Jonathan Bowman 

Towards a Computational Model of Consciousness

Summer 2007

Advisor: Dr. Jeff McKinstry

Abstract:

We explore the idea that consciousness is the ability to simulate the world in order to optimize behavior. A computer simulation of an autonomous agent was created in which the agent had to learn to explore its world and learn (using Bayesian Networks) that pushing a block into a hole would lead to a reward. Afterward, the agent was placed in a novel situation, and had to plan ahead via "mental" simulation to solve a novel problem. We improved on prior work by using a Dynamic Bayesian Network as a model of planning. The agent was able to solve the novel problem. In animal learning this type of behavior is called insight learning, and has been argued to be indirect evidence of consciousness in the absence of language. This work has implications for testing for consciousness in animals.

 

John Jones

Bayesian Network Learning as a model for the formation of Learning Sets

Summer 2007 - Spring 2008

Advisor: Dr. Jeff McKinstry

Abstract:

Primates are able to learn through trial and error to associate a particular stimulus with an appropriate action in order to obtain a reward. This is called discrimination learning. Harlow reported in 1949 that if you change the stimuli, but keep the problem the same, primates are able to relearn this new problem much faster than the first time they learned the task. In fact, the more sets of problems you give them, the faster they relearn. This has been called Learning Set formation. The formation of Learning Sets is one of the hallmarks of intelligence in higher mammals. No model to date can satisfactorily explain the mechanisms which allow this type of generalization. We are exploring the possibility that this type of learning can be explained by a specific learning algorithm for Bayesian Networks known as Expectation-Maximization. Preliminary results show that the algorithm can generate a model that generalizes from one problem to another when the stimuli are changed, the classic Learning Set result. The next step is to analyze the model to understand why it works, and to compare the results quantitatively with behavioral data from animals.

 

Stefanie Mooney 

To Teach, Shape and Send: A Statistical Analysis of Student Data to Assess PLNU Core Values

Summer 2007 - Spring 2008

Advisors: Dr. Greg Crow and Dr. Maria Zack

 Abstract:

While endowing students with the prerequisites for a good job and the ability to pursue further education are of premium significance, schools such as Point Loma Nazarene University also seek to influence the personal growth of the student. As evidenced by PLNU’s mission statement, the university “…exists to provide higher education in a vital Christian community where minds are engaged and challenged, character is modeled and formed, and service becomes an expression of faith.”

Understandably, it can be somewhat difficult to measure PLNU’s progress on more intangible concepts, such as being recognized for “spiritual vitality” and being characterized as a place where “all members are valued and encouraged to fulfill their potential.” As such, various surveys are presented to the students and faculty of PLNU on a regular basis in order to gain some semblance of how the institution is fulfilling their goal as summarized in the phrase “To Teach, To Shape, To Send.” By organizing and manipulating the summary and raw data from these surveys, research analyses may be conducted to see where PLNU is lacking, where PLNU is right on target, and where PLNU excels as a place that encourages students to seek their highest potential in all aspects of life. As a result, Point Loma may use this information to continue improving its methods of encouraging student growth.

 

Lauren Nelson

Analysis of Disease in Sub-Saharan Africa

Fall 2007 - Spring 2008

Advisors: Dr. Greg Crow and Dr. Maria Zack

Abstract:

The World Health Organization provides data regarding health and other epidemiological factors that affect the health of populations. The standards of life in every region of the world are different. Living and health conditions in Sub-Saharan Africa are unique. One unique factor is the lack of clean, or improved, water sources. A lack of clean water can negatively affect other factors. The goal of research is to find relations between the lack of clean water sources and other factors and to see what improved water sources could potentially provide for populations.

 

Johnathon Smith

Proving that Internet Cryptography is Not Necessarily Secure 

Fall 2007 - Spring 2008

Advisor: Dr. Jesus Jimenez

Abstract:

Solving the P vs. NP debate using the Subset-Sum problem. The Subset-Sum problem is NP because it is simple to check the solution, but the number of steps to find the solution may require the consideration of all the possible combinations which is equal to 2^n combinations, where n is the number of elements in the set we are considering. The approach used in this paper uses specific properties of addition and other logical optimizations to check only combinations that could be solutions rather then checking all of the combinations.

 

Erin Trine

Service Learning for Math Secondary Education Majors

Fall 2007 - Spring 2008

Advisor: Dr. Lori Carter

Abstract:

Service Learning is a unique experience where students step out of the classroom and serve their communities based on their particular field of study. The key in Service Learning is participation in a project where the serving and learning form a reciprocal relationship and there is ample time for reflection during the process. At Point Loma Nazarene University, an entire class was devoted to service learning. Juniors and seniors in math, computer science, and information systems were involved in four different projects which offered assistance to PLNU and the greater San Diego community. A group of five students supported the math faculty and students at Point Loma High School by providing in class and after school tutoring. This research will walk through this specific project and provide an outline for facilitating future service learning projects in the field of math secondary education.

 

Kait Wilcox

Calculus Then and Now

Summer 2007 - Spring 2008

Advisor: Dr. Maria Zack

Abstract:

The intellectual world was booming in 17th century Europe.  The Royal Society had just been founded and the publications of new scientific and mathematical discoveries were frequent.  In on all of the action were two mathematical geniuses, Isaac Newton and Gottfried Leibniz.  These two men were a part of one of the hottest disputes ever to hit the intellectual world.  They are the inventors of calculus; however they did not collaborate at all in this field of study.  With two entirely different approaches these two men covered many of the topics now covered today in high school and university calculus classes.  In order to better understand the subjects we now know as integral and differential calculus, we must first understand how it is that two men could work entirely independent of one another and still come up with the same mathematical theories.  Looking at the physical approach of Newton in contrast with the analytical approach of Leibniz will clearly develop a better understanding of the subject for all mathematicians.  This examination will begin with the lives and characters of these two men and will continue its discourse through their dispute over claims for priority and will finally compare and contrast their mathematical works and discoveries.