Liu
The National Institute of Standards and Technology is in the process of evaluating public-key digital signature algorithms through a public competition-like process for potential standardization. Any signature scheme eventually selected would augment

On a conjecture that strengthens Kundu's k-factor Theorem

October 6, 2024
Author(s)
James Shook
Let π = (d1, . . . , dn) be a non-increasing degree sequence with even n. In 1974, Kundu showed that if Dk(π) = (d1 − k, . . . , dn − k) is graphic, then some realization of π has a k-factor. For r ≤ 2, Busch et al. and later Seacrest for r ≤ 4 showed that

A Note on Tangential Quadrilaterals

September 2, 2024
Author(s)
Pradeep Das, Abhishek Juyal, Dustin Moody
A tangential quadrilateral is a convex quadrilateral whose sides are simultaneously tangent to a single circle. In this paper, the primary objective is to construct rational tangen- tial quadrilaterals characterized by having rational area, as well as

Multifaceted Neuroimaging Data Integration via Analysis of Subspaces

August 28, 2024
Author(s)
Andrew Ackerman, Zhengwu Zhang, Jan Hannig, Jack Prothero, J.S. Marron
Neuroimaging studies, such as the Human Connectome Project (HCP), often collect multifaceted and multi-block data to study the complex human brain. However, these data are often analyzed in a pairwise fashion, which can hinder our understanding of how

On the Semidirect Discrete Logarithm Problem in Finite Groups

June 6, 2024
Author(s)
Christopher Battarbee, Giacomo Borin, Julian Brough, Ryann Cartor, Tobias Hemmert, Nadia Heninger, David Jao, Delaram Kahrobaei, Laura Maddison, Edoardo Persichetti, Angela Robinson, Daniel Smith-Tone, Rainer Steinwandt
We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem (SDLP) in any finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post
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