The following are my extremely old ideas, which the then-young-sophomore called “Research”. Looking back, I find those ideas very funny, silly, and trivial but still, they’re all my kids and I’m proud of them. Since I’m cleaning my website, including the Research page, I’m gonna bring the kids over here so that they won’t be forgotten by their damn father.
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* Generalization of Poisson distribution and its application in Epidemiology (K.Tran, L. Meyers): Many infectious diseases spread through populations via the networks formed by physical contacts among individuals, which are called social networks. Understanding those social networks helps us predict the probability and demographic distribution of an outbreak. Determining the degree distribution is thus a study of interest, where the degree of a person in a community is the number of his/her contacts. Data collected in Vancouver, where there were four cases of SARS detected in 2003, suggested that the degree distribution of an urban center may resemble a Poisson distribution but with higher probability of super-spreaders (a super-spreader is a person who has a high degree of contacts). Hence, we are interested in generalizing the Poisson distribution and computing the corresponding probability mass function that best approximates the data.
(Social Networks is still a hot research topic but definitely, my contribution is infinitesimal, if not 0.)
* New Action Model for the Robots: a failed project. Basically, in standard, each movement action (in a very short time) of the robot is modeled by 3 variables: turn (angle), travel (distance), and turn again (angle). Since there’re always errors in measurements (sensor, lazer, etc.), you model these as 3 Gaussian variables. I proposed a model that uses only 2 Gaussian variables, which are the (tangential) velocity and the turning rate (angular velocity). Such an “improvement” would tremendously reduces the computation time. Of course, in the proposal, I also showed how to derive the 2 variables from the sensor readings (in Computer Science world, such a mathematical derivation is considered so trivial). Indeed, Prof. Kuipers was also very excited with this idea. However, the testing demonstrated that my model was terrible. It turned out that even in a very short time, the robot’s motion is not necessarily circular.
Note that the motion of the robot is controlled by the motor (velocity) and the turning of the wheels/legs (turning rate). If the parameters are kept the same for 1 second, the robot will travel on a circular arc during that second. The problem is that those parameters change continuously.
(In the picture above are Sony Aibos, the robot dogs that I worked on.)
* The Laptop Hanger: an invention to facilitate my laziness. You stick the frame to the wall, you place your laptop on this frame and then you can comfortably use the laptop while laying down on bed. I made it with my own hands. This product would look much nicer if I had wooden furniture manufacturers in Vietnam make it. There are several technical problems in this paper. I resolved all of those as well as made some improvements; however, I haven’t rewritten the paper yet (so it’s interesting if you can figure out yourself).
* The Hash Tree: during my first semester in college, I invented an efficient data structure for the dictionary problem and I called it a Hash Tree. I was crazy about this idea (jumped off the chair) and excitedly thought about a cool publication. I presented this idea to Dr. Lin, my algorithms & data structures course instructor, and he (a compiler expert) found it cool too. He really made me hope. However, I was still a kid who re-invented the wheel (I figured that out after talking to Dr. Ramachandran). The data structure is classical (in some sense, it’s trivial) and in liturature, it’s called a Radix Tree.
* On Viète Theorem: An Interesting Application. In this paper, I present an interesting application of Viète theorem, a fundalmetal theorem about the sum and product of 2 roots of a quadratic equation, in Number Theory. It was first written in Vietnamese, when I was still in high school, and was translated into English 2 years later.
* Some Web Development Ideas: in my first year, I proposed these web development ideas to the Departmental Honors Software Development Group (the first Turing Scholars founded it), but no member found them cool (stupid kids, I still find them cool
), so no real project has been launched.