To review the solution to Merlin's Magic Square, we begin by introducing our formal model. As usual, we use 1 to represent an ON light and 0 to represent an OFF light. When light and button are one unit as in Merlin we shall also speak of the button itself as being ON or OFF.

]]>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 the curve must be contained in the Northern Hemisphere. This type of proof not only answers the existence question, but also yields a specific hemisphere that contains your path.

We, however, thought the problem lent itself nicely to integral geometry, which required us to consider the space whose points are hemispheres. This led to a different existence proof and to a solution of the more general question: can you describe and measure the set of all hemispheres that contain γ?

An outline of the remainder of this paper follows. In Section 2 we introduce terminology and definitions. The existence of at least one hemisphere containing γ is proved using the ideas of integral geometry in Section 3. Classifying sets of such hemispheres for a single arc, a geodesic triangle, and a geodesic quadrilateral is accomplished in Section 4. Section 5 contains a discussion of convexity on the sphere and how it relates to our question. Our main theorem is stated and proved in Section 6.

]]>In this paper, we introduce a new and general methodology for automating the difficult process of job scheduler parameterization. Our proposed methodology is based on *online simulations* of a model of the actual system to provide on-the-fly suggestions to the scheduler for *automated parameter adjustment*. Detailed performance comparisons via simulation using actual supercomputing traces from the Parallel Workloads Archive indicate that this self-adaptive parameterization via online simulation consistently outperforms other workload-aware methods for scheduler parameterization. This methodology is unique, flexible, and *practical* in that it requires no a priori knowledge of the workload, it works well even in the presence of poor user runtime estimates, and it can be used to address any system statistic of interest.

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 public-key cryptosystems that are of a \low density." More importantly, we will be led to consider from a new point of view the effects of the unsigned addition, shift, exclusive-or and other logical bit string operators that are presently used in constructing secure hash algorithms: We will show how the use of publickey cryptosystems leads to \fragile" secure hash algorithms, and we will argue that circular shift operators are largely responsible for the security of modern high-speed secure hash algorithms.

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