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Mathematics & Statistics

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Displaying 151 - 175 of 473

Securing Tomorrow's Information through Post-Quantum Cryptography

February 27, 2018
Author(s)
Dustin Moody, Larry Feldman, Gregory A. Witte
In recent years, there has been a substantial amount of research on quantum computers - machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum

Hybrid Datafication of Maintenance Logs from AI-Assisted Human Tags

January 15, 2018
Author(s)
Thurston B. Sexton, Michael P. Brundage, Michael L. Hoffman, Katherine C. Morris
One of the main challenges of applying AI to some datasets derives from the datasets themselves being unstructured, unclear, and ambiguous. Furthermore, the insights that are to be gained reflect the quality of the data itself; if the data is skewed, so

One-Pass Graphic Approximation of Integer Sequences

December 18, 2017
Author(s)
Brian D. Cloteaux
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. This

Automatic Localization of Casting Defects with Convolutional Neural Networks

December 11, 2017
Author(s)
Ronay Ak, Max Ferguson, Yung-Tsun T. Lee, Kincho H. Law
Automatic localization of defects in metal castings is a challenging task, owing to the rare occurrence and variation in appearance of defects. Convolutional neural networks (CNN) have recently shown outstanding performance in both image classification and

The odd-even invariant and Hamiltonian circuits in tope graphs

October 27, 2017
Author(s)
Yvonne Kemper, James F. Lawrence
Questions of the existence of Hamiltonian circuits in the tope graphs of central arrangements of hyperplanes are considered. Connections between the existence of Hamiltonian circuits in the arrangement and the odd-even invariant of the arrangement are

Pattern selection in ternary mushy layers

August 25, 2017
Author(s)
Daniel M. Anderson
We consider finite-amplitude convection in a mushy layer during the primary solidification of a ternary alloy. A previous linear theory identified, for the case of vanishing latent heat, solute rejection and background solidification, a direct mode of

Heron Quadrilaterals via Elliptic Curves

August 5, 2017
Author(s)
Farzali Izadi, Foad Khoshnam, Dustin Moody
A Heron quadrilateral is a cyclic quadrilateral with rational area. In this work, we establish a correspondence between Heron quadrilaterals and a family of elliptic curves of the form y^2=x^3+\alpha x^2-n^2 x. This correspondence generalizes the notions

Transport Effects on Multiple-Component Reactions in Optical Bionsensors

August 1, 2017
Author(s)
Ryan M. Evans, David A. Edwards
Many biochemical reactions involve a stream of chemical reactants (ligand molecules) flowing over a surface to which other reactants (receptors) are confined. Scientists measure rate constants associated with these reactions in an optical biosensor: an

Receptor heterogeneity in optical biosensors

July 13, 2017
Author(s)
David A. Edwards, Ryan Evans
Many biochemical reactions in nature involve a stream of chemical reactants (ligand molecules) flowing over a surface to which other reactants (receptors) are confined. Scientists measure rate constants associated with these reactions in an optical

Part-of-Math Tagging and Applications

June 28, 2017
Author(s)
Abdou S. Youssef
Much of the mathematical literature, old and new, is online and mostly in natural-language form. Therefore, math content processing presents some of the same challenges faced in natural language processing (NLP), such as math disambiguation and math

Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors and Computer Algebra Systems

June 28, 2017
Author(s)
Howard S. Cohl, Bonita V. Saunders, Marjorie A. McClain, Moritz Schubotz, Joon Bang, Juergen Gerhardt, Andre Greiner Petter
There are many different approaches to represent mathematical expressions on computers. Word processors like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in

A Near Optimal Algorithm to Count Occurrences of Subsequences of a Given Length

June 21, 2017
Author(s)
Jose Torres-Jimenez, Idelfonso Izquierdo-Marquez, Daniel Ramirez-Acuna, Rene Peralta
For a positive integer k let S = 0, 1, . . . , k − 1} be the alphabet whose symbols are the integers from 0 to k − 1. The set off all strings of length n ∈ Z+ over S is denoted by S(n). We show a near optimal algorithm to solve the problem of counting the

Geometric Progressions on Elliptic Curves

June 13, 2017
Author(s)
Abdoul Aziz Ciss, Dustin Moody
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean

Fast Updating Multipole Coulombic Potential Calculation

June 6, 2017
Author(s)
Thomas Hoft, Bradley Alpert
We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position. Errors are bounded even after a large number of such
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