I started participate mathematical contest in modeling when I was a freshman and I participated four times.
It was the most frustrating, exhausting, challenging, exciting, and yet most rewording thing I have ever done as an undergraduate.
It really brings me a lot: honor, skill, method, and most important--happiness.
Mathematical Theory
In the CUMCM/2010 and ICM/2011, I was in charge of modeling. For this task, I need to figure out numerical recipes and numerical methods that can be well applied to the problems, and can be implemented on the computer
Generally speaking, no existing mathematical method can directly resolve the problem. We have to develop it, so as to match the specific of our problem.
As a result, my interest in mathematical theories and derivation of formulas was sparked.
Some works I have done:
To Win the Future:
Electric Vehicles on the Way
- The Honorable mention in the ICM2011
- Key words: Evaluation model; Bionics-based model; Multi-objective optimal
- Brief Introduction: We firstly establish an evaluation framework to assess the multiple impacts
caused by the prevalence of electric vehicles. And
a bionics-based model simulating the current auto industry is developed, predicting the significance of governmental funds invested in automobile research
institutes. Then we extend the evaluation framework to determine the amount
and type of road vehicles, which are featured by multiple benefits. Finally, further plans for reshaping the current energy structure are formulated based on
a multiobjective optimization model.
- full pdf file and judge's comment
Predict serial crime using geographic profiling
- Key words:Markovian Model
- Brief Introduction: Based on the features of serial crime, we summerize the process of predicting crime place as three Markov state transition, they are: determining average crime distance, determining center point, predicting next crime place. Finally, we use Bayes' formula to figure out crime place's probability density distribution on the map.
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Creating Food Systems: Re-Balancing Human-Influenced Ecosystems
- Key words: Differential Equation
- Brief Introduction: After analysing the current state of this eco-system, we find the best way to solve the environment problem and maintain income is marine polyculture.Firstly, we clarify the relationship of several main marine organism in an area in the Hilippines. Based on the food chain, we establish differential equations. Secondly, we stimulate this eco-system and adjust all organisms' starting quantity until we get a balance environment. Finally, we evaluate the economic and environment effects of polyculture.
The Postman Route Planning & Unmanned Spacecraft's Path Planning
- Key words: graph theory; Minimize Hamilton circuit; Minimize path; path planning
- Brief Introduction: We simplify the problem into a graphic problem. We establish Optimization model and use Lingo to figure out the best route.
Camera calibration
- Key words: Affine Transformation
- Brief Introduction: We use rotation matrix to describe the transition between the two three-dimension. In the last, we use different method to verify this model's robustness.
some other theory I have ever used:
- Queuing Theory--Ophthalmology Department's bed planning
- Comprehensive Assessment Model--Water Quality Evaluation of Yangtze river
Shanghai 2010 Expo's Effects on Economy
- Economic Models--Great Pacific Garbage Patch
Shanghai 2010 Expo's Effects on Economy
- Numerical Analysis--Murray's Dam Breaking Model
- Monte Carlo--Ophthalmology Department's bed planning
If you want full paper of above works, please send me email.
Writing Skill
When I participated in University's Mathematical Modeling Contest (2009&2010), I was responsible for writing paper. I like this job because the process of designing the construct of paper and describing method just like art. To do this, we need passion, logic and sense of aesthetic.
I have two strengths:
- I have a perfect command of LaTeX, which is a professional processing tool.
All of our papers of modeling were written in LaTeX and I was in charge of designing different templates.
By the way, I used Vim as my editor. I love it!
My Resume of Beamer Version also was written in LaTeX!
- I am good at designing beautiful construct of paper and them were easy to comprehend.
edit paper with latex
Programming Skill
In the modeling contest, the programming task can be very huge and I was involved in programming every time. I acquired good ability through my modeling experience, especially matlab and C language.
When I did program work, I learned we should balance precision and efficiency. For example, if you have a most precise model while its cost can be very huge, we cannot get a feasible solution in a limited time. So we have to make a concession in our precision and win more efficiency.
Something interesting: using Graphviz to draw graph (undigraph or digraph) is great! There are some samples I drwan:
Method of Recognizing things
The most precious gift Mathematical Modeling given me was the way we think and recognize this world.
Firstly, my thoughts in some things became more profound. I can use mathematics as tool to analyse and solve the problems in my daily life which I cannot figure out in the past.
Secondly, no matter what we are study or consider, ask ourselves only what are the facts, and what is truth behind the facts. Never be convinced by what we wish to believe, or by what we think could have beneficent social effects if we are believed. Look only and seriously, what are the facts.(paraphrase Russell's words)
Thirdly, I have learned to connect our theory to reality. For example, when I considered the Prediction of Criminality, I wanted to use Markovian model to describe guilty places' randomness. But I had a problem, from normal Markovian model's strict assumptions. So I develop a special Markovian model to match the reality. The end is we got pretty satisfactory results.
Finally, I have understood the words said by Einstein: beauty lies in simplicity. A good model which grasps the nature and core of problem does not need to be so complicated, it is usually simple, understandable, and grace. If a model is complicated or confusing, it is possible that it has no insight about what is questioned. And tangle some details which are not so important.
