Posts Tagged ‘research’

Blockers

September 17 2013

I started a new job. Part of what this means, at least for me, is cleaning up the directory named research on my computer. Most of the directories in research have names that remind me of what is in the directory and/or when I made it, such as the notes from October 2010 in a directory named “2010-okt”, the document and the presentation for my research initiation project is in a directory named “RIP”, the translation of a paper by a Hungarian Mathematician István Fáry is in a directory named “fary” (see my previous post as to why I translated this paper).  The scheme of how the directories are structured has changed a few times, sometimes labeled by project and sometimes by date, but I am usually able to remember what is in every directory.

One directory, however, I did not remember.  The directory was named “blockers”.  I was curious to know what this meant, so I looked into the directory and found two files: blockers.svg and blockers.pdf.  I opened one of them and saw the following figure:

blockers

blockers

I usually have a text file or a short LaTex document explaining what I was working on, but for this folder no such luck. Perhaps I thought that the figure says it all.  Then, I had an idea. This was probably an example that I shared with someone, so I searched my email and found the following:

 

Michael,

Attached is my counter example.  Well, it’s a simplified version of something more elaborate that I originally had.  Hopefully by simplifying it, I didn’t change the outcome.  I won’t fully explain it in this email so I don’t taint your thoughts when you look at it.  I was shopping too much to explain this to you today, so maybe we can try again tomorrow.  I’ll be around before noon, otherwise, I’ll see you for a drink in the evening.
~Brit~

Not much more help.  But now, I at least remember discussing an open problem with Michael and Dmitriy, perhaps when we were in Russia last year.  Oh, as I am writing this post, I am remembering a little more.  Maybe I can re-remember …

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Virtual Exposure

August 19 2012

HerbertGünter and I wrote a paper about Gaussian Mixtures that was presented at SoCG this year (hopefully it will be in the special issue of DCG as well … we have yet to hear about this).  It was a large part of my dissertation and is actually receiving a lot of attention.

Thanks to my friend Andy, I have found out that this paper is receiving a lot of attention in the machine learning community.  It was mentioned in a Stat/ML blog and tweeted about by a UBC master’s student on 4 August 2012.  Go us!

Computing Hessians in My Sleep

September 23 2011

Herbert and I are working on a paper that will be a good portion of my dissertation.  We want to prove that a particular critical value is a maximum.  Sounds easier than it is, since the function I am looking at is an n-dimensional Gaussian Mixture Model (a sum of Gaussians in high-dimensional space).  After my discussion with Herbert about graduating and finding a post-doc, I decided that I need to finish my dissertation first.  So, I’ve been working extra-hard to finish the result.  Seems like an obvious step, I guess.

After working on this one part of the problem for about a week, I was beginning to think that I should put it aside and start thinking about something else for a little while.  But — last night, Dave called me just as I was on the brink of falling asleep.  I right away ask him “when is e^(-x) = x?”  He was confused, but plotted it and told me that it was around 0.55, which was the answer that I was looking for.  Knowing that I wouldn’t be able to reconstruct my almost-sleeping thoughts, I had Dave send me an email to tell me this.  It took me all day to reconstruct the proof that I thought of in my mind in five minutes, but I believe that the proof is complete now!  Moreover, I convinced Herbert that it is plausible.