Here are some recent CAMCOS projects and some scientific publications
and talks that have resulted from them.
Optimal clustering in 1-dimensional and higher-dimensional
data, Spring 2002-Spring 2003
Dr. Jeff Scargle, an astronomer at NASA-Ames, has long been interested
in the problem of taking a region of 1- or 2- (or n-)
dimensional space, with selected data points in it, and dividing the
region into areas of roughly uniform density.
Under the supervision of Dr. Brad Jackson (SJSU Math), from Spring
2002-Spring 2003, student teams working on this project:
- devised and implemented an efficient yet provably optimal
algorithm that solves the 1-dimensional version of the problem;
- explored different approaches to the 2- (or actually, n-)
dimensional problem, and devised an n-dimensional algorithm
that is conjectured to be optimal, albeit too slow to solve large
- investigated effective and efficient 2-dimensional algorithms
for this problem, based on established methods in combinatorial
Resulting publications and talks:
- An algorithm for optimal partitioning of data on an
interval, Jackson, B.; Scargle, J.D.; Barnes, D.; Arabhi, S.;
Alt, A.; Gioumousis, P.; Gwin, E.; Sangtrakulcharoen, P.; Tan, L.; Tun
Tao Tsai. (All authors after the first two are CAMCOS students.)
IEEE Signal Processing Letters, Vol. 12, No. 2,
Feb. 2005, pp. 105-108.
- Gray Level Reduction for Segmentation, Threshholding, and
Binarization of Images Based on Optimal Partitioning on an
Interval, Mahmoud Queweider, Brad Jackson, and Jeffrey
D. Scargle, submitted.
- Talk by Jackson at Bay Area Discrete Math Day, UC Berkeley,
October 30, 2004. "Algorithms For Finding Optimal Partitions of
- Talk by Scargle at Institute for Pure and Applied Mathematics,
UCLA, Multiscale Geometry and Analysis, Workshop IV: Multiscale
Geometric Methods in Astronomical Data Analysis, November 8-12, 2004.
"Multiscale Data Analysis through Optimal Segmentation."
Statistical analysis of a nonlinear chemical equation using
numerical methods, Spring 2002
Dr. Laura Iraci, a chemist at NASA-Ames, investigates the reactions of
halogenated gases (HOBr, HBr, HCl) on aqueous sulfuric acid, which is
representative of the aerosol particles found in the Earth's
atmosphere at high altitudes. Dr. Iraci was interested in measuring
the extent to which a certain "unusual" reaction appeared in her
experiment. In Spring 2002, a student team supervised by Dr. Steve
Crunk used statistical and numerical methods to estimate certain
interesting reaction parameters and give 95% confidence intervals for
those parameters. In particular, it was determined with 95%
confidence that the "unusual" reaction actually occurred in several
- The team's results are used in an appendix to Uptake of
hypobromous acid (HOBr) by aqueous sulfuric acid solutions:
Low-temperature solubility and reaction, L. T. Iraci,
R. R. Michelsen, S. F. M. Ashbourn, T. A. Rammer, and D. M. Golden,
submitted to the Journal of Atmospheric Chemistry.