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 276 - 300 of 872

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