Broadly speaking, my research interests are in inverse problems with PDEs, numerical analysis, and medical imaging. Currently I am working with Arvind Saibaba on computational aspects of deterministic and statistical inverse problems, namely dimension reduction. My dissertation work was on optimization and uncertainty quantification in photoacoustic tomography.
Computationally efficient Markov Chain Monte Carlo methods for hierarchical Bayesian inverse problems
D. A. Brown, A. K. Saibaba and S. Vallélian. In revision. arxiv:1609.07180
T. Ding, K. Ren and S. Vallélian. 2015 Inverse Problems 31 095005.
Quantitative PAT with unknown ultrasound speed: uncertainty characterization and reconstruction methods
S. Vallélian. PhD Thesis.
Work in progress:
TeachingI love talking about and sharing mathematics and am always interested to learn new methods or resources for effective teaching.
Teaching at NCSU:
- Spring 2017: MA 405, Introduction to Linear Algebra
- Video Lectures by Gilbert Strang, MIT OpenCourseWare
- Proof-writing Resources (zip)
- Homeworks with Solutions (zip)
- Exam Reviews (zip)
- The $25,000,000,000 Eigenvector: The Linear Algebra behind Google
- A Survey of Eigenvector Methods for Web Information Retrieval
- PageRank demo code
- Cholesky Decomposition of Variance-Covariance Matrices in the Classic Twin Study
- The Monte Carlo Framework, Examples from Finance and Generating Correlated Random Variables
- Cholesky demo code
- We Recommend a Singular Value Decomposition
- Singular value decomposition and principal component analysis
- SVD demo code
- Fall 2016: MA 241, Calculus II for Engineers
In the last week of class, we explored applications of linear algebra, including: PageRank and eigenvectors; correlated random variables and Cholesky factorization; image compression and singular value decomposition. Here are the resources I used.
I gave a tutorial on X-ray Computed Tomography at the SAMSI CCNS Undergraduate Workshop in October 2015. Here are the resources:here).
For details about my past teaching experiences take a look in my CV.