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Mathematics & Statistics

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Displaying 326 - 350 of 872

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