A little about me
I am an undergraduate at the Massachusetts Institute of Technology (class of 2011) studying mathematics and computer science.
Academic and research interests
I am broadly interested in applied mathematics, with a strong interest in theory as well as applications. Here are some of my current academic interests.
- complex systems and their computational properties
- control theory, adaptive systems
- machine learning and computational learning theory, artificial intelligence
- optimization, mathematical programming
- machine vision, image/sound processing, signal processing in general
- probabilistic systems and stochastic processes, probability theory
- computational science, simulation and modeling of physical systems
- computer graphics and animation
Projects and Experience
A list of some projects/activities of various complexity that I've done in the past or am currently working on, either for a class or independently.
2009
Efficient Optimal Control of Fluids for Animation (Fall 2009)
Physically based simulations have become a vital part of realistic computer graphics and animation. However, unlike simulations for scientific applications, where the goal is to observe what happes for different parameters, the goal in animation is to create a certain desired dynamics. Because the physical systems in question are often so complex, it is difficult to predict and control these dynamics. A common approach is to apply forces to push the system toward desired states at different points in time -- such methods fall under the category of optimal control. Existing work in this area has highlighted the tradeoff between efficiency and accuracy/believability of the simulation. I am working on extending an existing 3-D fluid simulator and implementing novel optimal control methods for efficient and believable optimal control of fluid animations.
Stochastic models for bidirectional transport in biological networks (Summer 2009)
Cells require complex internal networks to manage intracellular transport. So far, the mechanisms that make possible bi-directional transport while avoiding traffic jams are poorly understood. We believe the dynamics of the network itself might be the key to enabling well-behaved bi-directional transport. I am currently working in the Statistical Physics of Nonequilibrium and Disordered Systems group in the Department of Theoretical Physics at Saarland University in Saarbrücken, Germany, part of the graduate school in Structure Formation and Transport in Complex Systems. In particular, I am simulating the dynamics and self organization of a network of microtubules in axons, a large part of which involves computational statistical mechanics. Once a good model of the network structure formation and dynamics exists, we can plug in existing models that simulate transport on the network. We hope this will shed light on how and why traffic jams form, and ultimately help identify the origin of certain neurodegenerative diseases.
Theoretical and computational neuroscience (Spring 2009)
Studied various topics in theoretical and computational neuroscience in MIT's class 8.594/9.641, a graduate level class in the theory of neural networks and computation. Topics included convolutional neural networks and models of the visual system, dynamics and computational properties of nonlinear recurrent networks, supervised and unsupervised learning (PCA, NMF, ICA, CHL, VQ, backpropagation, reinforcement learning), and associative memory models. Work included extensive coding of simulations in MATLAB, in addition to theoretical analysis.
2008
Fractor - (Summer 2008 - Present)
"Fractor is a simple, groundbreaking web application that matches news stories with opportunities for social activism and community service."(www.fractor.org). Currently developing a novel recommendation system to provide newsreaders with personalized recommendations for taking immediate, relevant charitable actions in response to unfolding news stories.
Probabilistic modeling of signal onset detection (Summer 2008 - Present)
Worked at the Consciousness and Computation Lab at Columbia University. Developed theoretical models and simulations of perception related signal detection, using principles of statistical signal detection theory, random processes, and signal processing.
Solving Laplace's equation using repeated-averaging diffusion (Spring 2008)
Solving Laplace's equation using diffusion (special project for 8.022: Electricity and Magnetism with Theory): Check out these videos, as well as the description. 1 | 2 | 3. This is a better quality (but quite large) video: difflaplace4.avi
Battlecode 2008 (Winter 2008)
Participated in MIT's Battlecode (6.370) competition
2007
M3 Challenge 2007 - Stochastic gradient ascent for portfolio optimization (Spring 2007)
Moody's Mega Math Challenge is a mathematical modeling competition for high school students. Teams of up to five students have 14 hours to read a problem, work out a solution, and write a paper about it. In 2007, the challenge was to come up with a method for compiling a stock portfolio given a list of stocks. I developed a stochastic gradient ascent algorithm to choose an optimal stock portfolio by maximizing an objective based on expected risk and payoff.
2006
3D Computer Graphics Engine (Spring 2006)
In a computer graphics class at Stuyvesant High School, I developed a 3D Computer graphics and animation system from the ground up. I implemented line drawing algorithms, curve and surface generation, lighting, shading, sphere ray-tracing, and a stack-based animation language. I had a lot of fun doing some neat shape modeling and animation, and probably spent a lot more time tweaking animation scripts than it would have taken to write a GUI.
TopicWeb (Spring 2006 - Winter 2007)
TopicWeb - a system for document similarity measurement and categorization that improves upon dot product similarity in the Vector Space Model. You can find the original paper here
I entered the project in the 2007
Intel Science Talent Search - an annual research competition for high school students - and was a semifinalist.
Classes
(
bold denotes graduate level classes)
Fall 2009 (tentative) (48 units)
6.046 - Design & Analysis of Algorithms (12 units)
6.867 - Machine Learning (12 units)
18.950 - Differential Geometry (12 units)
6.207J - Networks (12 units)
Spring 2009 (48 units)
6.006 - Introduction to Algorithms (12 units)
6.034 - Artificial Intelligence (12 units)
8.594/9.641 - Introduction to Neural Networks (12 units)
24.263 - The Nature of Creativity (12 units)
Fall 2008 (51 units)
6.255 - Optimization Methods (12 units)
6.01 - Introduction to EECS I (12 units)
18.100C - Real Analysis (15 units)
21L.421 - Comedy (12 units)
Spring 2008 (48 units)
6.041 - Probabilistic Systems Analysis (12 units)
18.086 - Computational Science and Engineering II (Listener)
18.03 - Differential Equations (12 units)
8.022 - Electricity and Magnetism with Theory (12 units)
24.09 - Minds and Machines (12 units)
IAP 2008 (6 units)
6.187 - BattleCode (6 units)
Fall 2007 (54 units)
18.06 - Linear Algebra (12 units)
8.012 - Classical Mechanics with Theory (12 units)
3.091 - Introduction to Solid State Chemistry (12 units)
24.118 - Paradox and Infinity (12 units)
12.A35 - Mother Nature's Mean Streak (6 units)
8.01 - Classical Mechanics (Advanced Placement credit)
18.01 - Single variable calculus (Advanced Placement credit)
18.02 - Multivariable Calculus (Advanced Standing Exam credit)
Awards and Recognition
DAAD RISE Scholar, Summer 2009
Intel Science Talent Search 2007 Semifinalist
Talks/Teaching
ESP teaching - Gave talks on various topics to students in grades 7-12 as part of MIT's Educational Studies Program.
Splash 2007:
Document Similarity Measurement and Clustering (1 hour): Vector space model for document similarity measurement, term weighting schemes, k-means and hierarchical clustering.
Dynamical Systems (2 hours): 1D dynamics and chaos, dynamics in 2D and higher, theory of discrete and continuous eigenproblems, Markov processes, linear homogeneous systems of ODEs.
Spark 2008:
Discrete and Continuous Eigenproblems (3 hours): Linear opeartors, eigenvectors, eigenvalues, Fibonacci numbers and the golden ratio, systems of linear autonomous ODEs, function spaces and eigenfunctions, differential operators, 1D Poisson eqn., 1D Heat eqn.
Hobbies and other activities
Art
I like drawing and painting and any type of visual art, from classical portraits to graffiti and abstract t-shirt design. I especially enjoy the fusion of art with mathematical or scientific concepts, both because art can be very mathematical in its properties and because mathematics is rich with constructs, analogies, and ways of thinking that allow for a unique form of expression.
I also enjoy philosophy, especially questions about mind and consciousness, and the nature of creativity.
Gymnastics
I have been doing gymnastics since sophomore year of high school. I was captain of my high school gymnastics team, and was a member of the MIT Men's Gymnastics Team from 2007 to 2008.
