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«Strengthening the Nation through Diversity, Innovation & Leadership in STEM San Antonio,Texas · October 3-6, 2013 Get Connected! Connect with the ...»

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Instituto Tecnologico Autonomo de Mexico, Mexico City, MX, 2University of California, Los Angeles, Los Angeles, CA, 1 Cornell University, Ithaca, NY, 4University of California, Riverside, Riverside, CA, 5St. Mary’s College of Maryland, St.

3 Mary’s City, MD.

GPS is a valuable tool and, as such, the optimization and accuracy of the techniques to measure the performance of satellites are of paramount importance. Two major measures relating to performance are visibility and dilution of precision (DOP). Visibility is defined by regions that share a direct line of sight with sufficiently many satellites in orbit.

The current system to determine the visibility and DOP of these satellites is accurate and useful; however, it is time consuming. Our hypothesis is that implementing level set methods (LSM) to measure visibility and DOP will prove to be more time efficient and equally as accurate as the systems that are currently used by analysts at The Aerospace Corporation. Our team members have been provided with several different programs in Mathematica and C. We have translated the coded formulations into MatLab, while simultaneously reviewing the necessary orbital mechanics and basic LSMs. We have tested static LSMs, calculating the level set functions at each time step, as well as dynamical LSMs, where the changes in regions of coverage are handled implicitly. Challenged with the task of improving GPS performance, LSMs have been used to test visibility and DOP. We are expecting the LSMs to be more efficient than previous methods but to be affected by a loss of mass and additional noise. The choice of LSMs for optimizing the

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Saba Nafees, Sean Rice.

Texas Tech University, Lubbock, TX.

Cystic fibrosis is a complex genetic disease caused by deletion of F508. Currently, there are no known mechanisms that explain how common mutations interact to inhibit efficient protein folding. These mutations join together to have a coupling effect on the protein folding machinery. Analyses of the amino acid sequence data could illuminate the mutations’ coupling interactions. Modeling this coupling effect is a profound mechanistic problem in illuminating this disease. In standard polynomial regression, the coefficients of each term are a function of the degree of the polynomial that we choose to fit. Therefore, the coefficients do not have independent biological meaning, and it is impossible to use polynomial curve fitting and obtain a function that precisely reveals the properties of the ambiguous dataset. We must rely on functions that are independent of each other and can be analyzed separately to give meaning to the coefficients. This is the basis of orthogonal polynomials. With regards to this disease, our goal is to build functions that capture the intrinsic properties of the amino acid sequences affected by the chief mutation of CF so we can assess the mutation’s coupling effect. Our ultimate goal is to develop a method that conserves intrinsic biological properties of any phenomenon being tested while simultaneously capturing its quantitative properties. We hope this will illuminate the interactions between, not only different variables in genetic diseases, but in a wide variety of phenomena, such as quantitative properties of interactions of different cancer drugs.




Laura Asaro1, Joanna Myers2, Carlos Vera3, Alan Wirkus-Camacho4, Baojun Song5.

East Central University, Ada, OK, 2University of North Caroline at Asheville, Asheville, NC, 3University of Puerto 1 Rico at Mayagüez, Mayagüez, PR, 4Herberger Young Scholars Academy, Glendale, AZ, 5Montclair State University, Montclair, NJ.

Studies on the mussel Mytilus edulis, resident off the coast of Ireland in 1995, showed high levels of contamination by the azaspiracid toxin in harvested individuals. The genus Protoperidinium, previously thought to be harmless, was


found to be responsible for the high levels of azaspiracid toxin found in the mussels. Hence, reducing the ratio of Protoperidinium to Heterocapsa algae may turn out to be an effective mode for reducing mussel toxin contamination.

In order to study this possibility, a nonlinear system of ordinary differential equations was introduced to model the dynamics of 2 dinoflagellate species and their most common predator. The model accounts for the fact that the toxin producing Protoperidinium preys on the nontoxic Heterocapsa while both ingest and, therefore, compete for the nutrients available in the system. The system supports multiple equilibria. A bifurcation analysis is conducted on the model that identifies at least 2 modes of coexistence: equilibrium or oscillatory. The impact of interventions, such as modifying nutrient flow, to reduce the levels of the azaspiracid toxin and observe their effect on the persistence of the system are considered and evaluated.



Wendy Caldwell1, Benjamin Freedman2, Luke Settles3, Michael M Thomas4, Erika Camacho5 University of Tennessee, Knoxville, TN, 2Bucknell University, Lewisburg, PA, 3Southern Illinois University 1 Edwardsville, Edwardsville, IL, 4Kennesaw State University, Kennesaw, GA, 5Arizona State University at the West Campus, Phoenix, AZ.

An estimated 2 million residents in the United States are abusing Vicodin, the nation’s most commonly prescribed pain reliever; the majority of abusers are those who had, at one time, used it under medical supervision. The goal of this project is to identify and evaluate a class of most effective strategies for reducing the overall prevalence of Vicodin abusers among those who had been introduced to the drug for legitimate medical reasons. The doctorpatient environment system involves multiple pressure points, and our goal is to identify the most effective prevention measures under clearly identified scenarios via the use of population-level mathematical models. Initially, an ordinary differential equation’s compartmental model that follows, at the population level, the transition of individuals from medically supervised Vicodin users into total recovery is formulated and analyzed, under the documented assumption that relapse rates are high. The stability of equilibrium solutions is investigated, and sensitivity analyses are conducted on the effectiveness of intervention methods to determine which strategy will have the greatest impact in reducing the number (prevalence) of Vicodin abusers among the population of those who were exposed to this pain reliever via a legitimate prescription.



Christopher Rackauckas1, Chenxiao Xu2, Colin Jarvis3, Weijie Cai4, Avery Ching4.

University of California, Irvine, Irvine, CA, 2Hong Kong Baptist University, Kowloon, HK, 3Macalester College, Saint 1 Paul, MN, 4Hong Kong University of Science and Technology, Kowloon, HK.

In the spring of 2013, Baidu, Inc. hosted a competition for teams to develop new algorithms for movie recommendation systems. The purpose of the competition was to develop better models for rating prediction and suggest methods for incorporating social media data into the prediction models. Our team was sponsored by Baidu, Inc. to develop a new statistical model for movie recommendations that used the knowledge gained from the top competitors of the competition. We developed a hybrid model that used various machine-learning techniques to synthesize the best performing models from the competition, Feature-Based Matrix Factorization, Ridge Regressions, and Factorization Machines, into a single prediction model. Our model satisfied 3 desired properties: computational viability, incorporation of social media data, and a higher degree of prediction accuracy than any model on its own.

Computational viability is important for the realizability of the algorithm in industry was achieved through a parallel implementation. The incorporation of social media data provides Baidu, Inc. a method for improving prediction accuracy and was accomplished through feature-engineering. Lastly, we provided a mathematical proof to show that our hybrid model’s predictive accuracy must be equal or better than the predictive accuracy of any of its components.



Leslie Hogben1, Jonathan Lai2, Brian Lois1, Kevin Palmowski1, Christofer Sheafe1, Trevor Steil3, Namrata Vaswani1.

Iowa State University, Ames, IA, 2University of Texas at Austin, Austin, TX, 3Michigan State University, East Lansing, 1 MI.

Compressed sensing is the problem of solving certain systems of equations with more unknowns than equations.

Mathematically, compressed sensing tries to recover the sparse n-vector x from the equation y = Ax, where A is an

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mxn matrix with m n. Unique solutions to this problem can often be found due to the fact that x is sparse. A simple way of approximating sparsity is to find the solution to x with minimal one-norm. This method is known as compressed sensing via basis pursuit (CS). Additional methods of solution can be used if some set T is known a priori to be approximately the support of x, where the support is defined as the set of all indices corresponding to nonzero entries of x. One such method is LS-CS, which uses least-squares approximation to obtain an initial estimate for x on T, and then uses CS on the error residual. Another method for sparse recovery with a support estimate T is known as modified-CS, in which the one-norm of x is minimized on the complement of T. It is hypothesized that modified CS will reconstruct x with the smallest error and that LS-CS will reconstruct x with a smaller error than CS. We will present numerical results of simulations testing these hypotheses and other related results.



Patrick Morgan1, Helena Puche2.

DePaul University, Chicago, IL, 2University of Illinois at Chicago, Chicago, IL.

1 Mosquitos, specifically the Asian tiger mosquito (Aedes albopictus) and the common house mosquito (Culex pipens) are common vectors of the West Nile Virus, and are also known to prey on humans and animals for blood. While obtaining blood, the mosquitos transfer the virus to their prey. This is especially dangerous to infants, the elderly, and those who have weakened immune systems. Mosquitos are found typically near their breeding ground, laying eggs in stagnant water which grow to become larvae. Larvae of mosquitos are known to tolerate certain water conditions from water temperature to the amount of oxygen available. The purpose of this project was to determine if water sources near drainage pipes were optimal for mosquito growth. For that purpose, 500 mL water samples were collect from 2 lakes and 2 ponds at the Dupage Forest Preserves at drainage pipes and 100 meters from each pipe. Specifically, we identified all of the macroinvertebrates in these locations and compared them using the Shannon-Wiener diversity index. Macroinvertebrates are small aquatic organisms that include mosquito larvae. Differences found in the macroinvertebrate fauna were found between locations of drainage pipes and areas without drainage.

Mathematics & Statistics SAT-393


Maryam Khan, Shana Kachaochana, Anuj Mubayi.

Northeastern Illinois University, Chicago, IL.

Crime is an integral part of societies; however, level of crime varies between regions. A complete criminal-free community may be difficult to attain because of the complexity involved. It is important to understand and identify the mechanisms that drive crime. In reality, crime is a dynamic process where incidences grow or decline based on population characteristics, interventions, and policies. Previous studies have shown that acts of crime are more prevalent in metropolitan areas. Furthermore, by better understanding spatial-temporal dynamics, we can lessen its impact. The aim of this study is to use statistical models to evaluate the impact of socio-economic factors such as wealth, unemployment rates, and educational levels and how they may play a role on the dynamics of Chicago’s narcotics crime. This study identifies various factors that may influence crime patterns and proposes multi-factor statistical procedures via multiple regressions method to describe the relationship between the input data and the output variables. Our goal is to suggest control policies that have long-lasting effects in controlling crime rates based on changing socio-economic status. This analysis will be able to forecast the probability of occurrence of crime in a community as a function of relevant community-related factors in the past few years. Our further objective is to investigate the impact of socio-economic factors on change in crime rates in each of the 77 community areas of Chicago, therefore providing a systematic procedure for possible intervention methods to lower the rate of narcotic crimes in the city of Chicago.



Horace Deans, Fidel Santamaria.

University of Texas at San Antonio, San Antonio, TX.

Molecular crowding occurs in the presence of a large number of non-reacting macromolecules and can influence the efficiency of biochemical reactions. We want to understand how crowding affects the biochemical reactions underlying cerebellar long-term depression (LTD). To this end, we built a Monte Carlo (MC) simulation based on an earlier mass-action model. LTD is quantified by the reduction in the number of a type of glutamate receptors (AMPAR)


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