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Mathematics & Statistics

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Displaying 201 - 225 of 473

Combinatorial Analysis of Diagonal, Box and Greater-Than Polynomials as Packing Functions

November 1, 2015
Author(s)
Pepe Torres Jimenez, Nelson Rangel-Valdez, Raghu N. Kacker, James F. Lawrence
Packing functions (PFs) are bijections between a set of m-dimensional vectors V over N m and nonnegative integers N. PFs have several applications, e.g. in partitioning schemes or text compression. Two important categories of PFs are diagonal polynomials

New Results on Packing Degree Sequences and the 2-Color Discrete Tomography Problem

October 27, 2015
Author(s)
James Shook, Michael Ferrara, Jennifer Diemunsch, Sogol Jahanbekam
A sequence $\pi=(d_1,\ldots,d_n)$ is graphic if there is a simple graph $G$ with vertex set $\{v_1,\ldots,v_n\}$ such that the degree of $v_i$ is the $i$th entry of $\pi$. We say that graphic sequences $\pi_1=(d_1^{(1)},\ldots,d_n^{(1)})$ and $\pi_2=(d_1^{

The Number of Boolean Functions with Multiplicative Complexity 2

October 27, 2015
Author(s)
Magnus G. Find, Daniel C. Smith-Tone, Meltem Sonmez Turan
Multiplicative complexity is a complexity measure, which is defined as the minimum number of AND gates required to implement a given primitive by a circuit over the basis (AND, XOR, NOT), with an unlimited number of NOT and XOR gates. Implementations of

Equilibrium and stability of axisymmetric drops on a conical substrate under gravity

October 4, 2015
Author(s)
Asha K. Nurse, Sean A. Colbert-Kelly, Sam R. Coriell, Geoffrey B. McFadden
Motivated by recent investigations of toroidal tissue clusters that are observed to climb conical obstacles after self-assembly, we study a related problem of the determination of the equilibrium and stability of axisymmetric drops on a conical substrate

Multiplicative Complexity of Vector Value Boolean Functions

September 21, 2015
Author(s)
Magnus G. Find, Joan Boyar
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$ circuits, we show

Predictive Models for Min-Entropy Estimation

September 13, 2015
Author(s)
John M. Kelsey, Kerry McKay, Meltem Sonmez Turan
Random numbers are essential for cryptography. In most real-world systems, these values come from a cryptographic pseudorandom number generator (PRNG), which in turn is seeded by an entropy source. The security of the entire cryptographic system then

FFT-based Alignment of 2d Closed Curves with Application to Elastic Shape Analysis

September 10, 2015
Author(s)
Gunay Dogan, Javier Bernal, Robert Hagwood
For many shape analysis problems in computer vision and scientific imaging (e.g., computational anatomy, morphological cytometry), the ability to align two closed curves in the plane is crucial. In this paper, we concentrate on rigidly aligning pairs of

The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

May 28, 2015
Author(s)
Felipe Vico, Leslie Greengard, Miguel Ferrando, Zydrunas Gimbutas
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A, φ in the Lorenz gauge, we

Tower of Covering Arrays

April 25, 2015
Author(s)
Raghu N. Kacker, Jose Torres Jimenez
Covering arrays are combinatorial objects that have several practical applications, specially in the design of experiments for software and hardware testing. A covering array CA(N;t,k,v) of strength t and order v is an N×k array over Z v with the property

On the Stability of Rotating Drops

April 20, 2015
Author(s)
Asha K. Nurse, Sam R. Coriell, Geoffrey B. McFadden
We consider the equilibrium and stability of rotating axisymmetric fluid drops by appealing to a variational principle that characterizes the equilibria as stationary states of a functional containing surface energy and rotational energy contributions

Constraint Handling In Combinatorial Test Generation Using Forbidden Tuples

April 13, 2015
Author(s)
Raghu N. Kacker, David R. Kuhn, Yu Lei
Constraint handling is a challenging problem in combinatorial test generation. In general, there are two ways to handle constraints, i.e., constraint solving and forbidden tuples. In our early work we proposed a constraint handling approach based on

Improving IPOGs Vertical Growth Based on a Graph Coloring Scheme

April 13, 2015
Author(s)
Raghu N. Kacker, David R. Kuhn, Yu Lei
In this paper, we show that the vertical growth phase of IPOG is optimal for t-way test generation when t = 2, but it is no longer optimal when t is greater than 2. We present an improvement that reduces the number of tests generated during vertical growth

The Multiplicative Complexity of Boolean Functions on Four and Five Variables

March 17, 2015
Author(s)
Meltem Sonmez Turan, Rene C. Peralta
A generic way to design lightweight cryptographic primitives is to construct simple rounds using small nonlinear components such as 4x4 S-boxes and use these iteratively (e.g., PRESENT and SPONGENT). In order to efficiently implement the primitive, optimal

Obtaining a Trapezoidal Distribution

March 9, 2015
Author(s)
James F. Lawrence, Raghu N. Kacker, Ruediger Kessel
Given a most believed value for a quantity together with upper and lower possible deviations from that value, a rectangular distribution might be used to represent state-of-knowledge about the quantity. If the deviations are themselves known by probability

Improved Indifferentiability Security Bound for the JH Mode

February 15, 2015
Author(s)
Dustin Moody, Daniel C. Smith-Tone, Souradyuti Paul
Indifferentiability security of a hash mode of operation guarantees the mode's resistance against all generic attacks. It is also useful to establish the security of protocols that use hash functions as random functions. The JH hash function was one of the
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