St. Lawrence University

Festival of Science  2001

Math & Computer Science
Student Participants

For a more detailed description of each presentation click on the names listed below.

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To see the complete FOS itinerary for 2001, click here

Vivek Bachhawat
Computer Aided Instruction Tools in JAVA for Different On-Campus Departments

Rose Blanding
Properties of Line Graphs

Matt Hoek
Scaling Analysis of Mid-Ocean Ridge Lava Flows

Gretchen Koch
Coding Theory
Vivek Bachhawat
Advisor: Dr. Brian Ladd (Computer Science)
Client to Project:  Dr. Robin Lock (Mathematics)
SLU Festival of Science 2001 Oral Presentation

Computer Aided Instruction Tools in JAVA for Different On-Campus Departments

   My project was to research and create a software package that can be used by different departments on campus for instructional purposes. I spent 8 weeks during summer of 2000 learning Java and designing this package, under the SLU Fellowship program. Using this package, students can visualize the theoretical ideas they work on in a class. Texts on any topic provide static information whereas computer based applets (web software) are interactive and hence helps constructive learning of the topic. With computer-generated programs, students can see how changes in a single data point affect the results of data analysis dynamically. This package can be customized and be used by any department on campus and as an example, I specialized the package for Mathematics department at St. Lawrence University. Any student who wishes to explore introductory statistics can use this package. I created the software to be used as a teaching-learning tool, which is not achieved by conventional software. Here students can use one part of the software to learn the concepts and then use the other part, as a game, to test the skills acquired. The following applets that I created using the package are targeted for statistics students but anyone interested in the subject can use it with ease.
(i)  Distribution Applet 
(ii)  Distribution Game Applet and 
(iii) Hypothesis Testing Applet 
(i)  The Distribution Applet
is a tool for learning Statistics Distributions. It generates different Statistics ‘Random number distributions’ viz Uniform, Discrete Uniform, Geometric, Normal, Binomial, Exponential and Poisson distribution based on student’s selection. The Applet has various inputs depending on the type of distribution chosen and the help files describe the procedure and gives description of the different types of distribution.
(ii)  The Distribution Game Applet
is complementary to the Distribution applet. This applet is designed as a game that tests the knowledge of the student about Statistics distributions. Students are presented with a set of data, randomly generated by the computer, and are asked to make an educated guess of the distribution, based on the given data. The Distribution applet helps student learn various Statistics distribution concepts and the Distribution Game applet tests the skills acquired by the former applet. Thus both the applets work together as a teaching-learning tool.
(iii)  Hypothesis Testing Applet
uses the hypothesis testing procedure of a given statistical theory and gives the null hypothesis “the benefit of a doubt”, that is to accept the null hypothesis unless there is strong evidence to support the alternative. The students can control the various variables of the given hypothesis and the applet updates the changes dynamically.
Also, this package is available online at http://it.stlawu.edu/~vbachh33/projects.html with complete source code and documentation for anybody interested in downloading and customizing the package for personal use.
Rose M. Blanding
Advisor:  Dr. Patti Frazer Lock
SLU Festival of Science 2001 Oral Presentation
Properties of Line Graphs
 
My independent study concentrates on a field of graph theory called line graphs.  In graph theory, a graph consists of a set of vertices and edges.  The line graph is a manipulation of these vertices and edges to create a new graph.  The method for drawing out the line graph L(G) of a graph G is shown below.
The line graph L(G) of a graph G is defined as:
1.  The vertices of L(G) correspond to the edges of G.
2.  Two vertices in L(G) are adjacent iff the corresponding edges in G are adjacent.
 
The number of edges in a graph G is equal to the number of vertices in its line graph L(G).  The number of edges in a line graph is equal to [(the sum of the degrees for each edge uv)-2].
 
I have investigated line graphs of special classes of graphs, such as cycle graphs, path graphs, and star graphs.
For cycle graphs:  when G = Cn, L(G) = Cn

For path graphs:  when G = Pn, L(G) = Pn-1

 For star graphs:  when G = Kn,1, L(G) = Kn

There is also a method for drawing a graph from it’s line graph.  This method is known as a Krausz decomposition.
Theorem:  A nonempty graph H is a line graph iff E(H) can be partitioned into subsets such that:
a)  the subgraph induced by each member of the partition is complete and
b)  no vertex of H lies in more than two of these induced subgraphs
Bipartite Graphs:  I will discuss the connection between line graphs of bipartite graphs and a class of graphs known as ‘board graphs’.
Matt Hoek
Advisor:  Dr. Brian Watson
SLU Festival of Science 2001 Poster Presentation
 
Scaling Analysis of Mid-Ocean Ridge Lava Flows
 
During the Spring of 1999, a team of scientists from the Lamont-Doherty Earth Observatory conducted a research cruise along the East Pacific Rise (17 28’ S latitude).  The scientists on the cruise were assisted by the underwater robot ABE, which stands for Autonomous Benthic Explorer.  ABE gathered a high-resolution data set as it tracked along the sea floor of the Rise, accurately mapping the topography of the bottom to within 10 centimeters.In addition to gathering navigation, latitude, longitude, heading, depth, and altitude data, ABE also took pictures of the lava flows on the sea floor with a camera mounted on its flotation device.
The goal of this analysis was to determine the multifractal and scaling properties of the lava’s visual reflectance field and to compare them to those of a similar study (Laferrière and Gaonac’h, 1999) conducted on reflectance fields of volcanoes at Mt. Etna and Mauna Loa.  While these two volcanoes are traditional cone volcanoes, the source of lava at the East Pacific Rise is a three kilometer fissure in the ocean floor.  There are several differences between the volcanoes at Mt. Etna and Mauna Loa and the mid-ocean ridge of the East Pacific Rise.  Because the ridge is about 2700 meters below sea level, the lava that floods out of the fissure is under extremely high pressure.  The lava is also quickly cooled by the surrounding seawater, which is at a temperature of  2°C.  Because the lava in our photos is produced by different flow mechanisms than the lava of Mt. Etna and Mauna Loa, we were interested to see how our results would compare to those of the 1999 study.
We first examined the scaling properties of several types of lava flows by performing Fast Fourier Transforms (FFT) on the digital images.  Our results were similar to the small-scale results from the study of Laferrière.  Preliminary results showed some interesting differences in the spectrum based on flow type.  For example, the talus morphology spectrum has an anomalous structure that we tentatively identify with the two-stage formation process of talus.  We also conducted a multifractal analysis of the images.  For each lava type, we hoped to find typical values of the universal multifractal parameters a and C1, where a measures the degree of multifractality and C1 measures the sparseness of the field.  The results of the multifractal analysis will be presented at the festival.

 
 
Gretchen Koch
Advisor:  Dr. Maegan Bos
SLU Festival of Science 2001 Oral Presentation
 
Coding Theory
Description of Project:
Coding theory is the field of mathematics that describes how to retrieve a message transmitted through a channel.  In particular, it emphasizes how to design a code so that one can detect and correct errors created by noise in the channel.  Noise is any disturbance that distorts the message being sent.  Additionally, coding theory has practical applications.  For example, the Pathfinder that was sent to Mars transmitted digital images back to Earth.  Each image was broken down into a grid of pixels, and each pixel color was encoded as strings of zeroes and ones.  Other applications include ensuring telephone conversations do not have interference and making sure that scratches on compact discs do not distort the information on the CD.
There are several assumptions we will make in coding theory.  First, the codes are binary codes; they are composed of zeroes and ones known as bits.  Another main assumption is that the probability that a bit is sent correctly is greater than the probability that it is sent incorrectly.  Thus, although this assumption allows errors to be made, it makes it possible to detect and correct those errors.  A third assumption is that every channel used is a binary symmetric channel; thus, the chances that a certain bit is received is independent of whether that bit is a zero or a one.  Another important idea in coding theory is that the code is a block code.  Block codes consist of several codewords made up of the same number of bits; so, codewords are all of the same length.  Finally, there is an assumption made when one corrects errors.  If one has the set of codewords, and the word received is not in that set, then one decodes the word received to the “closest match” among the codewords.  There are several ways of doing this.  Finding the error pattern of the code is one way while using an algorithm such as maximum likelihood decoding is a method that works better for larger codes.  Each different code has an associated method of detecting and correcting errors.
There are different types of codes in coding theory.  One category of codes is linear codes.  One manipulates these codes via the theorems and methods of linear algebra.  Two other codes worth noting are Hamming codes and Golay codes.  Hamming codes are designed to correct any single error, while Golay codes corrects three or fewer errors.  The Golay code was used to encode pictures from Jupiter and Saturn.
For my oral presentation, I will discuss the basics of coding theory as well as several codes and their implementation.  I will work through an example of a linear code that covers these basic principles of coding theory.

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May 1, 2001
Maintained & Created  by:  P. Barkley
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