Prerequisites: Some experience programming and instructor approval.
100% grade = 30% labs, 30% presentation, 30% class project, 10% class participation; class attendance is required.
Topics:
Concepts in artificial intelligence, data science, and machine learning and their applications in the integration and comparison of different types of high-throughput omic data acquired by different technologies and from different studies toward discovery, verification, and validation of biomedical principles.
- Technologies, for for high-throughput acquisition of different types of molecular biological data, e.g., omics, imaging, and patient clinical information.
- Databases, from the Cancer Genome Atlas (TCGA) at the Genomic Data Commons (GDC) to the Cancer Image Archive (TCIA).
- Mathematical frameworks, from the singular value decomposition (SVD) and principal component analysis (PCA) to multi-matrix tensor decompositions, neural networks, and deep learning.
- Applications toward better understanding of biology and practice of medicine, e.g., personalized cancer diagnostics, prognostics, and therapeutics.
Skills:
- Proving mathematical theorems and programming symbolic computations.
- Designing algorithms and programming numerical computations.
- Working with databases and modeling biomedical data.
Activities:
- In-class presentations of scientific journal articles and patents.
- Participation in guest lectures and seminars on campus and discussions of conference reports.
- End-of-class celebration.
January 6:
- Welcome!
- So much more to discover:
Comparative Spectral Decompositions for Personalized Cancer Diagnostics, Prognostics, and Therapeutics, Alter, 2018 SIAM Conference on Applied Linear Algebra (2018).
- Technologies and databases: On the Utah origin of the human genome project
The Alta Summit, US Department of Energy.
- Mathematical frameworks: The singular value decomposition (SVD) in the news
If You Liked This, You're Sure to Love That, New York Times.
- Applications and a note on ethics: Personalized medicine
How Bright Promise in Cancer Testing Fell Apart, New York Times.
January 8:
- Slides 1: Technologies: Examples of high-throughput biotechnologies
- Genomics after the human genome project:
Paper 1: A Vision for the Future of Genomics Research, Collins et al., Nature (2003);
Acknowledgements.
- Databases: TCGA
Paper 2: Comprehensive Genomic Characterization Defines Human Glioblastoma Genes and Core Pathways, TCGA Research Network, Nature (2008).
January 13:
- Mathematical frameworks: The SVD
- Numerical Linear Algebra, Trefethen and Bau, III (1997).
- Notebook 1: Computation and Visualization of the SVD
Mathematica Code: Notebook_1.nb
- Lab 1:
Code the SVD of synthetic data and its visualization. Test and debug your code.
January 15:
- Stanford University Institute for Computational and Mathematical Engineering Seminar (Stanford, CA, January 16, 2020).
January 20:
- Happy Dr. Martin Luther King, Jr. Day!
"Injustice anywhere is a threat to justice everywhere."
January 22:
- Slides 2: From data organization to analysis and interpretation
- Paper 3: Cluster Analysis and Display of Genome-Wide Expression Patterns, Eisen et al., Proc Natl Acad Sci USA (1998).
- In-Class Project 1: Derive the hypergeometric distribution from first combinatorics principles.
January 27:
- In-Class Project 2: Download two interrelated omic profiles from TCGA via GDC, e.g., (i) RNA sequencing profiles of the tumors of two different patients of the same type of cancer or two different types of cancer, (ii) gene expression profiles from the tumor of one cancer patient measured by two different biotechnologies, or (iii) DNA methylation and protein expression profiles of the tumor of one cancer patient. How would you interpret these profiles?
January 30, Thursday, 10:00–11:00pm, in lieu of any one Lab:
- Amazon Web Services (AWS) Education Research Webinar
February 10:
- Mathematical properties of the SVD
February 12:
- Lab 1 Due In-Class
- Slides 3: Discovery of data patterns by using the SVD
- Paper 4: Molecular Characterisation of Soft Tissue Tumours: a Gene Expression Study, Nielsen et al., Lancet (2002);
Supplement.
- Happy International Darwin Day!
Timeline of the human genome project:
From Darwin and Mendel to the human genome project, National Human Genome Research Institute.
February 17:
- Happy Presidents Day!
- Slides 4: SVD as a Transform
- Quantum Harmonic Oscillator from Wikipedia
- Image Compression via the SVD from Mathworld
- Image Compression via the Fourier Transform from Mathworld
- A Hard Day's Night Opening Chord from Wikipedia
- In-Class Work on Lab 2:
Compute and visualize the SVD 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.
February 19:
- Examples of interpretation of TCGA data:
Paper 5: Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival Phenotype, Aiello et al., APL Bioeng (2018).
Paper 6: GSVD Comparison of Patient-Matched Normal and Tumor aCGH Profiles Reveals Global Copy-Number Alterations Predicting Glioblastoma Multiforme Survival, Lee et al., PLoS One (2012).
- Examples of assessing the statistical significance of an interpretation:
Paper 7: Systematic Determination of Genetic Network Architecture, Tavazoie et al., Nat Genet (1999).
Paper 8: GOrilla: A Tool for Discovery and Visualization of Enriched GO Terms in Ranked Gene Lists, Eden et al., BMC Bioinformatics (2009).
Paper 9: Discovering Motifs in Ranked Lists of DNA Sequences, Eden et al., PLoS Comput Biol (2007).
February 21, Friday, 8:00–11:00am, Utah State Capitol Rotunda, 350 North State Street, Salt Lake City, in lieu of any one Lab:
- 2020 Utah American Cancer Society (ACS) Cancer Action Network (CAN) Day at the Capitol
February 24:
- Slides 5: The SVD vs. PCA
Paper 10: Correspondence Analysis Applied to Microarray Data, Fellenberg et al., Proc Natl Acad Sci USA (2001).
- Mathematical variations on the SVD and PCA:
Independent component analysis (ICA):
Paper 11: Linear Modes of Gene Expression Determined by Independent Component Analysis, Liebermeister, Bioinformatics (2002).
- Nonnegative matrix factorization (NMF):
Paper 12: Metagenes and Molecular Pattern Discovery Using Matrix Factorization, Brunet et al., Proc Natl Acad Sci USA (2004).
February 29:
- Gene H. Golub's Birthday!
Paper 13: Calculating the Singular Values and Pseudo-Inverse of a Matrix, Golub and Kahan, SIAM J Numer Anal (1965).
March 2:
- Selection of a cutoff of the singular values:
Paper 14: Component Retention in Principal Component Analysis with Application to cDNA Microarray Data, Cangelosi and Goriely, Biol Direct (2007).
Paper 15: The Optimal Hard Threshold for Singular Values is 4/√3, Gavish and Donoho, IEEE Trans Inform Theory (2014).
March 4:
- Lab 2 "Data Clinic"
March 9 and 11:
- Happy Spring Break!
March 16:
- Slides 6: Data integration by using the pesudoinverse
- Mathematics of the pseudoinverse:
March 18:
- "State of the Project" Presentations
March 23:
- Paper 16: Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation between DNA Replication and RNA Transcription, Alter and Golub, Proc Natl Acad Sci USA (2004).
Paper 17: Reconstructing the Pathways of a Cellular System from Genome-Scale Signals by Using Matrix and Tensor Computations, Alter and Golub, Proc Natl Acad Sci USA (2005).
Paper 18: Distinct Physiological States of Plasmodium falciparum in Malaria-Infected Patients, Daly et al., Nature (2007).
Paper 19: Using Pre-Existing Microarray Datasets to Increase Experimental Power: Application to Insulin Resistance, Daigle et al., PLoS One (2010).
March 25:
- Slides 7: From correlation to causal coordination by using the pesudoinverse
- Computation of the pseudoinverse:
Notebook 2: Pseudoinverse Projection of Measured Data
Mathematica Code: Notebook_2.nb
April 1:
- Slides 8: Comparative Generalized SVD (GSVD)
- Computation of the GSVD:
Notebook 3: GSVD of Synthetic Data
Mathematica Code: Notebook_3.nb
April 3:
- Paper 17: Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Datasets of Two Different Organisms, Alter et al., Proc Natl Acad Sci USA (2003).
Paper 18: Combining Transcriptional Datasets Using the Generalized Singular Value Decomposition, by Schreiber et al., BMC Bioinformatics (2008).
Paper 19: Exploring Metabolic Pathway Disruption in the Subchronic Phencyclidine Model of Schizophrenia with the Generalized Singular Value Decomposition, by Xiao et al., BMC Syst Biol (2011).
April 8:
- Paper 20: A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms, Ponnapalli et al., PLoS One (2011).
Paper 21: Multi-Tissue Analysis of Co-expression Networks by Higher-Order Generalized Singular Value Decomposition Identifies Functionally Coherent Transcriptional Modules, by Xiao et al., PLoS Genet (2014).
- Paper 22: Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival, Sankaranarayanan et al., PLoS One (2015).
Paper 23: TNF-Insulin Crosstalk at the Transcription Factor GATA6 is Revealed by a Model that Links Signaling and Transcriptomic Data Tensors, by Chitforoushzadeh et al., Sci Signal (2016).
April 10 and 15:
- In-Class Work on Lab 3:
Select two or more datasets, and explain how you might compare or integrate these data by using, e.g., pseudoinverse projection or GSVD. Explain also and the mathematical variables, and if possible also the mathematical operations, operations of your integrative or comparative model might mean biologically.
April 16, Tuesday, 10:00am–12:00pm, WEB 3780:
- Class Project "Data Clinic"
Happy Summer Break!
- DNA from xkcd
See you in Fall 2019 in BIOEN 6900-003: Data Science for Bioengineers