Computational and applied mathematics, geometric methods for analysis of large data sets, data analysis on manifolds, optimal low-dimensional systems and modeling, optimization and mathematical modeling, non-linear signal and image processing with applications in electrical engineering, finance, computer science, statistics, chemistry and atmospheric sciences.
As a graduate research assistant at the Department of Mathematics, I am involved in conducting fundamental research in mathematics of large data sets and nonlinear signal processing.
This involves design of new Radial Basis Functions, basic and efficient contributions to the literature of constructing nonlinear models from high-dimensional scattered data. The developed methods utilize RBFs and do not require adjustment of any ad hoc parameters. The extension of the algorithms to multivariate cases and real-time implementation are also considered. The developed algorithms have a wide range of applications such as modeling data on manifolds and prediction of financial time-series.
As a graduate
research assistant/associate at the digital signal/image processing
laboratory
at electrical engineering, I worked on biological inspired adaptive
methods for
object classification in changing environments from multi-aspect views
and
studied object identification using Zernike moments and neural
networks. I learned
various feature extraction schemes and neural network paradigms and
other signal processing tools such as wavelets and different variations
of
the Kalman filter.
“Geometric Representation of High Dimensional Scattered Data as Graph of Functions”, Workshop on Applications of Topology in Science and Engineering, Mathematical Science Research Institute, University of California-Berkeley, (Berkeley, CA), September 2006.
“Parsimonious
Geometric Modeling of Financial Instruments”, SIAM
Conference on Financial Mathematics
and
Engineering, (Boston, MA),
July 2006.
“Examples
of Compactly
Supported functions for Radial Basis Function Approximations”,
International Conference on Machine Learning; Models, Technologies and
Applications, and International Conference on Scientific Computing,
(Las Vegas,
NV), June 2006.
“A New
Spatio-Temporal Resource Allocation Network (ST-RAN)”, Seminar
in Geometric Methods for the
Analysis of
High-Dimensional Data, CSU, (Fort Collins, CO), Spring 2005.
“Low
Order Nonlinear Models”, Information Science and Technology
Colloquium,
CSU, (Fort Collins, CO), April 2005. (Poster)
“Radial Basis Function Model Order Determination Using Statistical Hypothesis Testing”, Third Annual Intermountain/Southwest Conference on Industrial and Interdisciplinary Mathematics, Arizona State University, (Tempe, AZ), February 2004. (Poster)
“Target
Identification using Zernike Moments and
Neural Networks”, SPIE
conference
on Automatic Target Recognition XI,
(Orlando, FL), April 2001.
“Comparison
of Confidence Level of Different
Classification Paradigms for Underwater Target Discrimination”, SPIE conference on Detection and Remediation
Technologies for Mines and Mine like Targets VI, (Orlando, FL),
April
2001.
Workshop
on Topological Methods in Combinatorics, Computational
Geometry, and the Study of Algorithms, Mathematical Science Research
Institute,
University of California-Berkeley, (Berkeley, CA), October 2-6, 2006.
Supported
by an MSRI award.
Workshop
on Data Driven Modeling, Department of Mathematics, CSU,
(Fort Collins, CO), September 28, 2006.
Workshop
on Applications of Topology in Science and Engineering,
Mathematical Science Research Institute, University of
California-Berkeley,
(Berkeley, CA), September 18-22, 2006. Supported by an MSRI award.
Graduate
Summer School: Data Assimilation for the Carbon Cycle,
Mathematical Science Research Institute, University of
California-Berkeley,
(Berkeley, CA), July 16-29, 2006. Supported by an MSRI award.
Multi-scale
Methods and Statistics, Graybill Workshop, CSU, (Fort
Collins, CO), June 11-13, 2006.
Graduate
Summer School: Intelligent Extraction of Information from
Graphs and High Dimensional Data, Institute of Pure and Applied
Mathematics,
UCLA, (Los Angeles, CA), July 11-29, 2005. Supported by IPAM.
Statistics
in Information Theory, Graybill Workshop, CSU, (Fort
Collins, CO), June 2-3, 2005.
Workshop
on Geometry and Symmetry in Numerical Computation, CSU, (Fort Collins,
CO),
August 8-10, 2005.