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Mathematics & Statistics

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Displaying 176 - 200 of 473

Arithmetic Progressions on Conics

December 27, 2016
Author(s)
Abdoul Aziz Ciss, Dustin Moody
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the

A better-than-3n lower bound for the circuit complexity of an explicit function

December 15, 2016
Author(s)
Magnus G. Find, Alexander Golovnev, Edward Hirsch, Alexander Kulikov
We consider Boolean circuits over the full binary basis. We prove a $(3+\frac{1}{86})n-o(n)$ lower bound on the size of such a circuit for an explicitly defined predicate, namely an affine disperser. This improves the $3n-o(n)$ bound of Norbert Blum (1984)

High Rank Elliptic Curves with Torsion Z/4Z induced by Kihara's Curves

October 5, 2016
Author(s)
Foad Khoshnam, Dustin Moody
Working over the field Q(t), Kihara constructed an elliptic curve with torsion group Z/4Z and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves with torsion group Z

Optimal joint detection and estimation that maximizes ROC-type curves

September 1, 2016
Author(s)
Adam J. Wunderlich, Bart Goossens, Craig K. Abbey
Combined detection-estimation tasks are frequently encountered in medical imaging. Hence, optimal methods for joint detection and estimation are of interest because they provide upper bounds on observer performance and can motivate practical image analysis

Separating OR, SUM, and XOR Circuits

August 23, 2016
Author(s)
Magnus G. Find, Mika Goos, Matti Jarvisalo, Petteri Kaski, Miko Koivisto, Janne Korhonen
Given a boolean n x n matrix A we consider arithmetic circuits for computing the transformation x 7! Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and

Evaluating the Effectiveness of BEN in Locating Different Types of Software Fault

August 4, 2016
Author(s)
Raghu N. Kacker, David R. Kuhn, Jagan Chandrasekaran, Yu Lei
Debugging or fault localization is one of the most challenging tasks during software development. Automated fault localization tools have been developed to reduce the amount of effort and time software developers have to spend on debugging. In this paper

Fast Dynamic Programming for Elastic Registration of Curves

June 30, 2016
Author(s)
Javier Bernal, Gunay Dogan, Robert Hagwood
Curve registration problems in data analysis and com- puter vision can often be reduced to the problem of match- ing two functions defined on an interval. Dynamic Pro- gramming (DP) is an effective approach to solve this prob- lem. In this paper, we

Estimating t-way Fault Profile Evolution During Testing

June 10, 2016
Author(s)
Raghu N. Kacker, David R. Kuhn
Empirical studies have shown that most software interaction faults involve one or two variables interacting, with progressively fewer triggered by three or more, and no failure has been reported involving more than six variables interacting. This paper

Removing divergence of JCGM documents from the GUM (1993)

June 1, 2016
Author(s)
Raghu N. Kacker
The stated mission of the Joint Committee for Guides in Metrology (JCGM) is to maintain and promote the use of the Guide to the Expression of Uncertainty in Measurement (GUM) and the International Vocabulary of Metrology (VIM, 2nd edition). The JCGM has

Report on Post-Quantum Cryptography

April 28, 2016
Author(s)
Lidong Chen, Stephen P. Jordan, Yi-Kai Liu, Dustin Moody, Rene C. Peralta, Ray A. Perlner, Daniel C. Smith-Tone
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

Predicting Structures of Ru-Centered Dyes: A Computational Screening Tool

March 16, 2016
Author(s)
Lisa A. Fredin, Thomas C. Allison
Dye-sensitized solar cells (DSCs) represent a viable means for harvesting solar energy to produce electrical power. Though a number of light harvesting dyes are in use, the search continues for more efficient and effective compounds to make commercially

Linear Time Vertex Partitioning on Massive Graphs

March 7, 2016
Author(s)
Peter M. Mell, Richard Harang, Assane Gueye
The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds

Vulnerabilities of "McEliece in the World of Escher"

March 3, 2016
Author(s)
Dustin Moody, Ray A. Perlner
Recently, Gligoroski et al. proposed code-based encryption and signature schemes using list decoding, blockwise triangular private keys, and a nonuniform error pattern based on "generalized error sets." The general approach was referred to as "McEliece in

Using Combinatorial Testing to Build Navigation Graphs for Dynamic Web Applications

February 2, 2016
Author(s)
Wenhua Wang, Sreedevi Sampath, Yu Lei, Raghu N. Kacker, D. Richard Kuhn, James F. Lawrence
Modelling a software system is often a challenging prerequisite to automatic test case generation. Modelling the navigation structure of a dynamic web application is particularly challenging because of the presence of a large number of pages that are

Polymer Glass-Formation in Variable Dimension

January 14, 2016
Author(s)
Jack F. Douglas, Freed Karl, Wensheng Xu
We explore the nature of glass-formation in variable spatial dimensionality (d) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established
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