Research Statement v1.0 - thank Victor R. Jose for proofreading

Kuan-ming Lin
Feb. 7, 2005. All Rights Reserved. 
  
0. Challenges in Computer Science: Order, Chaos, and Complexity

  Thanks to the explosive progress in computer science, 
  computation now has been considered as an integrated
  part of scientific methods. However, when applied to other fields
  like social science and biology, the computational model has been
  challenged for its mechanical, inflexible nature. For example, 
  whereas computers can solve chess games which are
  beyond human intelligence, they are still unable to simulate the
  subtle feelings when one listens to a short melody. Nevertheless,
  scientists have recently developed some mathematical and physical
  concepts, e.g. chaos and complexity theories, to explain 
  the origin of "actual intelligence." Therefore, it is time for 
  computer scientists to combine these fruitful results to tackle 
  problems which were considered unsolvable. In my view, the concepts of 
  order, chaos, and complexity can help me to develop new techniques 
  for solving the following problems.

1. The "Order" Category: Efficient and Economic Algorithms

  Although computer scientists have invented numerous algorithms 
  to solve a considerable class of practical problems, new challenges 
  continue to arise. For example, nowadays we have databases 
  distributed in thousands of servers storing billions of records, 
  thus inducing a need for new searching and indexing algorithms. 
  Biogeometry is another example. Since it has only been recently 
  that computational geometry had played an important role in solving 
  molecular biological problems, more algorithm experts are needed to 
  collaborate with fundamental biology researchers and invent 
  efficient algorithms to accelerate the understanding of biology. 
  These challenges, however, are still in the scope of "order" or 
  classical science since they are eventually (from an optimistic aspect) 
  solvable by the clever use of traditional algorithm skills.

2. The "Chaos" Category: Non-determinism and PRNG
    
  As known in the computational complexity area, there are 
  problems which can be easily solved via exponential-sized 
  computation trees, called the NP problems. Also, there are problems 
  which can be easily solved through a perfect random number generator (RNG), 
  called the RP (or more strictly, ZPP) problems. Yet the existence of 
  these computational models is still in question. Recently, from 
  chaos theory, mathematicians have shown numerous ways to generate 
  nearly unpredictable shapes and sequences with simple recursive 
  functions. Therefore, I believe that these chaos-generating functions 
  can be a powerful tool for computer scientists to gain insights 
  in designing pseudo-random number generators (PRNG), one-way 
  hash functions, integer factorizers, or even nondeterministic 
  Turing machines.

3. The "Complexity" Category: Learning

  The elaborate structure of live organisms, such as cells, the 
  human brain, economic entities, and the Internet, is currently 
  considered to be too complex to analyze. However, from complexity
  science perspective, they all share a common feature, self-organization, 
  which is still not well-defined, and thus computational simulations on 
  studying it remain coarse. Though it is unlikely that any successful model 
  will be invented in the near future, the complexity science at present 
  can help in current research fields. For example, evolution algorithms, 
  though inefficient for typical optimization problems, may be used 
  to generate infinite patterns to improve the quality of unsupervised 
  learning models. 

4. My research goal this year
 
  My ideal career goal is to engage in any of these interesting
  problems. However, being a new Ph.D. student, I am aware of my 
  insufficient knowledge in any of these subfields; as a result, my
  short-term goal for this year lies in solidifying my background 
  knowledge as well as identifying suitable research teams 
  and partners. To be more concrete, this year I want to continue my 
  coursework as well as to target on some small but important problems 
  for my initiation project.