The Proceedings of the Conference on Information Systems Applied Research 2008: §3554    Home    Papers/Indices    prev (§3553)    Next (§4113)
Sat, Nov 8, 3:00 - 3:25, Kachina B     Paper (refereed)
Recommended Citation: Frank, R I.  A Computing Research Example: Following a Question.  In The Proceedings of the Conference on Information Systems Applied Research 2008, v 1 (Phoenix): §3554. ISSN: 0000-0000.
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A Computing Research Example: Following a Question

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Refereed7 pages
Ronald I. Frank    [a1] [a2]
Pace University    [u1] [u2]
Pleasantville, New York, USA    [c1] [c2]

We give an example of research: how an observation and a question about what it means leads to new insights - if diligently followed. This is an ongoing example, still in progress and requires only basic college mathematics to follow. We start from an observation about cubic arrays and ask what the formula implies. Following the trail, we discover the possibility of defining "arrays" that have strange properties such as negative length and fractional dimension. Along the way, we discover a polynomial that generates all of the sub arrays of a given array. This is a problem of interest in the design of parallel computers such as hypercube machines. It also pops up in data mart data cubes used in OLAP. We talk in terms of data arrays, but the reader can also think of arrays of processors or of array structured clusters.

Keywords: Research example, Array structure, Characteristic polynomial, Fractional dimension, Complex Length, Negative Length, Array function.

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