- Finished editing the manuscript for the 2nd edition of the Perl::PDQ book, which was published in August.
- Finalized the invited chapter A Methodology for Optimizing Multithreaded System Scalability on Multicores (co-authored with Shanti Subramanyam and Stefan Parvu) for the edited volume: Programming Multi-core and Many-core Computing Systems (Wiley-Blackwell).
- Sommerfeld-Dirac Paradox: In 1916, Arnold Sommerfeld calculated the relativistic corrections to the Bohr atom and found that the associated perihelion precession produced the known fine structure of the hydrogen spectrum. Remarkably, this is the same result as discovered by Dirac more than a decade later in 1928. The paradox is that the Sommerfeld model does not involve electron (fermionic) spin, whereas spin is intimately involved with the Dirac solution. I originally heard about this paradox from my Masters thesis advisor, Prof. Christie Eliezer, who had been one of Dirac's research students. Recently, it has been suggested that the paradox arises from a fortuitous ambiguity in the way certain of the quantum numbers are defined. If this is so, I believe there ought to be a topological proof. I've got the Lie group algebras down, but it's still a work in progress.
- My ongoing effort to provide a simple pictorial derivation of the Erlang M/M/m queue has been simplified even further.
In case there's any doubt, here's the proof on my whiteboard dated April 13, 2011. :)
This "proof" turned out to be not so coherent. However, the correct approach has finally been obtained in 2016. See my post entitled, Erlang Redux Resolved! (This time for real) complete with animation of the morphing process.
- Steve Jenkin asked me why the electrical power consumed by a magnetic disk increases as the fifth power of the platter radius. I didn't know it did! So, I decided to see if I could derive the physics from first principles. I was able to do so, but I've yet to find the time to blog about the details. The main point is that the consumed electrical power (Watts) grows as the 5th power of the disk diameter and the 3rd power of the angular speed (RPM). Since these are very fast functions, this relationship is an important result for green datacenter design.
- Together with my colleagues at HP Labs, I've been working on a mathematical model of color naming. If you find yourself having trouble even parsing that sentence, now you know how I felt when I was introduced to this subject. Neuroscientists speculate that the left side of the brain, which deals with language, is also involved in processing colors in the right visual field. More colorful background information can be found on the XKCD blog. This is also a work in progress and I can't say more about our results until they are finally published. I can report, however, that quite unexpectedly, it's turned out to be one of the most exiting pieces of science that I've worked on in a long time.
- In response to having been challenged both publicly (without any supporting data) and privately (with supporting data that I can't reveal publicly) over the need to model so-called superlinear scaling, I've developed a theorem that states such superlinear modifications to the Universal Scalability Law are unnecessary. More on this later.
- I believe I can construct a theorem, which says something like this: The system performance of any computer system, no matter how big or distributed, can always be modeled with just a surprisingly few queueing nodes. How can this be? If you look carefully in my PPDQ book, you'll notice that most (if not all) of the models are relatively simple. Although I've observed this effect many times, over many years, I never put much stock in it. This year, that all changed. I now believe I know why it always works out that way, in general. There will, of course, be some exceptions because you can always add more detail. This theorem also means that it will finally be possible to automatically build your PDQ model directly from collected performance data.
- Designed and road-tested the new GDAT training course.
- Fixed "string" variables (there are no strings in C) in the PDQ library that were causing the R Console to crash. Still have to export the fix to SourceForge.
- Constructed multiple optimization functions for an M/M/m queue to demonstrate that there is no unique way to define optimal load points (ρ*) or "knees" (a misnomer) for response time curves.
For example, for any configuration of m-servers in the above table, which of the functions Y1, Y2 or Y3 represents the correct optimal load (ρ* values in each row)?
- Wrote this blog post. OK, that doesn't count but an odd-numbered list might be unlucky in an even year. :P