Mentioning incomplete research on personal statement?

[Simfish]

Okay, so one year ago, I did a small project with an applied math professor. Basically, what I did was write a program (in C, for speed) to simulate neural spiking (basically, when sufficiently depolarized, the neuron will "fire" and generate an action potential). The program then computed the correlation function between the firing rate and the stimulus (we tried two values of stimuli - constant stimuli and white noise stimuli, and various "time bins" to show which stimuli decayed over time and which stimuli didn't decay over time) - and used that correlation function to produce a diagram of the spike-triggered average stimulus. After plotting the correlation function over time for a Gaussian stimulus, we eventually able to match the figures that were predicted in the book (from Figure 1.9 in Abbott's "Theoretical Neuroscience").

The reading and project ultimately took around 6 months (I was also reading papers for the next step - papers involving taking the integrals of stochastic integrals). Unfortunately, my research stalled after that (I took a very heavy course load that quarter, and I was also experiencing some technical difficulties as well [1] - it's actually very hard to get help for certain disciplines involving the C language, since people in my school usually don't code things in C, and none of the popular websites even help). After a sufficiently long break, I ultimately learned that my chances were a lot better for astronomy than for applied math/theoretical neuroscience, and switched to astronomy (I actually always liked astronomy - the decision was really one between astronomy and theoretical biology). What this means is that my research ended unfinished.

So I did manage to produce something useful (albeit something that the researchers already did). And I do feel that it was a valuable learning experience. However, the fact that I left could stir up some suspicion that I don't carry projects to completion (although I do hope to show that what happened then isn't going to happen for astronomy - because I really don't see myself doing anything other than astronomy now).

[1] See https://www.physicsforums.com/showthread.php?t=360041 for details - I'm sure that I could eventually get it corrected with time, but by the time my heavy quarter was over, I had already decided to switch to astro

 

[twofish-quant]

So I did manage to produce something useful (albeit something that the researchers already did). And I do feel that it was a valuable learning experience. However, the fact that I left could stir up some suspicion that I don't carry projects to completion.

You got results. That's completion.

Also, you can't please everyone and in graduate school admissions there is no point trying. You just need to get one committee to say yes, and if it makes you worse off with everyone else, it doesn't make any difference.

 

[Simfish]

Okay, good points. That's definitely true.

 

[Andy Resnick]

The program then computed the correlation function between the firing rate and the stimulus (we tried two values of stimuli - constant stimuli and white noise stimuli, and various "time bins" to show which stimuli decayed over time and which stimuli didn't decay over time) - and used that correlation function to produce a diagram of the spike-triggered average stimulus. After plotting the correlation function over time for a Gaussian stimulus, we eventually able to match the figures that were predicted in the book (from Figure 1.9 in Abbott's "Theoretical Neuroscience").

<snip>

So I did manage to produce something useful (albeit something that the researchers already did). And I do feel that it was a valuable learning experience.

I second twofish's comment, definitely include this experience. Spending a paragraph expanding on why this was a good learning experience- what you learned about the process of research, for example- should impress the committee.