Previous Semesters

Winter 2020

MATH/BIOINF-547: Mathematics of Data

Syllabus (PDF)

Credits: 3

Instructor: Prof. Indika Rajapakse

This course is open to graduate students and upper-level undergraduates in applied mathematics, bioinformatics, statistics, and engineering, who are interested in learning from data. Students with other backgrounds such as life sciences are also welcome, provided they have maturity in mathematics. The mathematical content in this course will be linear algebra, multilinear algebra, dynamical systems, and information theory. This content is required to understand some common algorithms in data science. I will start with a very basic introduction to data representation as vectors, matrices, and tensors. Then I will teach geometric methods for dimension reduction, also known as manifold learning (e.g. diffusion maps, t-distributed stochastic neighbor embedding (t-SNE), etc.), and topological data reduction (introduction to computational homology groups, etc.). I will bring an application-based approach to spectral graph theory, addressing the combinatorial meaning of eigenvalues and eigenvectors of their associated graph matrices and extensions to hypergraphs via tensors [1, 2]. I will also provide an introduction to the application of dynamical systems theory to data including dynamic mode decomposition [3, 4]. Real data examples will be given where possible and I will work with you write code implementing these algorithms to solve these problems. The methods discussed in this class are shown primarily for biological data, but are useful in handling data across many fields. A course features several gust lectures from industry and government.

Homework and Projects: We will have homework assignments every two weeks, mini-projects, and a final project in lieu of a final exam.

Fall 2019

MATH/BIOINF-540: Mathematics of Biological Networks

Syllabus (PDF)

Credits: 3

Category: Advanced Bioinformatics and Computational Biology

Instructor: Prof. Indika Rajapakse

Description: Data-guided modeling, analysis, and visualization of networks is critical for understanding biological processes. With appropriate methods, we can explore answers to many questions including:

  • How do cells respond to internal and external stimuli, and how can we reprogram them?

  • How do cellular proteins interact with one another?

  • How do cellular metabolic processes interconnect to produce energy and make new substances?

  • How do cell and tissue functions emerge from dynamical forces within (genome) and between cells?

This course explores methods and principles for constructing and studying the structure and function of biological networks using examples from real datasets. We will begin with a discussion of some general properties of networks. I will introduce some basics in linear algebra, which provides a natural language for describing and analyzing networks.

Some topics that I anticipate covering in this course:

  • Review of linear algebra and MATLAB

  • Overview of genomics technologies and associated data

  • Spectral graph theory: Eigenvalues and eigenvectors of matrices associated with graphs, applications

  • Many examples of graphs and their Laplacians; Fiedler number and Fiedler vector

  • Network inference, dynamics and Controllability of networks

  • Dynamic Mode Decomposition (DMD), Tensor Factorizations

  • Mathematics of emergence

Winter 2019

MATH/BIOINF-547: Mathematics of Data

Syllabus (PDF)

Credits: 3

Category: Advanced Bioinformatics and Computational Biology

Instructor: Prof. Indika Rajapakse

This class is motivated by my own experience with data and mathematics, and also inspired by Dr. Steve Smale’s work. Over the past few years, I have worked with Dr. Smale and with my funding institute DARPA on many problems that have required knowledge at the interface of mathematics and data. The new DARPA initiative on Artificial Intelligence and the Lifelong Learning Machines (L2M) program within it, exemplify types of work at this interface. My own lab has a dual approach of generating time series data in-house and using mathematics to identify patterns in data and determine major unknowns. The methods discussed in this class reflect our approaches and those that are useful in handling data across many fields. Guest lecturers from industry and academia will also participate.

Fall 2018

MATH/BIOINF-540: Mathematics of Biological Networks

Syllabus (PDF)

Credits: 3

Category: Advanced Bioinformatics and Computational Biology

Instructor: Prof. Indika Rajapakse

Offered every Fall term.

This course addresses methods and principles involved in constructing and studying the structure and function of biological networks using examples from real datasets. The course is structured so that any necessary background will be introduced as needed. A comprehensive website containing all reading materials and class notes will be maintained throughout the term.

Winter 2018

BIOINF-547: Probabilistic Modeling in Bioinformatics

Credits: 3

Category: Advanced Bioinformatics and Computational Biology

Instructor: Prof. Indika Rajapakse and Prof. Dan Burns

This course will review some classical problems in DNA sequence analysis, problems such as multiple sequence alignment, protein families and parsing the linear structure of protein coding gene sequences, and then proceed to more recent epigenetic and structural features of DNA. We will discuss how recent mathematical methods used to describe protein folding can be applied to understanding chromatin dynamics. This course will furthermore detail quantitative and experimental techniques used to define the multi-dimensional genome, and how to integrate information from multiple methodologies into a framework for understanding genome dynamics. These principles can be applied to the analysis of high-dimensional biological data.

BIOINF-520: Computational Systems Biology in Physiology

Credits: 3

Category: Elective

This course is an introduction to dynamic modeling in physiology for both experimental and theoretical inclined students. We use selected physiological systems to introduce concepts in computational systems biology. This is done through the use of increasingly more complex cellular functions modeled with scientific software.