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Mathematics & Statistics

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Displaying 276 - 300 of 473

Isomorphism Classes of Edwards Curves over Finite Fields

May 18, 2012
Author(s)
Reza Farashahi, Dustin Moody, Hongfeng Wu
Edwards curves are a new model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of F_q-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R

Combinatorial Testing of ACTS: A Case Study

April 21, 2012
Author(s)
Mehra N. Borazjany, Linbin Yu, Yu Lei, Raghu N. Kacker, D. Richard Kuhn
In this paper we present a case study of applying combinatorial testing to test a combinatorial test generation tool called ACTS. The purpose of this study is two-fold. First, we want to gain experience and insights about how to apply combinatorial testing

Improved Indifferentiability Security Bound for the JH Mode

March 22, 2012
Author(s)
Dustin Moody, Souradyuti Paul, Daniel C. Smith-Tone
The JH hash function is one of the five fi nalists of the ongoing NIST SHA3 hash function competition. Despite several earlier attempts, and years of analysis, the indi fferentiability security bound of the JH mode has so far remained remarkably low, only

An Evaluation of Local Shape Descriptors for 3D Shape Retrieval

March 8, 2012
Author(s)
Sarah Y. Tang
As the usage of 3D models increases, so does the importance of developing accurate 3D shape retrieval algorithms. Most prominently, shape descriptors are used to describe the geometric and topological properties of objects and compared to determine two

Light a Single Candle: Studying Supernovae

March 1, 2012
Author(s)
Dianne M. O'Leary, Bert W. Rust
At peak luminosity, Type Ia supernovae can be even brighter than their parent galaxies, and their light curves display a very uniform and regular behavior. This makes them excellent candidates for a role as standard candles in measuring the distances to

Families of Elliptic Curves with Rational 3-torsion

January 30, 2012
Author(s)
Dustin Moody, Hongfeng Wu
In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of Fq-isogeny classes

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

January 17, 2012
Author(s)
Gregg M. Gallatin
We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss' law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can

Social and Physical Aspects of Seismic Risk

December 31, 2011
Author(s)
Carmen D. Gon?alves, Antonio Possolo
Seismic risk has social and physical aspects: although very different in nature, they are intertwined and share striking similarities. Seismic risk assessment involves models and data, and judgments of the potential impact of earthquakes, which must be

Counting the Leaves of Trees

December 19, 2011
Author(s)
Brian D. Cloteaux, Luis A. Valentin
A number of important combinatorial counting problems can be reformulated into the problem of counting the number of leaf nodes on a tree. Since the basic leaf-counting problem is #P-complete, there is strong evidence that no polynomial time algorithm

Linear Algebra and Sequential Importance Ssampling for Network Reliability

December 11, 2011
Author(s)
David G. Harris, Francis Sullivan, Isabel M. Beichl
The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various sizes

Combining Results from Multiple Evaluations of the Same Measurand

December 1, 2011
Author(s)
Raghu N. Kacker, Klaus-Dieter Sommer
According to the Guide to the Expression of Uncertainty in Measurement (GUM), a result of measurement consists of a measured value together with its associated standard uncertainty. The measured value and the standard uncertainty are interpreted as the

Computing Network Reliability Coefficients

December 1, 2011
Author(s)
Elizabeth R. Moseman, Isabel M. Beichl, Francis Sullivan
When a network is modeled by a graph and edges of the graph remain reliable with a given probability p, the probability of the graph remaining connected is called the reliability of the network. One form of the reliability polynomial has as coefficients

A Special Functions Handbook for the Digital Age

August 1, 2011
Author(s)
Ronald F. Boisvert, Charles W. Clark, Daniel W. Lozier, Frank W. Olver
The NIST Digital Library of Mathematical Functions (DLMF) is a reference work providing information on the properties of the special functions of applied mathematics. It is a successor to the highly successful NBS Handbook of Mathematical Functions

Division Polynomials for Jacobi Quartic Curves

June 13, 2011
Author(s)
Dustin Moody
In this paper we fi nd division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to the more common Weierstrass equation. Division polynomials for Weierstrass curves are well known, and the division polynomials we fi
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