Festival of Science 2004 Math, Computer Science and Statistics Students

St. Lawrence University

Festival of Science 2004
Math & Computer Science
Student Participants

Travis Atkinson, Scott Cipriano, Katie Livingstone,
Jeremy Ouellette, Sarah Post

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To see the complete FOS itinerary for 2004, click here

"Approximate Confidence Interval Estimation for Beta-bionominal
Proportions of Biometric Identification Devices"
Travis Atkinson
Advisor: Dr. Michael Schuckers

The goal of this project was to determine the performance of confidence interval estimation using the methodology of Agresti and Coull (1998) on proportions from a Beta-binomial distribution. Agresti and Coull applied their approach to the binomial distribution, specifically for estimation proportions. In this research we tried determine the appropriate manner in which to extend that work to proportions from a Beta-binomial distribution. In particular we were interested in applying such a methodology to data from biometric identification devices such as fingerprint scanners or iris recognitions systems. The approach we took was to simulate data from a variety of Beta-binomial distributions and compare the performance of the augmented approach of Agresti and Coull to more traditional approaches to interval estimation. Specifically we considered four ways to extend this work. For the binomial n independent binary observations are augmented with 2 successes and two failures. For the Beta-binomial we have k individuals with m binary observations each. To augment the Beta-binomial data, we first considered adding 2 successes and 2 failures to a single individual. Second we considered adding a success and a failure to the counts for 2 individuals. Third we considered adding 1 success to the data from each of 2 individuals and 1 failure to the data for 2 different individuals. Last we considered adding a new individual n+1 who was given 2 successes and 2 failures. We used a Monte Carlo approach for evaluating the performance of these four augmented approaches.

"Single beam holography "
Scott P Cipriano
Advisor: Catherine Jahncke

The process of holography, as coined by the Hungarian physicist Dennis Gabor, was originally investigated in an attempt to increase the resolution of the current electron microscope. Gabor ended up using a light beam instead of a beam of electrons to make the first hologram, but it wasn’t till 1960’s when the LASER was invented that holography begin to take off. Since Gabor’s original design numerous processes have developed that each create unique types of holograms. For the purposes of this project these different variations have been studied and several have been replicated.

"Modeling disease: mathematics in epidemiology and
applications to the SARS virus"
Katie Livingstone
Advisor: Dr. Patti Frazer Lock

Epidemiology is a field of science that has made many significant advances in studies of the spread of disease. Studies of epidemics and disease spread have vast mathematical components. Epidemiological models are based on differential equations that provide the foundations for modeling change over time. These are useful in modeling rates of infection, rates of recovery, contact rates, birth and death rates, etc. Such models can predict the impact of a disease on a population and can suggest valuable strategies for its control. This study presented the most basic epidemiological model and examined the common uses and implications of certain features. It looked at several more complex models and explained how to modify a disease model according to the characteristics of a disease. Lastly, this study examined how researchers have modeled SARS, one of the most recent disease outbreaks, in three published articles.

"Flux of cosmic ray muons at low energies"
Jeremy Ouellette
Advisor: Daniel Koon

Muons are one the more easily observed fundamental particles. Created in the upper atmosphere due to collisions of cosmic protons and atmospheric nuclei, they come streaking down to earth at a wide variety of energies. The number of muons (flux) present at high energies is well known, but low energy measurements have been more difficult to find. At these low energies, local atmospheric conditions such as humidity and air pressure may have a much larger effect on these particles. Extrapolation from the well known high energy data allow us to create a simple theoretical model of the low energy muon flux, and the effect of atmospheric conditions on this spectrum can be experimentally tested using a simple apparatus. The theory, experimental apparatus, analysis, and results will be discussed.

"Quantum Mechanics"

Sarah Post

Advisors: Dr.’s Maegan Bos and Mike Sheard

In this project, I investigate the philosophy of mathematics in general and in relation to the application of mathematics in science, using the specific example of the mathematical foundations of quantum theory. I first give an overview and criticism of the classical schools of thought in the philosophy of mathematics: Platonism, logicism, and formalism. I then describe new theories which take into account the linguistic and socially constructed nature of mathematics and which are more congenial to current trends in philosophy in general and in the philosophy of science in particular. From these theories, I draw out the philosophical implications, most importantly those pertaining to epistemology, of the prevalence of mathematics in science. I argue that as mathematics is a socially constructed representation of structures through a specific and highly logically based manifestation of human reason. This philosophical description of mathematics questions the ontological priority given to mathematics reasoning and also the epistemological certainty given to mathematical formulations of reality, inline with current trends in the philosophy of science. I then give a brief introduction to the foundations of Quantum mechanics and the Dirac formalism in particular and discuss the implications of such a view of mathematics to that of philosophy of science. It is my hope that such an investigation offers a philosophical understanding that is more nuanced than the previous absolutist views and which highlights the importance of creativity in both the practice of pure mathematics and its applications in science.

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