Aileen Ang 
The Algorithmic Manipulation of MIDI Files Through Perl 

 Sarah E. Auer
Using Environmental Data and Computer Software to Teach Statistical Concepts 

Stacey Benson
The effect of the drag force on model rocket flight 

Caleb Crane
Beowulf Clusters 

Brendan Hogan
The Effect of Water Depth and Trim Angle on Efficiency in Marathon Racing Canoes. 

Tim Singleton
Operating Systems 

Allen Zoracki
An Overview of the Steiner Problem 
 

     Since 1982, Musical Instrument Digital Interface (MIDI) has been a standard for communication and storage between electronic musical instruments.  MIDI is stored information that can take and interpreted though a medium, which allows for sound output.  This differs from most music files that are saved in wave formats in which “real sound,” or audio such as voices can be heard.  Most modern computers can interpret the sequence of sound events in a MIDI file and play back the music. 
     Many graphical composition packages have been developed using MIDI. They provide a broad range of manipulation tools.  Often, so many of these make it difficult to find any particular transformation in the mix. Approaching the problem from the other direction, I have designed a series
of seven simple, algorithmic music transformations in Perl, which support simple MIDI composition.  The transformations are interfaced through the World Wide Web, permitting users to manipulate MIDI files through their Web browser.  The transformations include transposing, offset, ostinato,
mirroring, adding major and minor chords, changing the instrument, and joining two files.  The MIDI files can then be played or used as the basis for additional composition. 
     Using a Perl (Practical Extraction Report Language) package, MIDI::Simple,  and learning the structure of the MIDI file used by the package, some of the transformations, such as transposition, offset, mirroring  were created by manipulating a midi file to change the value of a note or duration. Other manipulations such as changing the instrument, ostinato (taking a sequence of notes and repeating them several times, usually use as a base to a music piece), and adding chords requires
notes or information to be added to the structure with some changes to the properties of the new notes. 
     In this project I have combined concepts that are being taught in both the Computer Science and Music curriculums.  By using simple algorithms in programs to transform a musical idea, variations of the musical idea can be expanded.  As composers have done through out history, these variations can be used to expand and create compositions. 

     As an independent project for the spring semester I choose to explore how Fathom, a statistic software program could be used to teach statistical concepts within the context of a high school statistics course. In addition, the data used are focused on environmental issues. My intention for doing this project rather than taking a traditional math course within the department was driven by a desire to incorporate an interest in environmental education, a minor in education, and a future career as a high school math teacher into the final requirements for my mathematics major. I felt that such a project would be the most beneficial and educational approach to take as a way of enhancing my knowledge in the field that I am choosing to pursue. 
     The project has involved creating a series of activities to be used to guide students through various components of the software program while at the same time introducing them to statistical concepts. Information regarding topics that would be appropriate to cover at the high school level
was obtained from the curriculum of the Advanced Placement Statistics course provided by the College Board and the following textbook: Moore, David S. The Basic Practice of Statistics. W.H. Freeman and Company: New York, 1995. 
     Since Fathom cannot be utilized to aid in the instruction of every statistical concept within a curriculum, I chose topics where I felt Fathom could most effectively be used as an instructional tool. The first group of activities leads students through an exploration of bivariate data. This includes concepts such as analyzing patterns in scatterplots, linearity, least squares regression line, residual plots, outliers, influential points, correlation and transformation. The second section focuses on statistical inference using confidence intervals and tests of significance. 
     My presentation for the Festival of Science will demonstrate the capabilities of Fathom to teach statistical concepts with an environmental focus. I could use an oral session format whereby I would give a brief introduction to my project followed by a demonstration of how students would carry out one of the activities. Otherwise, I could present my project in poster format by visually displaying the capabilities of Fathom and also allow interested participants to try one of the activities for themselves. In this case I would need access to a computer. 

     In our previous studies of the height achieved by model rockets, we have found that our simple model used to predict the height is inadequate; the drag force must be taken into account.  We present the results of a study of the thrust of Estes* model rocket engines and the drag coefficient of model rockets.  In order to accomplish this we have divided the study into two components.  In the first part we determined the thrust and impulse of Estes model rocket engines.  In the second part we determined the drag coefficient of the rocket and the thrust of the engine.  Two types of rocket
engines were tested: 1/2A-6 and A8-3.  For A8-3 engines the average thrust was measured to be 3.00 +/- 0.39 N, and for the 1/2A-6 the average thrust was measured to be 4.32 +/- 0.38 N.  These are well below the Estes' reported averages. However the measured impulses are in excellent
agreement with Estes' published data.  The measured A8-3 impulse is 2.36 +/- 0.07 as compared with Estes' data of 2.5 +/-.25 Ns and the 1/2 A-6 has a measured impulse of 1.24 +/- 0.3 Ns as compared with Estes' prediction of 1.25 +/- .125 Ns.  The next step in the research process was to determine how the drag coefficient influences rocket flight.  To accomplish this we digitized a video-tape of the rocket trajectories for of both types of engines.  We developed a model describing the height of the rocket as a function of time that included the drag force of the air.  We fit the model to the data in order to determine the drag coefficient of the rocket and the average thrust of the model rocket engine. 
*Estes is the leading manufacturer of model rocket engines. 

Assume for a moment that the physics department at St. Lawrence University needs to crunch an incredible number of astronomical related numbers. The person in charge of the project could attempt to complete the project with a typical lab PC, and fifty years later they would get the results. Given the current computer technology, if they wanted to complete their
project in a reasonable amount of time they would have to purchase a parallel computer. 

 A parallel computer is capable of executing multiple instructions in parallel, while a classical sequential computer, a lab PC, is only capable of executing a single instruction at a time. 

 Now our physics department technician has two choices for purchasing a parallel computer. They could contact Silicon Graphics and buy a Cray supercomputer for several million dollars. The other alternative is to build a Beowulf cluster. In order to build a Beowulf the technician would need to log onto the Internet and order fifty modestly priced PCs and a high-speed network switch to connect them. Total cost for a Beowulf, around fifty thousand dollars. 

My senior project used donated PCs and the Linux operating system to build a small Beowulf cluster. A program to take advantage of the parallel architecture of the Beowulf was written in order to demonstrate the benefits of parallel computing. This program solved a one-dimensional equation,
which calculates the diffusion of heat through a substrate. Running time of this model on one, two, three and four processors is presented. 

      In the world of marathon canoe racing, technology is increasingly being used to ensure that competitors have the greatest chance for success.  Typical races are up to fifteen miles and two hours in length and for that reason even small improvements in efficiency will have a significant effect
on performance.  One proposed improvement is to shift the center of gravity of the boat forwards when the boat is in shallow water.  The idea is that having the canoe trimmed bow down (the front end lower then the back end) is more efficient when traveling through shallow water. 
      The purpose of my project is to access the validity of that claim.  I will be using a one-sixth scale model of a racing canoe and simulating the effect of paddling through still water by holding the model in place while a current of water flows past it.  By measuring the drag of the model while it sits at a
range of different trim angles, I can determine how the weight should be positioned in the canoe for a given depth.  By repeating that procedure at a range of different depths I will be able to determine whether moving the weight forward in a canoe does have the desired improvement in efficiency when traveling in shallow water.  The results may then be extrapolated to life-sized canoes by using scaling laws. 
      My results to date indicate that there is a surprisingly significant change in efficiency of the canoe for even small changes of the trim angle.  For example, in the deep water regime, a change of only one degree in trim angle changes the drag by a factor of four. 

      Advisor:  Brian Ladd, Math Department 

     With the recent release of Windows 2000 and Microsoft’s anti-trust proceedings, the term “Operating System” has been thrown around a lot lately.  They have given recent cause for comparisons between operating systems such as Windows, SunOS and Novell’s operating system, and Linux. 
     Most people have heard the words “Operating System” before; many could probably list some of the more important aspects of one.  The operating system is arguably the most important component of any running computer. Unfortunately, most of the people who use computers today neither have the time nor the inclination to research how it works and what goes on underneath Microsoft’s pretty graphical user interface. 
     Simply put, an operating system is a program that controls the computer: it runs other programs, it communicates with the hardware, it mediates multiple applications running at the same time, all while seeming completely transparent to the user.  As described in the verse at the top of the page, the
operating system acts transparently by giving the user no indication that so much is happening, it acts as seamlessly as the he or she is expecting.  Those lines simplify operating systems quite a bit, but they touch on some of the major aspects of them.
     My project explored what operating systems are and how they work.  I examined how software and hardware interact through this thing called an “operating system”.  The file system was a large portion of the project, dealing with how files are handled from the point of view of the application
and the hardware.  I covered virtual memory (sometimes called “paging”) and how that works and fits in with the rest of the system.  Anything that is virtual attempts to cover over the fact that the computer is lacking resources by making the programs and user believe they really are there.  Virtual
memory gives the impression that there is much more RAM, or main memory, than there actually is. Among other things, I also covered shared resources, and how different programs and computers can use the same memory or CPU. 

      The Steiner Problem is a topic in Graph Theory in mathematics that explores the question: what is the shortest network of edges interconnecting an arbitrary set of points?  This question has been answered for very few cases.  In particular, the first that was considered was the case of three
vertices, for which the shortest network is a set of three edges meeting at a junction point in such a way that the edges form 120o angles with one another.  However, for larger sets of vertices, the Steiner Problem cannot be solved in a reasonable amount of time. 
      The Steiner Problem is NP-complete, meaning that it is in the class of the hardest of all problems without a solution in polynomial time.  The difficulty of the problem arrives from the large number of possible solutions that must be checked in order to find out which has the shortest length.  For example, for sets of ten points, the number of possible solutions is in the millions, and for sets of twenty points, the number of possible solutions is in the billions. 
    The few cases for which the Steiner Problem has been solved are sets of three points, sets of four points, ladder graphs, square lattice graphs, vertices of a regular n-gon, vertices on a zig-zag line, and vertices of a splitting tree.  I have done an in depth study on the first four of these categories. These few topics alone cover a majority of what is known about the Steiner Problem.  The most interesting property of the Steiner Problem is that it is easy to understand, but extremely hard to solve.  Thus, making conjectures about the solution to a certain problem is easy with basic
knowledge about the properties of Steiner trees and using the method of trial and error.  I have studied the case of a 5 x 6 lattice and made a conjecture as to what the shortest network is for this graph, and I have shown that this conjecture is a good answer to the problem, without proving it to be the best solution.  While good solutions can be attained in most  situations, a complete solution to the problem will probably never be found.