BME 6770: Genomic Signal Processing
- For postdoctoral, graduate, and advanced undergraduate students in Engineering, Sciences, and Medicine, and professionals in industry.
- Spring 2026, Mondays and Wednesdays 11:50am–1:10pm, Meldrum Conference Room WEB 2760 and Zoom; office hours by request or Wednesdays 11:00am, WEB 3803.
Prerequisites: Some experience programming and instructor approval.
100% grade = 40% labs and quizzes, 30% class project, 20% presentation, 10% class participation; late assignments are not accepted; class attendance is required.
May be pivotal for your career:
This project-oriented genomics, data science, and artificial intelligence and machine learning (AI/ML) course covers:
- Technologies: For high-throughput acquisition of molecular biological data on genomic and proteomic scales, such whole-genome sequencing and protein arrays.
- Databases and Large-Scale Datasets: Generated by national and international consortia as well as individual research groups using these technologies..
- Comparative and Integrative Modeling: Using concepts from signal processing, and AI/ML, from the singular value decomposition (SVD) and principal component analysis (PCA), to the pseudoinverse projection and linear regression, and to large language models (LLMs).
- Biological and Medical Predictions: Made by these comparative and integrative models, their experimental tests and their applications toward better understanding of basic biology as well as improved medical diagnosis, treatment, and drug design.
Objective/Outcome:
The design and realization of a data science project by each student.
Skills:
- Proving mathematical theorems and coding symbolic computations.
- Designing algorithms and programming numerical computations.
- Working with biomedical databases.
- Modeling biomedical data.
Activities:
- In-class presentations of, e.g., scientific journal articles and patents.
- Participation in guest lectures and seminars on campus and discussions of professional conference reports.
- End-of-class celebration and discussion of future directions.
Readings on the SVD and deep learning:
- The syllabus is subject to change at the discretion of the instructor.
- Spring 2026 Calendar and Spring 2026 PCE Guidelines
- University Policies
- Health, Wellness, and Counseling
January 5:
January 7:
January 14:
Numerical Linear Algebra, Trefethen and Bau, III (1997).
Notebook 1: Computation and Visualization of the SVD
Lab 1:
Code the SVD or the pseudoinverse projection of synthetic data and its visualization. Test and debug your code.
January 19:
Happy Martin Luther King Jr. Day!
January 21:
Composition and decomposition of synthetic data:
Notebook 2: The SVD of Synthetic Data
January 26:
Mathematics of the pseudoinverse projection:
January 28:
Computation of the pseudoinverse projection:
Notebook 3: The Pseudoinverse Projection of Measured Data
February 2:
Modeling nonlinear phenomena with linear algebra
February 4:
February 9:
February 11:
February 12:
February 16:
February 18:
February 23:
Notebook 4: The Hypergeometric Probability Distribution and P-Value
February 25:
In-Class Work on Lab 2:
Compute and visualize the SVD or the pseudoinverse projection of your data. Interpret your data based upon its SVD. Use at least two different approaches each for preprocessing and sorting your data and for assessing the statistical significance of your interpretation.
March 2:
Matrix Computations, Golub and Van Loan (1996).
March 4:
March 9:
March 11:
March 16:
From the SVD to PCA:
March 18:
March 23:
Mathematical variations on the SVD and PCA for blind source separation (BSS):
March 25:
Mathematics of the generalized SVD (GSVD):
March 30:
Computation of the GSVD:
Notebook 5: The GSVD of Synthetic Data
April 1:
April 6:
April 8:
April 13:
April 15:
"State of the project" presentations
April 20:
End-of-class celebration!
"State of the project" presentations
Happy Summer Break!
