The following is an (more or less unedited) excerpt from my dissertation, which is in progress.
Gradients run from most recently activated (black) to recovering (grey) to recovered (white). Black dots indicate locations of stimulus application. Black lines indicate propagation of activation from the region of the applied stimulus. Flat line endings mark termination of propagation, while the black arrow represents continued propagation. A: Resetting of re-entry in a ring following stimulus application in the excitable gap. B: Termination of re-entry in a ring following stimulus application in the excitable gap.
Resetting and termination in a ring
The classic model of re-entry is the one-dimensional system of a wave propagating within a ring composed of an excitable medium (see figure above). If the ring is longer than the wavelength of the wave of excitation, there will be an excitable gap between the tail of the wave and the head (white regions in figure). A stimulus applied in that gap can either reset or terminate re-entry. Resetting occurs when the stimulus results in an orthodromic wave (that is, moving in the same direction as the original wave) and an antidromic wave (that is, moving in the opposite direction from the original wave) in the excitable gap and the following happens: the antidromic wave collides with the original wavefront and terminates it, while the orthodromic wave follows the recovering tail of the original wave and becomes the starting point of a new re-entrant wave (figure panel A). If, however, the orthodromic wave collides with the recovering tail of the original wave and terminates, then re-entry will be terminated entirely (figure panel B). Thus, if a stimulus were applied at the appropriate time and position to consume the excitable gap, it would terminate re-entry.
Interesting aside. I was at first stumped on how to make ring gradients like what you see above. I used a combination of what I found here and going back and forth from GIMP to OmniGraffle Pro. They key appears to be the use of an asymmetrical conical gradient in GIMP.
I’m working on my graduate thesis in the LaTeX document mark-up format, and trying to apply Anthony Burgess’ Martini Method. Basically, set a certain desired word count and let yourself relax after you’ve achieved that word count every day. I started off pretty well with this method, but the next day my wife Amanda went into labor, and my productivity has basically been a train wreck ever since.
I’m getting back on the horse.
Anyway, it’s a little tricky to apply the Martini Method when using LaTeX — as a markup language a bit like HTML, it’s full of special words, symbols, characters and whatnot that are not actually part of what you’re writing. A simple Emacs word count will not do the trick. Much as I’d love to count all of those extra words, the point here is to produce a certain volume of output and that would miss the point. Plus, it’s dishonest. There exists a PERL script that will parse LaTeX and count the non-special words. However, someone’s gone even a step further and made a nice web interface for it, with color coding and everything. That interface is here, apparently hosted by one Einar Andreas Rødland in Norway.
So far, it’s working quite well for me. Unfortunately, it just informed me that I’m not quite to my desired word count yet. More writing!
I had to take a “Graduate Board Oral Examination” — typically called a GBO and synonymous with “qualifier” — in order to be able to get a Hopkins PhD. It’s necessary and not sufficient, of course, as I still need to do a thesis defense. I was fairly worried about it, and with good reason, but things went very well and now I’m one step closer to graduation.
Now all that’s between me and the PhD are a few simulations and a lot of writing. I think I’m going to employ Anthony Burgess’ Martini Method. 1000 words per day, after which I can have a martini, relax, etc.
There’s also the small issue of my baby arriving soon, which will certainly complicate matters.
Thinking about E-Prime ( introduced here ) has given me a new perspective on the word “is”. I’m in the process of putting together a manuscript with a co-author, and the various catch-alls committed by the use of “is” are jumping out at me.
The fact is, writing in E-Prime would be extremely awkward as compared with the status quo. Not only that, my advisor would probably fire me if I attempted it. What can be done when writing a paper is to take a hard look at every use of “is”, and determine whether each one can be replaced by a better verb. For example, “This figure is a set of images from …” can be replaced with, “This figure contains a set of images from …”.
Also, I don’t know if I’ve mentioned this before, but I commit a few punctuation atrocities intentionally, and I don’t intend to change them. Foremost is my placement of final sentence punctuation outside of quotes. As a programmer, it just drives me crazy to place punctuation inside of a quote, where it doesn’t belong, simply because the rules say so. I have read that my placement is more accepted in British English writing, which is I guess some consolation. Here’s an example of breakage and how my use circumvents it:
Tom leaned forward, a glint in his eyes, and said, “You don’t really mean to imply that we should eat babies, do you?”
Tom’s sentence ends with a question mark, but the sentence overall is a statement! (Perhaps there’s already some convention about this that I’m unaware of. I really should read Strunk and White one of these days.) I would therefore write:
Tom leaned forward, a glint in his eyes, and said, “You don’t really mean to imply that we should eat babies, do you?”.
Now you know my dirty little secret, and it’s out in the open. Lest you be tempted to correct me.
Yesterday at the climbing wall I overheard a discussion on grammar, and one of the people mentioned that he couldn’t remember the difference between “which” and “that”.
This is one of those things that I know how to write property, but I can’t explain why.
Or couldn’t — for now I can. While waiting for the hopkins med campus shuttle today, I sat and wrote some sample “which” and “that” sentences and tried to discern what differentiates them. Here are the examples that I wrote. (Or, here are the examples, which I wrote.)
“This is the house that Jack built.”
“This is aspirin, which is used for headaches.”
“This is the aspirin that I took for my headache.”
The last sentence is when the answer snapped into focus for me: the difference was analogous to the difference between classes and their instantiations in object-oriented programming. “This is aspirin” describes the aspirin class — any and all aspirin. “Which is used for headaches” specifies more detail about the aspirin. On the other hand, “That I took for my headache” specifies a particular instance of the class “aspirin”, namely, the specific aspirin that I took for my headache. I wrote this note next:
“Look up whether ‘classes’ and ‘instances’ have analogous counterparts in language — they must.”
Sure enough, upon looking up the question, I found that I was almost exactly right. If you are uncertain about the proper usages of “that” and “which”, I suggest you read about the issue here.