Contents:
Research interests
I am interested in a wide range of topics I loosely call the study of Complex Systems. It is hard to find a rigorous definition of the term, and I’d like to let it be a project in its own right. A “phenomenology” of candidate topics may be the best way to go about doing this and that is what I’ve been doing.
Topics I have worked on in the past include:
- Theoretical Neuroscience: given a modest empirical model of the interactions between neurons and the connectivity patterns in neural tissues, one can study neural activity pattern formation and signal propagation in different areas of the cortex. In particular, the effects of the architecture of the visual cortex on visual perception has been a popular research area in part due to the fact that the geometric nature of the stimuli makes it possible for a wide variety of carefully chosen structures to be presented to human subjects, and the responses can be equally detailed an illuminating. I studied the emergence of certain visual hallucinations from simple mathematical models of neural dynamics
- Protein design/folding: Proteins are the building blocks of life: long chains of Amino-acids that fold onto themselves as a result of the electromagnetic interactions between pairs of amino-acids, or between amino acids and the water molecules in the environment. The ultimate spatial form of the folded bundle as well as its structural stability are crucial to its biochemical functionality, and one can study both by understanding the energy landscape of the system. However, due to the extremely large size of the state space, one often uses Monte Carlo methods and in special cases direct enumeration methods to study the mapping between the initial sequence of the aminoacids and the equilibrium state of the protein. A practical application of the theory is protein design, namely the problem of finding a sequence of Amino-acids that if assembled and left to fold, ends up in an equilibrium state of the desired shape and hence function. This may be exploited to design drugs for extremely specialized purposes, i.e, drugs that target specific proteins on cells and thus exact specific behavior from the cell. I was part of a project to investigate geometrical properties of highly stable proteins.
- Low-dimensional models of turbulent flows : Currently as my PhD thesis, I’m studying methods of reducing the dynamics of infinite-dimensional dynamical systems to that of approximate low-dimensional systems.
Reduced order Rayleigh-Benard convection
The question is how much of the topology of the phase space can still be reproduced after drastic truncations of the state space, and where is the balance in the trade-off between loyalty to the actual system and analytical tractability of the reduced system. My model problem is Heat transport in a fluid-saturated porous medium.
Courses
SI 618: Exploratory Data Analysis
Aims to help students get started with their own data acquisition and analysis. Data analysis is crucial to evaluating and designing solutions and applications as well as to understanding information needs and use. Students in this course (who will have just completed SI 601: “Data Manipulation”) will learn techniques of exploratory data analysis using scripting, text parsing, structured query language, regular expressions, graphing, and clustering methods to explore data. Students will be able to make sense of and see patterns in otherwise intractable quantities of data. (From The University of Michigan School of Information)
Here is my Course Website for SI 618, where I have posted my assignments and notes.