A more faithful, flexible algorithm implemented on a personal computer would be useful (1) for planning minimally invasive treatments, (2) for calibrating the MRI
machines, (3) for investigating structures oriented obliquely in space, such as postmortem tissue sections in animal research, (4) for enabling cross-sections at any angle
through a brain atlas consisting of black-and-white line drawings. To design such an algorithm, one can access the values and locations of the pixels, but not the initial data
gathered by the scanner.

Problem:
Design and test an algorithm that produces sections of three-dimensional arrays by planes in any orientation in space, preserving the original gray-scale values as closely as possible.

Data Sets:
The typical data set consists of a three-dimensional array A of numbers A(i,j,k) which indicates the density A(i,j,k) of the object at the location (x,y,z)_{ijk} . Typically,
A(i,j,k) can range from 0 through 255. In most applications; the data set is quite large. Teams should design data sets to test and demonstrate their algorithms. The data sets
should reflect conditions likely to be of diagnostic interest. Teams should also characterize data sets that limit the effectiveness of their algorithms.

Summary:

The algorithm must produce a picture of the slice of the three-dimensional array by a plane in space. The plane can have any orientation and any location in space. (The
plane can miss some or all data points.) The result of the algorithm should be a model of the density of the scanned object over the selected plane.

Problem B:
Background:
Some college administrators are concerned about the grading at A Better Class (ABC) college. On average, the faculty at ABC have been giving out high grades (the
average grade now given out is an A-), and it is impossible to distinguish between the good and mediocre students. The terms of a very generous scholarship only allow
the top 10% of the students to be funded, so a class ranking is required.

The dean had the thought of comparing each student to the other students in each class, and using this information to build up a ranking. For example, if a student obtains
an A in a class in which all students obtain an A, then this student is only "average" in this class. On the other hand, if a student obtains the only A in a class, then that
student is clearly "above average". Combining information from several classes might allow students to be placed in deciles (top 10%, next 10%, etc.) across the college.

Problem:
Assuming that the grades given out are (A+, A, A-, B+, ... ) can the dean's idea be made to work? Assuming that the grades given out are only (A, B, C, ... ) can the dean's
idea be made to work? Can any other schemes produce a desired ranking? A concern is that the grade in a single class could change many student's deciles. Is this possible?

Data Sets:
Teams should design data sets to test and demonstrate their algorithms. Teams should characterize data sets that limit the effectiveness of their algorithms.