Applied Math Project Day 2013

Location

Serra Hall, Room 312

Free

List of Presentations:

Presentation 1 (40-45 minutes + questions)

Title: Basketball Fortune-Telling

Student Presenters: Chris Quam and Evan Karkazis

Thesis Advisor: Dr. Cameron Parker

Committee Members: Dr. Cameron Parker, Philip Lau, Dr. Ani Velo

Abstract:
There are various factors that go into building a successful basketball team. Simply having the best player is no longer sufficient to ensure victory from game to game; team chemistry, defense, and streaks must also be considered.

In this research we use both traditional and contemporary statistical methods to predict game-by-game and seasonal outcomes in NBA basketball. Our work uses the Probit model to determine the probability of a team winning a game versus another opponent, as well as calculate probabilities of a win or loss. Through game simulation, we construct teams’ probabilities of winning, and make an educated choice of who will succeed in a particular match-up. In order to encompass an optimal amount of variables, the Hollinger Player Efficiency Rating (PER), as well as Points Per Game (PPG) and Opponent’s Points Per Game (OPPG) averages are included as explanatory variables.

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Presentation 2 (30-35 minutes + questions)

Title: A Mathematical Model of Serotonin Concentration

Student Presenter: Erica Nederend

Thesis Advisor: Dr. Seth Haney

Committee Members: Dr. Seth Haney, Dr. Diane Hoffoss, Dr. Ani Velo

Abstract:
Serotonin is a neurotransmitter that regulates mood, behavior, aggression, suicidality, and body weight. Regulation of serotonin is very complex and levels of serotonin tend to fluctuate in response to many factors.

We have created a mathematical model of this complex system, based on differential equations to model the concentration of serotonin in a single neuron. Our simplified model allows us to analyze the behavior of serotonin based on different parameters in order to consider the states at which all levels of serotonin are constant. Furthermore, we can input our model into capable software in order to visually observe the model and the effects of the various parameters in order to make predictions about the long-term behavior of serotonin in the body and make conclusions of the impact that these changes have on mental health.

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Presentation 3 (30-35 minutes + questions)

Predicting Extinction Using Sighting Records and Bootstrapping

Student Presenter: William Tressel

Thesis Advisor: Dr. Jane Friedman

Committee Members: Dr. Jane Friedman, Dr. John Glick, Dr. Ani Velo

Abstract:
In this work, we evaluate statistical methods which use sighting records to predict when a species has gone extinct. Sighting records are poor data, but they are readily available, so these methods seek to make the most of this limited information. We have developed new methods based upon the idea of change points for predicting the time of extinction of a species. Change points are points at which the behavior of a function, such as the one which measures the sighting rate, differs before and after this point in time. In our work, we specifically consider change points where a positive-valued function becomes equal to zero, representing how the probability of sighting a species before its extinction is positive, and the same probability after extinction is zero.

We evaluate how one currently established method from the literature performs for examples of species which are critically endangered or extinct, and more interestingly, examples of species which have been assumed to have gone extinct, but which reappear years later. We also evaluate our methods in comparison with the currently established method. Our methods involve making inferences by bootstrapping the sighting records of the species. Robust methods should be able to predict extinction in those cases when the species has gone extinct, and to not rule out survival in cases when the species reappears.