Student Projects

Students in the Applied Math major work on a variety of projects under the direction of one or more faculty members.

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A mathematical model of gang membership accounting for possible rehabilitation (2015)

Students: Nate Annen, Jacob Clement
Adviser: Dr. Danilo Diedrichs

The Chicago area has a long history with gangs, and is still one of the most active centers for gang activity in the United States.  In 2011, a quarter of all homicides in Chicago were gang-motivated.  Though the gangs make up a small proportion of the population, they have a powerful presence in the Chicago area.  We use an epidemiology model to determine strategies to reduce crime rates and deter gang membership.  We consider the possibilities of fringe gang members ending up in jail as well as core gang members being rehabilitated and reintegrating the normal population.

Exploratory analysis of a High-Speed Intercity Passenger Rail (HSIPR) in the Midwest (2015)

Students: Miriam Agamah, Kyu Lim Lee
Adviser: Dr. Danilo Diedrichs

The HSIPR program was initially developed to link all major cities in the U.S. by a high speed railroad.  Although the nationwide program was abandoned, we study the feasibility of a smaller-scale program between select cities in the Midwest.  Using population and economic data, we build a dynamic domestic trade model to estimate the ridership of a high speed railroad and examine the possibility of amortizing the construction costs within a 50-year time horizon.

Clustering trends of obesity in Dupage County K-12 students (2015)

Students: Melissa Gray, Robin Kong
Advisers: Dr. Danilo Diedrichs, Dr. Nate Thom

The increasing prevalence of overweight and obesity in elementary through high school students in Dupage County has prompted a large scale collection of Body Mass Index (BMI) data from K-12 students in Dupage County public and private schools over the past 4 years.  Using hierarchical and k-means clustering techniques, we examine trends in the geographical distribution of BMI data.  We correlate these data with various other data sets, such as ethnicity and income, using Principal Component Analysis and dimension reduction methods.

Agent-based simulation of crime in society (2015)

Students: Johnny Edman, Richard Ndekezi
Adviser: Dr. Danilo Diedrichs

This project in computational criminology uses a random number generator to build an agent-based model of society with the goal of studying the prevalence of crime in different neighborhoods.  Probability distributions are used to sample the members of this simulated society having different characteristics including age, income level, educational attainment, ethnicity and occupational status.  Long term simulations give insight into the societal pressures leading to criminal behavior.  Solutions to prevent an increase in criminal activity are suggested.   

Quantifying communication effects in disaster response logistics: A multiple network system dynamics model (2014)

Student: Kaile Phelps
Advisers: Dr. Danilo Diedrichs, Dr. Paul Isihara

Complementing the importance of adequate relief supplies and transportation capacity in the first two weeks of post-disaster logistics, efficient communication, information sharing and informed decision-making play a crucial yet often underestimated role in reducing wasted material resources and loss of human life.  A mathematical discrete dynamical system is used to model transportation of different commodities from multiple relief suppliers to disaster sites across a network of limited capacity with variable signal delays, information sharing, prioritization, distribution and redistribution strategies.  Simulations results highlight how communication deficiencies and indiscriminate shipping of resources result in material convergence and shortage of urgent supplies observed in actual emergencies, thus providing a useful quantitative tool for decision-making and training volunteer managers in the importance of a smart response protocol.  

 

The Schedule Effect: can recurrent peak infections be reduced without vaccines, quarantines or school closings? (2013)

Student: Doeke Buursma
Advisers: Dr. Danilo Diedrichs, Dr. Paul Isihara

CalendarUsing a standard SIR (Susceptible-Infected-Recovered) model with seasonal dynamics, we study the "schedule effect", which allows for a significant reduction in recurrent peak infections of endemic diseases in schools by varying the traditional school calendar.  Analysis of the phase plane explains the relationship between the maximum recurring infection peaks and the period of an oscillating transmission function. The response may exhibit period-doubling and chaos induced at certain periods, leading to increased peaks. We show how to take these effects into consideration to design an optimum school schedule.

 

A Mathematical Model for the Growth and Decline of the Church in DuPage County (2013)

Student: Daniela Cuba
Adviser: Dr. Danilo Diedrichs

UEB modelThe project analyzes the population dynamics that affect size of the church in DuPage County, Illinois.  A dynamic model (which we name the UEB model), similar to the SIR model used in epidemiology, divides the population into compartments of Unbelievers, Enthusiasts (who actively bring unbelievers into the church), and passive Believers. In addition to the conversion dynamics, our model also incorporates the long-term demographic fluctuations of DuPage County.  The parameters of the model are determined by fitting church and demographic data obtained from the Census Bureau.  The results of this study are useful to identify the most impactful strategies for churches to increase their membership.

 

Constrained Optimization Model for Quantitative Criminology (2013)

Student: Korey Clement
Adviser: Dr. Danilo Diedrichs

FingerprintThe constrained optimization model for quantitative criminology, first introduced by criminologists Alfred Blumstein and Daniel Nagin, is used to control and minimize the crime rate of a given population. Using the most recent data on crime and punishment available (2009), we use this model to determine the lowest crime rate that can achieved in the United States. The sensitivity analysis of the model's parameters reveals what steps must be carried forth in order to reduce the crime rate to a global minimum.

 

Development of an Application for Indoor Temperature Control Efficiency (2013)

Student: Roland Hesse
Adviser: Dr. Danilo Diedrichs

Temperature ProfileUsing numerical techniques to discretize and solve heat equation (a partial differential equation) in three dimensions, we devise a computerized application that models the heat flow and determines temperature gradients in a building.  The application allows for the geometry of the rooms and insulation properties of the boundaries to be specified, as well as the indoor locations where people are most likely to be found.  We use this system to locate the optimal placements of HVAC (Heating, Ventilation, and Air Conditioning) for overall efficiency in temperature control and reduction of wasted energy and climate-control costs.

 

Computational Composition of Traditional Scottish Music (2013)

Student: Tim Macdonald
Adviser: Dr. Danilo Diedrichs

Scottish MusicTraditional Scottish music has recurring patterns at the harmonic, melodic, and structural levels. Using a combination of automated pattern recognition techniques and domain-specific knowledge, we develop a system that, seeded with a corpus of existing tunes, composes original music in the same style. This is accomplished using a long short term memory network---a type of recurrent neural network.  The corpus used was the complete works of 18th century composer William Marshall, which was transformed into a sequence of integers suitable for inputting into the network.  Post-conversion, the music was used to train the network, and the trained network was used for generating new music.

 

Inventory Models in Disaster Relief (2012)

Student: Nate Veldt
Adviser: Dr. Danilo Diedrichs

CycloneModels for supply chain management can be used to assist humanitarian relief organizations in calculating how to efficiently provide for a population affected by a natural disaster. This project explores in detail a single period probabilistic model for fulfilling a demand while minimizing costs.  The model is implemented in MATLAB and several examples are given of how this model might be used in a specific disaster relief situation. A Monte Carlo simulation is used to generate potential values for demand to then analyze how this model might be used to meet a demand that stretches over multiple periods.

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