Digital Commons Network^™

Self-Adaptive Scheduler Parameterization, Barry Lawson, Evgenia Smirni

Department of Math & Statistics Technical Report Series

High-end parallel systems present a tremendous research challenge on how to best allocate their resources to match dynamic workload characteristics and user habits that are often unique to each system. Although thoroughly investigated, job scheduling for production systems remains an inexact science, requiring significant experience and intuition from system administrators to properly configure batch schedulers. State-of-the-art schedulers provide many parameters for their configuration, but tuning these to optimize performance and to appropriately respond to the continuously varying characteristics of the workloads can be very difficult — the effects of different parameters and their interactions are often unintuitive.

In this paper, …

An Examination Of Codewords With Optimal Merit Factor, Michael W. Cammarano, Anthony G. Kirilusha

Department of Math & Statistics Technical Report Series

We examine the codewords with best possible merit factor (minimum sum of squares of periodic autocorrelations) for a variety of lengths. Many different approaches were tried in an attempt to find construction methods for such codewords, or for codewords with good but non-optimal merit factors.

Integer Maxima In Power Envelopes Of Golay Codewords, Michael W. Cammarano, Meredith L. Walker

Department of Math & Statistics Technical Report Series

This paper examines the distribution of integer peaks amoung Golay cosets in Ζ_4. It will prove that the envelope power of at least one element of every Golay coset of Ζ₄ of length 2^m (for m-even) will have a maximum at exactly 2^m+1. Similarly it will be proven that one element of every Golay coset of Ζ₄ of length 2^m (for m-odd) will have a maximum at exactly 2^m+1. Observations and partial arguments will be made about why Golay cosets of Ζ₄ of length 2^{m …}

Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner

Department of Math & Statistics Technical Report Series

This paper examines codewords of length 2^m in Z₈ with envelope power maxima of 3 ∗ 2^m. Using the general form for Golay pairs as a base, a general form is derived for the set of coset leaders that generate these codewords. From this general form it will be proven that there exists at least one element in the coset that achieves a power of 3 ∗ 2^m for each m-even and m-odd case.

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will examine the backward shift operator Lƒ = (ƒ – ƒ(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of "pseudocontinuation" of functions across the unit circle ∏.

Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku

Department of Math & Statistics Technical Report Series

This article gives an introduction to Elliptic Curve Cryptography and Quantum Computing. It includes an analysis of Peter Shor’s algorithm for the quantum computer breakdown of Discrete Log Cryptosystems and an analog to Shor’s algorithm for Elliptic Curve Cryptosystems. An extended example is included which illustrates how this modified Shor’s algorithm will work.

On Quaternionic Pseudo-Random Number Generators, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

There is no dearth of published literature on the design, implementation, analysis, or use of pseudo-random number generators or PRNGs. For example, [6] [7] [14] and the references therein, provide a broad overview and firm grounding for the subject. This report complements and elaborates upon the work of McKeever [9], who investigated PRNGs constructed in a non-commutative setting with the target application being so-called cryptographically secure PRNGs as discussed in [12] or [13]. Novel "solutions" to the problem of designing cryptographically secure PRNGS continue to be proposed [1] [2] [10] [15], so despite the caution and skepticism required, the area …

Secure Trapdoor Hash Functions Based On Public-Key Cryptosystems, Gary R. Greenfield, Sarah Agnes Spence

Department of Math & Statistics Technical Report Series

In this paper we systematically consider examples representative of the various families of public-key cryptosystems to see if it would be possible to incorporate them into trapdoor hash functions, and we attempt to evaluate the resulting strengths and weaknesses of the functions we are able to construct. We are motivated by the following question:

Question 1.2 How likely is it that the discoverer of a heretofore unknown public-key cryptosystem could subvert it for use in a plausible secure trapdoor hash algorithm?

In subsequent sections, our investigations will lead to a variety of constructions and bring to light the non-adaptability of …

Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross

Department of Math & Statistics Technical Report Series

In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space L^p_a(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces D_q, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on L^p_a(𝔻), 1 < p < 2.

On Uniform And Relative Distribution In The Brauer Group, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

In this progress/technical report our objective is twofold. First, to formalize and expand upon remarks appearing in [7] concerning the relativization of the fundamental identity in the setting of the Brauer group of a ring, and second to exhibit a construction which shows how to interpret uniform distribution as a homological phenomenon.