1. Determining the Flow of Matter Around a Black Hole.
   In our program we solve the problem of how matter flows into a black hole from a companion star in a double star system. e account for the actual forces on the matter such as the gravity due to the black hole and the companion star and the centrifugal and Coridis forces due to the rotation of the system. We use Newton's Method to find the position between the star and the black hole where the forces are in balance. We then folow the motion of matter fom this point using both Euler's Method and a fourth order Runge-Kutta Method. We find that the trajectories cross each other so a drag force is needed to allow the matter to spiral into the black hole.
2. Teaching Computers to Understand:Voice Recognition and Neural Networks
   A common complaint of modern computer interfaces is that they lack real understanding of humans: computers cannot understand speech or gesture. Accordingly, speech recognition work is one of the most exciting areas of modern computer science research. It is also one of the most difficult. The sheer variety and complexity of a word makes recognizing similar words very difficult.

   Last year, I approached a very different pattern recognition problem: recognizing simple shapes. For this task, I used a neural network. A neural network is a collection of layers of neurons, simulating the human brain structure. Each layer of neurons is connected to the next, but each connection has a certain weight. Every time the neural network processes some input, it adjusts these weights to make the output closer to a given desired value for the output.

   This year, I decided to apply the same technique to the different problem of speech recognition. No one had ever used Neural networks as the core of a speech recognizer before, but I thought that they were up to the task.

   I designed and constructed a voice recognition system in C++, using a flexible neural network and several mathematical techniques to abstract the sounds. Then, I tested the system with several short, monosyllable words. First, the network would train using two samples of each word, and then I tested it using those same two samples. Within these training sets, the recognizer worked quite well. The recognizer achieve moderate results with other samples of the words. With larger vocabularies, the recognizer was only able to identify about half the of words. However, considering the great variation in the waveforms of words, I think that this system can be deemed a success.

3. Graph Theory:Locations and the Global Positioning System
   Our problem is: can a vehicle efficiently calculate the shortest distance between two points using Global Positioning Systems (GPS)? The project that we finally decided upon consists of finding the shortest distance from one point to another in a matrix such as a large city. This city will consist of numerous nodes numbering in the thousands, and our program will calculate the shortest distance between two nodes using a modified version of Djikstra's algorithm written in FORTRAN 90.

   The practical applications of this program will involve the future of America and the transportation system. Programs such as the one we plan to write will guide cars to their destinations using (GPS) without the driver having to be aware of outside influences (outside the panels of the vehicle). GPS will tell the car where it is, and our program will tell the car how to get to its destination. Our idea is that this will create less vehicular traffic, and it will better the environment by decreasing the wasteful driving that most people do. By reducing the excess driving, people will also find that driving will become more cost-effective for their purposes.

   The programs we have used during our project are Netscape 2.0 (a World Wide Web browser), Spyglass Transform and Plot (a Macintosh graphics package), and NCSA Telnet 2.6. Along with the programs we used, we also had help from a Power Macintosh 5300, a Sun 4c workstation at Colorado State University (CSU), and a CRAY Y-MP supercomputer at the National Center for Atmospheric Research (NCAR).

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