Note the style is not "I give you a specific project and tell you how to do it". Rather, please read "general styles of possible future projects" and browse some of the previous projects below. An ideal project will find interesting real-world data for which some notion of "chance" is involved, and then describe the data, either qualitatively or via some quantitative analysis. Other projects involve simulating math models by writing code -- in particular drawing graphics or devising algorithms to compute things. The point is to find some project relevant to your interests and expertize.
To be accepted, we need to agree on a project, over the first 2 weeks of the semester. There is a weekly meeting in which everyone says what they have done in the last week. The regular weekly meeting will be Friday 9.30 - 10.30 in room 443 Evans.
Students
Project
Description
Weijian (James) Han [Work-study]
Vishal Kalyanasundaram [independent study]
Comparing tech company valuations during the dot-com bubble and how to predict a boom and bust.
proposal
Jiangzhen (Jane) Yu [Volunteer]
Random Eulerian circuits.
Simulations related to
this open problem
TianTian Li [Volunteer]
Quantitative Investment Research Based on Merrill Lynch Investment Cycle
proposal
Jian Wang [Honors Thesis]
Relation between foreign stock markets and exchange rates
proposal
EuiSeok Kim [Honors Thesis]
Mathematical model for optimal cost-efficient installation of automatically operated
public transportation system
proposal
Students
Project
Description
Fayd Shelley (Summer 2006); Sunny Zhao (Fall 2008)
Coincidences in Wikipedia (RW)
Data appears in this
unfinished draft paper.
Dennis Moy (Fall 2006)
A regression model using common baseball statistics
to project offensive and defensive efficiency.
Undergraduate honors thesis.
Yanjiao Cheng, Jesse Friedman, Yu-Jay Huoh, Wayne Lee, Harrison Liu (Spring 2007)
Statistics of road networks
Data collection for Figure 1 of this paper.
URAP and VIGRE.
Tamar Lando (Spring 2008)
Efficient Networks and
Enumerations on Forests
Masters thesis. Part will appear as section xxx of xxx.
Julian Shun (Spring 2008)
Optimal spatial networks
Simulations, forming a substantial part of our joint paper.
Robert Huang (Spring 2008)
Exploratory data
analysis of amazon.com book review data.
VIGRE.
Eric Chao and Regina Wu (Spring 2009)
This and the next are continuations of the same project. URAP.
Timothy Wong (Spring 2009)
Exploratory Data Analysis of Amazon.com Book Reviews
Undergraduate honors thesis.
Amy Huang and Irvin Liu (Spring 2009)
References to chance in blogs (RW)
What type of things do "ordinary people" attribute to chance?
One way to study this is to search through blogs. URAP.
Amy Huang and Irvin Liu (Spring 2009)
The 1.4 trillion dollar project (RW).
A Google search on "1.4 trillion dollars" gets a surprisingly large number of hits,
which can be traced back to some smaller number of different appearances of
"1.4 trillion dollars" in some authoritative data. The project was to count this
"number of different appearances" for a variety of dollar amounts (2.8 trillion; 1.8 billion, etc) to see
whether they follow a particular "informationless" distribution. URAP.
Tung Phan (Spring 2009)
Benford's law. (RW)
Data collection, forming a substantial part of our short joint paper When Can One Test an Explanation?
Compare and Contrast Benford's Law and the Fuzzy CLT exhibiting a typical undergrad project.
Priscilla Ku and Janet Larwood (Spring 2009)
40,000 coin tosses yield ambiguous evidence for dynamical bias (RW)
Testing a prediction of Persi Diaconis et al that in coin-tossing there is a small bias -- maybe 1/100 - towards
the coin landing the same way as it started. URAP.
Alan Choi (Spring 2009)
Statistics of road networks
Data collection, forming a substantial part of our short joint paper
A Route-Length Efficiency Statistic for Road
Networks
.
Wei Zhou and Jonathan Ong (Spring 2009)
Empires and percolation .
Simulations and pictures, used to complement theory in
our joint paper
Empires and percolation: stochastic merging of adjacent regions.
Bowei Zheng (2008-2009)
Java simulations for a "parking process"
The process was studied analytically in this old paper.
Tung Phan (Fall 2009)
What can you predict about a team's performance next season? (RW)
Quantifies the regression effect for sports teams.
Karthik Ganesan [VIGRE] (Spring 2012)
Empirical Study on Route-Length Efficiency of Road Networks
Data collection for route-length efficiency of road networks. Graphics used in
this talk
Hyerim Hong [Independent study] (Spring 2012)
Perception on role of chance in different aspects of life
Via a survey
Bowen Huang [VIGRE] (Spring 2012)
City Growth Model Simulation
Here is a slightly complicated model for city growth
in which cities have positions, populations and spheres of influence.
It's not hard to simulate the process, but I want some pretty pictures of
the spheres of influence.
Willy Lai [VIGRE] (Spring 2012)
Fitting power-law distributions to data
Testing data for fit to power-law distributions. e.g. this
data
on family names.
Russell Mays [volunteer] (Spring 2012)
Road route networks linking 4 addresses
Take 4 street addresses, whose positions form roughly a square, of side length roughly
5 miles or 50 miles or 500 miles. Use e.g. Google maps to find the routes between each of the
6 pairs of addresses, and draw a map showing these 6 routes together. Mathematically there are about 45 topologically different possibilities
for the map; presumably some come up often and others rarely, but which? And does it vary with
distance (side-length of square)?
Max Moacanin [volunteer] (Spring 2012)
Lucky vs Unlucky teams
Assuming gambling odds give true probabilities,
one can classify a team as having been lucky or unlucky so far.
Do results of matches between lucky and unlucky teams fit the gambling odds?
Selene Xu [Independent study] (Spring 2012)
Study of Auction Theory in eBay Data
Collecting and studying data about auction prices.
Amy Zhang [honors thesis] (Spring 2012)
Pairs trading
A simulation study to explore possible relationship and
connection between profit and different variables associated with
stock selections in pairs trading.
Yiming Zhou [Independent study] (Spring 2012)
Spatial Poisson processes
Draft of possible Wikipedia article
Xiaoyu (Lily) Wang [Volunteer] (Summer 2012)
Design of simulation of efficient road networks
Continuing the theme of heuristic algorithms in this paper
to study models with junctions.
Jian Li [Volunteer] (Summer 2012)
Dynamic random Gabriel networks
Computer simulations and graphics.
Morgan Thompson [graduate volunteer] (Fall 2011 - Summer 2012)
Data on dust-to-dust models
Producing data used in Chapter 11 of
Draft write-up of 13 lectures.
Karthik Ganesan [Independent study] (Summer-Fall 2012)
math models of road networks
Graphics and simulation data for the "binary hierarchy" model; used in
this paper
Bowen Huang [Volunteer] (Summer-Fall 2012)
Simulations of a model for city growth
Graphics and simulation data
appear in
this paper.
Xiaoyu (Lily) Wang [Independent study] (Fall 2012)
Dynamic Gabriel graphs
The file of dynamic simulations of a network model is too large to show, but
here is a static snapshot.
Weijian (James) Han [work-study] (Fall 2012)
References to chance in micro-blogs
Examples/analysis posted here.
Weijian (James) Han [work-study] (Fall 2012)
Simulations of the Waves in long lines model
Brief write-up of model description,
simulation results and math conjectures.
Weijian (James) Han [work-study] (Fall 2012)
Distribution of Losses Due to Structural Fires
Analysis of data from Berkeley CA.
Weijian (James) Han [work-study] (Spring 2013)
Simulation of a model of Random Particle Motion
related to this model.
Description on this page
(applet doesn't work on Macs).
Weijian (James) Han [work-study] (Spring 2013)
Simulation of multilevel Dyson's Brownian motion as studied by
Mykhaylo Shkolnikov.
Description on this page
(applet doesn't work on Macs).
Max Moacanin [volunteer] (Spring 2013)
Simulation data
from the iPod process where favorites are played.
Wen Liang [senior thesis] (Spring 2013)
Life Expectancy Index model and Risk Management
Understanding what J.P.Morgan's LifeMetrics does.
Bonghyun Kim [Independent study] (Spring 2013)
Event Dispersal Simulation
Simulating the dispersal of Facebook Events.
Misha Jhaveri [Independent study] (Spring 2013)
Investigating the game of Hangman
Progress report
MoonSoo Choi [Independent study] (Spring 2013)
Statistical Analysis of Nuel Tournaments.
These are N-person duels. Here is the
Cal Day poster.
Seungjun Lee and Mingu Jo [Independent study] (Spring 2013)
Simulation of Interactions on Campus
Data and modeling of the chance of meeting different students while walking on campus.
Note a nice example of a poster for Cal Day.
Wenyu Zhang [Independent study] (Spring 2013)
Trends in Iphone 5 Sales on Ebay
Collection and analysis of data.
Yu Haihan (Mark) [Independent study] (Spring 2013)
Expanding Civilizations and the Fermi Paradox
Simulation of a model.
Weijian (James) Han [work-study] (Fall 2013)
Simulating a greedy tree
Part of ongoing theory research project
Yee Tung (Alice) Man [Independent study] (Fall 2013)
Spatial network simulation
Java simulations.
Yuan He [Independent study] (Fall 2013)
Predicting market value of soccer players
How well can their market value be predicted
from available quantitative data?
Chan Ik Jang and Kody Law [Independent study] (Fall 2013)
The Relationship between Intellectual Property
Infringement and Economic Indicators.
Conventional wisdom meets empirical data.
Max Moacanin [volunteer] (Fall 2013)
Simulation data for the iPod process
Working with Dan Lanoue.
Zhijun (Steven) Yang [volunteer] (Fall 2013)
Simulation of Brownian motion
Zhijun (Steven) Yang [volunteer] (Fall 2013)
Computational analysis in risk and profit problem
Zhijun (Steven) Yang [volunteer] (Fall 2013)
Geometric Brownian Motion Model in Financial Market
Zhijun (Steven) Yang [volunteer] (Fall 2013)
Escaping Time and Particle Collision Modelling and Simulation
Yijia Mao [Independent study] (Fall 2013)
Risk of alcohol and caffeine
Report on the scientific literature.
Weijian (James) Han [work-study] (Spring 2014)
Simulations of the Compulsive Gambler process.
Jane Wenjin Liang [Independent study] (Spring 2014)
Generic vs Brand Name Food Packaging.
Teeranan (Ben) Pokaprakarn [Volunteer] (Spring 2014)
Anti-Streaky behavior in Currency Markets.
Sida Ye [Independent study] (Spring 2014)
Sentiment analysis for iPad 2 and linear modeling.
Cal Day poster
Frances Chen [Volunteer] (Summer 2014)
Spatial networks.
Continuing the theme of heuristic algorithms in this paper
to study models with junctions.
Yijia Mao [Volunteer] (Summer 2014)
Credit Risks in Daily Lives and Bond Rating Analysis.
Brief literature surveys.
Weijian (James) Han [Volunteer] (Summer 2014)
Numerical calculations related to
this project.
Yongtae Lee [Volunteer].
Correlation between Nationalism and Social Welfare.
Proposal.
Tiffany Chang [Volunteer].
Selecting Energy Efficiency Indicators for Sustainable Development using Regression Analysis.
Proposal.