Fashion Trends in a Fashion Trends in a Middle SchoolMiddle SchoolSupercomputing Challenge Supercomputing Challenge

Summer InstituteSummer InstituteFinal ReportFinal ReportJuly 27, 2006July 27, 2006

Capshaw Middle School - Team #01Capshaw Middle School - Team #01

Theresa Anaya Burney Peter ColehourTheresa Anaya Burney Peter Colehour

Susan GibbsSusan Gibbs Thansewi J. MartinezThansewi J. Martinez

Makoena MoneseMakoena Monese

IntroductionIntroduction Middle school students arrive at school

wanting both to conform to fashion norms and to be recognized as individuals. Each student also has a relative degree of shyness or sociability. These factors affect each student’s susceptibility to a fashion trend. The research supports the relative shyness and resistance levels of students, and tipping points in the spread of a trend.

Executive SummaryExecutive SummaryOur computational model: Our computational model:

Allows multiple trials of how the initial percentage of Allows multiple trials of how the initial percentage of resistant students affects speed of a trend’s spreadresistant students affects speed of a trend’s spread

Imitates the real-world school environment:Imitates the real-world school environment:• Shows relative shyness and susceptibility of studentsShows relative shyness and susceptibility of students• Recognizes that the relative percentage of resistant students Recognizes that the relative percentage of resistant students

determines the speed of the trend’s spread. determines the speed of the trend’s spread. Can be used to study relevant middle school topics: Can be used to study relevant middle school topics:

• bullyingbullying• spread of disease spread of disease • the susceptibility of individuals to drug, alcohol, tobacco use, the susceptibility of individuals to drug, alcohol, tobacco use,

and sexual activities. and sexual activities.

The Project HypothesesThe Project Hypotheses The StarLogo model will graph the The StarLogo model will graph the

spread of a trend, comparable to an spread of a trend, comparable to an infection model. infection model.

The lower the initial percentage of The lower the initial percentage of followers, the slower the trend will followers, the slower the trend will spread. spread.

A tipping point may exist in the initial A tipping point may exist in the initial percentage of followers, above which the percentage of followers, above which the trend spreads much more quickly.trend spreads much more quickly.

Mathematica ModelMathematica Model

Our infection model set two contact rates (30% Our infection model set two contact rates (30% of agents have fewer contacts) and used an of agents have fewer contacts) and used an infection variable for the percentage of the infection variable for the percentage of the population that was susceptible (infection after population that was susceptible (infection after 2 exposures) or immune (after 4 exposures).2 exposures) or immune (after 4 exposures).

ddPPII /dt= rcP /dt= rcPII (1-P (1-PII))Expected number of susceptible individuals Expected number of susceptible individuals who will become infected in the time who will become infected in the time ΔΔt, t, assuming rc = 1. assuming rc = 1.

Starlogo ModelStarlogo Model

Our STARLOGO Our STARLOGO model allows students model allows students to manipulate the to manipulate the original percent of original percent of students students characterized as characterized as “followers” “followers” (susceptible) and (susceptible) and “freethinkers” “freethinkers” (relatively immune).(relatively immune).

ResultsResults

All 3 Hypotheses provedAll 3 Hypotheses proved1.1. The StarLogo model is comparable to an The StarLogo model is comparable to an

an infection model. an infection model. 2.2. The lower the initial percentage of The lower the initial percentage of

followers, the slower the trend will followers, the slower the trend will spread. spread.

3.3. Two tipping points exist in the initial Two tipping points exist in the initial percentage of followers, above which the percentage of followers, above which the trend spreads much more quicklytrend spreads much more quickly

RecommendationsRecommendations

Students:Students: Expand model to apply to new issuesExpand model to apply to new issues Expand and refine model to show affect of Expand and refine model to show affect of

advertising, new conflicting trends, and advertising, new conflicting trends, and Conduct real-world experiments on the spread Conduct real-world experiments on the spread

of trendsof trends

Teachers:Teachers:Create a StarLogo TNG modelCreate a StarLogo TNG modelUse model to entice students into ChallengeUse model to entice students into Challenge

AcknowledgementsAcknowledgements

We appreciate:We appreciate:

STI Team - for all their support and patience. STI Team - for all their support and patience.

Dylan Allegreti - for supporting the process Dylan Allegreti - for supporting the process and working with us.and working with us.