What happens when I do too much revision

2007 Engineering Tripos Part IIB (Information and Computer Engineering)
Synoptic paper

1. (Machine Learning) Consider the task of training a neural network to answer Tripos questions on Machine Learning. If only a single "sample exam paper", which may or may not reflect the content of the exam, is available (due to this being the first year the subject has been offered), describe the dangers of overfitting and whether any prediction can be made about the performance of the trained system on the actual task.

2. (Computer graphics) Define the term rasterisation, by analogy with a hungry student methodically scraping the last spoonful of ice cream from the bottom of a container.

3. (Computer vision) In stereo vision we attempt to reconstruct the world from a pair of images. Which of the following pairs would produce the best results?

i. The view from the top of Great St Mary's, and a depiction of particle traces in a bubble chamber
ii. A portrait of Queen Victoria, and a photomicrograph of a flea
iii. The Earth from space, and the first fragment of the Dead Sea Scrolls
iv. The Eiffel Tower, and a single soap bubble

Give a mathematical justification for your choice.

4. (Robust and optimal control) Using the Hamilton-Jacobi-Bellman equations, derive an optimal plan for a final-year engineering undergraduate trying to decide what to do with the rest of their life.

5. (Computational systems biology) Define the terms paralogy, orthology and xenology. If a set of lecture notes contains slides that have diverged from a common ancestor; slides that were modelled on those through which the lecturer was made aware of the concept; and slides that were borrowed from other lectures, discuss which of the above terms apply.

6. (Nonlinear and predictive control) If a Part IIB Engineering module is modelled as a vector in a D-dimensional space, prove that no eight of such modules can form a linearly independent set. Show also that the gradient of knowledge must be locally Lipschitz on x.