Seemed to have contracted a nasty lung infection on 29 September. Had to stop training and been off the bike ever since (with a 3 day exception in the middle of the month averaging 20-30 km). None of the doctors have been able to figure out which bacteria it is; except that it is not one of the common ones. Zithromax seemed to help a little bit last week, but started regressing again when it wore off.
While staying at home for some people may seem like a vacation, it starts to feel like jail for awhile. After starting and completing Command & Conquer (Tiberium Wars), gained enough mental facility to consider an interesting problem somebody posed to me at work. It has to do with constellations and QAM. For QAM, engineers use 4, 8, 16, 64, .... QAM for signal modulation. The friend was thinking of using hexagonal tiling instead, but some group published a paper last year. I suggested to use a Penrose Tiling. It uses quasi-five fold symmetry and initial results does show that it is more efficient than other symmetries (assuming the size of the n-fold polygons are the same with elements at the vertices). In terms of the inter-element spacing, n-fold polygons with smaller n are more efficient (completely logical). There is probably some horribly complex math that can be done to prove all of this, but Apple Keynote worked fine enough for me. What's interesting is how everything works in circles....The 5-fold symmetry is a problem I spent a year doing at UCSC when working on my thesis: 3D Visualizations of Quasi-Crystals (published a couple years later in a Physics journal).
For more information on Wikipedia:
http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation
http://en.wikipedia.org/wiki/Constellation_diagram
No comments:
Post a Comment