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2018 NREUP Projects

 

  • Project Title: Vaccination Games
  • Project Directors: Ajanta Roy
  • Project Summary: The research project we will offer to students belongs to the field of mathematical biology and can be informally called "vaccination games.'' It involves applying game-theoretic methods to individual decisions on the use of personal protective measures against an infectious disease. In particular, it addresses the following fundamental question: Can an infectious disease be eradicated through voluntary participation in personal protective measures, such as vaccination? Individual-level vaccination (or other personal protective measure) decisions can be modeled by game theory since the strategy of a given individual depends on what the rest of the population does: if a sufficient proportion of the population is already immune, then even the slight cost or risks associated with vaccination can outweigh the risk of infection. Students will pick an infectious disease to study. They will use an existing epidemiological model of the disease to obtain the information which is going to be fed into the game-theoretic model of voluntary vaccination decisions for that disease. The students will solve the game-theoretic model and identify optimal vaccination strategies.
  • Project Title: Central Convergence REU
  • Project Director: Brandy Wiegers
  • Project Summary:Central Convergence REU will provide early-career undergraduate students, who have at least a year and a half remaining in their degree program at the time of their REU application, a unique summer research experience that will encourage them to fully immerse in the mathematical professional community. The summer project will begin with a growth mindset-focused training in Mathematica and problem-solving activities to prepare them to approach research problems. Then students will be involved in their research projects in epidemiology modelling and mathematical biology for five weeks, while also receiving professional development mentorship to provide them with the tools and knowledge to be more engaged in the mathematics profession. By the end of the REU, students will have had an authentic mathematical research experience, worked with computational mathematical tools, and practice with multiple forms of mathematical communication including talks, posters, and written articles. Through the coordinated post-REU activities, students will leave the experience being prepared, encouraged, and supported to find future experiences such as other research opportunities, conferences, and related courses as they pursue their careers in mathematics.
  • Project Title:Howard's NREUP
  • Project Director: Dennis Davenport
  • Project Summary:An important goal of this program is to encourage Howard University students from underrepresented groups to compete and succeed in the mathematical sciences. The program seeks undergraduate first and second-year students who have completed at least Calculus II with distinction and have at least a 3.0 GPA. Students will be given continued group support and valuable role models after the completion of the seven-week program. As a follow-up, each student will be required to enroll in a 3-credit hour readings course in the Fall of 2017 to continue their research and to learn more about combinatorics. Another goal is to have academic year undergraduate research embedded into the mathematics curriculum at HU. This project will be used as a proof of concept on how to better use undergraduate research at HU during the academic year. Hence, an important component will be tracking the students once they complete the program.
  • Project Title: Summer Program in Research and Learning (SPIRAL)
  • Project Director: Leon Woodson
  • Project Summary:The primary goal of The Summer Program In Research And Learning (SPIRAL) program is to provide a mentoring structure for underrepresented minorities and women that promotes active engagement in mathematics and statistics through a Research Experience for Undergraduates (REU) program. With a supportive structure, the participants will be encouraged to remain in math and statistics with the hopes that they strengthen the diversity of the talent pool of fully trained mathematicians and statisticians in academia, government, and industry. The 7-week program will be three-pronged: (1) Students will participate in research seminars in math/stat, in which research projects will be investigated in teams. The student will meet with their research team Monday-Friday. Students will participate in scientific lectures in the mornings. In the afternoon, the students will work on research project that relate to the material learned from the morning. Each team writes a research paper and gives an oral presentation. (2) There will be an intensive 5 -week course - emphasizing proof, with problem workshops and daily homework- consisting of three modules, foundations of mathematics, applied mathematics and statistics that connect to the research projects. Graduate students assist the research mentors with the students’ research. (3) One day a week will be devoted to professional development with visits from researchers in industry, academia, and government to share career opportunities.
  • Project Title: Graph Theory and Percolation
  • Project Director: Lazaros Gallos
  • Project Summary:The MAA/NREUP students will be part of the larger DIMACS REU cohort and will be mentored by Rutgers faculty. In this project the students will explore the core concepts of graph theory and percolation. The projects will illustrate the practical potential of mathematical models in applied problems, such as information spreading in social networks or disease transmission. The projects aim to the development of the students mathematical intuition and the improvement of their analytical and modeling skills. The students will form research teams, joined by additional students in the DIMACS REU program. One team will study aspects of multi-layer graph theory in connection to percolation. The other team will study the frog model and focus on modifying various aspects of the model, inspired by possible applications. We will expose the students to a broader range of possible projects, trying to increase their interest to diverse research topics and research areas. Students will participate in planned social and professional activities such as picnics, cultural day, weekly seminars, workshops, and field trips giving the students more opportunities to interact socially. Students will be introduced to industrial research by a trip to DIMACS partner industry (IBM). The students will be given a tour of the facilities and attend several technical presentations. Students will be encouraged to take advantage of DIMACS activities including the many on-going seminars and workshops.
  • Project Title: Experimenting with Mathematica and Magma
  • Project Directors: Mehmet Celik
  • Project Summary:In this summer research program students will look at the following two problems: Conformal maps: If a map preserves the shape of small-scale features, it is conformal. Many problems in the fields of engineering, physics, and mathematics are formulated in regions with “inconvenient geometries”. By a suitable conformal map, one may transform the problem from an inconvenient region into a nice one and after solving the problem by using the same conformal map one can transform the solutions back to its original region. Participants will investigate how smoothness of a conformal map relates to smoothness of a boundary point of a region by using the computer algebra system Mathematica. Linear Complementary Dual Codes from Strongly Regular Graphs: Error-correcting codes are necessary to detect and correct errors in communication. As we increasingly rely on intelligent devices, our automated homes and medical devices are targeted by intruders using side-channel and fault noninvasive attacks. Finding new classes of error correcting codes that can withstand these attacks is crucial to security. Participants will explore codes from adjacency and incidence matrices of strongly regular graphs by using the computer algebra system Magma. Participants will do research by testing with computer algebra systems. The group work will help organizers to maintain communication among participants, set a collaborative learning atmosphere, foster a sense of community, and promote exchange of ideas
  • Project Title:Game Theory and Applications
  • Project Directors: Hyunju Oh
  • Project Summary: Students will be introduced to the fundamental game-theoretical concepts such as Nash equilibria and evolutionarily stable strategy and taught how to use computational tools (NetLogo), as well as analytical tools (optimization and linear algebra) to identify such strategies in real game theoretical models with applications in medicine - “vaccination games” where individuals have to make decisions whether to protect themselves from infectious diseases by taking costly actions such as taking a vaccine. The students will further be trained in all aspects of research, starting with the ethics code, going through the workshops on using library and online resources and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers.
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  • Project Title:Allee Effeccts and Chaos in a Food Chain Model
  • Project Directors: Zhifu Xie
  • Project Summary:In population dynamics, the spatial distribution of populations can be affected by depressed growth rate at lower density, which is called the Allee effect. The Allee effect was shown to bring essential changes to the population dynamics and it has drawn considerable attention in almost every aspect of ecology. However, there is not much work that has been done for food chain or food web models with an Allee effect in prey. An interesting question is how the dynamical properties of a food chain model can change when the prey experiences Allee effects. We propose to investigate the dynamical complexity of the ODE and PDE version with Allee effects in prey. Undergraduate researchers will be asked to investigate numerically and theoretically the possible rich dynamical properties of the ODE version. They will learn how to conduct linear stability analysis on equilibrium solutions to understand the long-time behavior of the predators and prey in an ODE system. Several workshops will be held for them regarding (A) how to read research paper, (B) how to write a research paper and use LaTex, (C) how to prepare for a poster or oral presentation, and (D) how to apply to graduate school. Students are expected to submit a final report in a research paper format and give a presentation in local or national conferences. Students may also continue to work with mentors on the PDE version of the problem in the Fall semester of 2017.
  • Project Title: Stochastic Burgers Equations and Extensions
  • Project Directors: Tamer Oraby
  • Project Summary:We are planning to host an REU event. It will involve training four undergraduate students on two problems with the promise of submitting the results to peer-reviewed journals. The research problems that we are proposing for this REU are challenging but certainly doable within the 8 week time frame we have outlined, particularly with the support of the short courses as an intense review of differential equations (which they have all studied either currently or in a previous semester) and focus on the specific areas they will need to apply to our research questions. We have taught these courses many times before and are confident that we will be able to tailor the course content to our individual needs and time constraints. We are also enthusiastic about structuring in time for practice and application of mathematics modeling programs like MATLAB and Mathematica; these skills will serve our students well through their last years as undergraduates, throughout their graduate studies, and beyond.
  • Project Title: Enhancing and further developing emerging non-smooth optimization methods
  • Project Director: Milagros Loreto
  • Project Summary:During the NREUP at University of Washington Bothell (UWB), the students will be introduced to fundamental concepts in nonsmooth optimization such as subdifferentials, optimality conditions and step lengths. Spectral Sampling Gradient (SpecSampling) and Modified Spectral Projected Subgradient (MSPS) are emerging nonsmooth optimization methods. Students will work in one of these two projects: 1) Enhancing and further developing the SpecSampling, where they will learn about the SpecSampling and develop a suitable nonmonotone linesearch technique; 2) Correcting zigzagging of kind II for the MSPS, where they will learn about MSPS and develop heuristics to correct zigzagging behavior of it. They will learn how to use computational tools such as MATLAB to implement the artifacts described above, and to conduce a broad numerical experimentation. The NREUP at UWB will provide an integral program to prepare students on researching, writing and reporting about that research using LATEX, communicating and presenting results, deciding about their own future as researchers and understanding the impact of diversity and inclusion on their work. The PI expects to submit at least two papers to referee-based journals, and to present this work at local conferences and the next Joint Mathematics Meeting.

 

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