Selected Publications
Jonathan Tran, Ted Yoo, Shane Stahlheber, Alex Small, Journal of Statistical Mechanics: Theory and Experiment, P05014 (2013)
Alex Small, Nature Methods, 9, pg. 655656 (July 2012)
This is an invited article discussing two papers in Nature Methods. The papers introduce better image analysis tools for superresolution localization microscopy (PALM and STORM). Ertan Salik, Alex Small, Optics and Photonics News, pg. 1011 (June 2012)
We were invited to submit an article describing our efforts to grow the number of physics majors at Cal Poly Pomona. In the past 3 years we've gone from averaging 10 or fewer per year to a graduating class of 21 in 2012! I am one of the coordinators of the group of faculty that informally steers our recruitment efforts, and it was gratifying to see this article come out describing our accomplishments in the same month that our first growth cohort (we began our intensive efforts with the group that were sophomores in 2010) graduates.
Rebecca Starr, Shane Stahlheber, Alex Small, Optics Letters, 37, pg. 413415 (2012)
Here we describe an algorithm for determining the coordinates of a fluorescent molecule by looking at a picture of it. Essentially this amounts to fitting a 2dimensional function to the image data (i.e. an array of photon counter per pixel). While many algorithms are available for this task, ours has the advantage that the number of steps in most timeconsuming part is only proportional to the square root of the number of pixels, rather than the number of pixels. Since our results converge in 23 iterations, and we do it twice (once for the xcoordinate, once for the ycoordinate) the number of steps is about 6*the square root of the number of pixels, multiplied by the number of function evaluations per step. There are singlestep algorithms out there, but they still require a number of operations proportional to 2x the number of pixels. Our algorithm wins if the number of pixels is about 9x9 or more. Also, our algorithm is based on Maximum Likelihood Estimation (MLE) and thus should achieve the theoretical minimum variance in the position estimates (or, at least, something very close to it, given that we make a few assumptions and thus don't have a perfect probability model). Alex Small, Biomedical Optics Express, 2, 934949 (2011)
This paper is a followup to the Optics Letters paper below. Now we consider what happens if you have only one laser in the experiment instead of 2. The laser that bleaches molecules is also the one that activates them, so controlling error rates, activation, and bleaching is actually more complicated rather than less complicated. Sure, you have only one variable to play with, but now that means that everything changes together; you can't separate activation and bleaching. The lesson is that in this more complicated case you need much more detailed knowledge of the photophysics of your system. Alex Small, Kai S. Lam, American Journal of Physics, 79, 678681 (2011)
This paper describes a simple way of deriving two classic equations of optics and mechanics. I worked with my colleague Kai Lam on this after teaching upper division classical mechanics and deciding that I want an easier to way to show the students Hamiltonian mechanics. The usual approach from Goldstein is way too tedious for undergraduates; this approach is just based on the action integral, and makes for nice analogies with optics.
This paper is by my first Masters student (Edward Shore, Applied Mathematics program) and describes a scheme for optimizing the acquisition of images when the molecules are getting bleached and hence the bound on the activation probability (1/# of unbleached molecules) is changing in time. Theoretical investigation of optical patterning of monolayers with subwavelength resolution
Triet Nguyen, Michael Mansell, Alex Small, Physics Letters A, 374, 26812687 (2010)
Due to an oversight on our part, the following acknowledgment was not included in the article: "This work was supported by the Research Corporation, the Keith and Jean Kellogg Honors College, and California State Polytechnic University." We regret the error and apologize to our sponsors.

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