The SIAM-Simons Undergraduate Summer Research Program establishes five sites across the United States each year for a summer program of research and learning in applied mathematics and computational science.
Students accepted to the program will:
This program targets U.S. students from groups underrepresented in applied mathematics and computational mathematics in the U.S., specifically ethnic minorities (African American/Black, Hispanic, Native American/Indigenous Peoples, Native Alaskan, Native Hawaiian/Other Pacific Islander). The program is intended to broaden participation in mathematics by students who are underrepresented and historically marginalized in our discipline.
Applications to participate in summer 2024 are closed. Applications for summer 2025 will open in December of 2024.
You are eligible to apply if you meet the following criteria:
Applicants will be asked to submit:
Interest Rate Modeling and Asset Pricing in Incomplete Markets
The modern approach to quantitative finance is as deeply connected to the mathematical tools utilized as it is to the financial economic theory it is based upon. In this project, we will apply basic linear algebra, optimization, and statistical tools to the areas of research and practice in the financial, banking and insurance sectors. Our approach is two-fold: In the area of fixed-income securities, we will utilize a time series econometrics-based framework to the modeling, analysis and forecasting of interest rate dynamics. In the area of behavioral finance, we will apply option-theoretic approach to explore the issues in pricing and optimization in incomplete markets.
Mentor: Sooie-Hoe Loke
Characterizing Biological Patterns Using Optimal Transport and Topological Data Analysis
Patterns are present all around us in nature: examples include butterfly wings, stripes and spots in fish skin, venation on leaves, and fur on cats. Across these examples, determining whether two patterns are similar or different is often a qualitative process. But how similar is “similar”, and in what ways are two images of biological patterns different? Addressing this question can help provide insight into when genetic mutations and evolution give rise to different patterns and tissue. To do so, we need quantitative approaches that allow us to summarize many patterns in detail. In this project, we will distinguish and characterize images of biological patterns using computational methods from optimal transport and topological data analysis. For example, we may use persistent homology to quantify the “shape of data” or apply optimal-transport approaches to “morph” one image of a biological pattern into another and measure the difference between them.
Mentor: Alexandria Volkening
Fun at the Intersection of Linear Algebra and Probability
Our project will focus on strengthening our foundation in linear algebra. We will study randomized methods for efficiently representing the column space (range) of matrices in order to build robust and effective algorithms for facial recognition, music recommendation and cancer detection.
Mentor: Henry Boateng
Data Augmentation Applied to Tabular Data
Classification methods have become valuable tools in multiple sectors of society. Examples of classification applications include self-driving cars, ad targeting, fraud detection, face recognition, protein function prediction, and medical diagnosis. Due to its extensive use, scientists have developed powerful machine-learning techniques for data classification. One of the issues with current state-of-the-art classification approaches, such as deep learning, is that these require lots of data. However, collecting sufficient data to create reliable models is not always possible. For example, data collected from patients can be time-consuming and costly or even impossible if they no longer want to participate in the data collection. In Computer Vision, researchers get around the lack of data by applying data augmentation approaches. Data augmentation refers to creating new data points without collecting any further data. For example, in Computer Vision, new images are created by rotating, scaling, flipping, or recoloring the original image set. This process is applied so that machine learning techniques have large enough data sets to classify data accurately. We will develop and test our data augmentation methods with real tabular data, or data organized by rows and columns, to see how well our techniques keep the intrinsic patterns and if accuracy is improved.
Mentor: Dr. Vazquez Landrove
Biomimetic Design Criteria for Self-Assembly and Self-Folding Viral Capsid Models
Many complex biological structures are formed by random processes (entropy-driven), and we seek to understand how complex, beautiful structures self-organize. In our lab, we are particularly focused on viral capsids such as the now familiar COVID structure that has recently received so much attention. We will focus on three avenues: (1) self-folding origami: developing new measurable variables associated with symmetry properties of planar nets of icosahedra and testing them with an origami simulator to see which nets fold quickly, completely, and without imperfections; (2) self-assembling physical models: developing quasicrystalline models (e.g., using tiles such as the recently discovered uni-tiles as well as Penrose kites and darts) of viral capsids and seeing if we can get them to self-assemble; and, (3) conducting form finding analyses of tensegrity expandohedra models of viral capsids: build models that expand from an icosahedron to an icosadodecahedron. Geometrically, viral capsids are of two different types: icosahedra (and higher level versions with 60, 120, 180, etc. individual subunits) and helices. Some icosahedra-type viral capsids do not fit a classic Goldberg polyhedral model, but are quasicrystals instead. We have successfully produced 4D printed (both self-assembled and self-folded) meso-models of viral capsids with up to 60 subunits. We have a database of Dürer nets and Schlegel diagrams of all 43, 380 configurations of dodecahedra and icosahedra. Besides building physical models that self-fold by placing them in warm water, we analyze their self-follding by using an origami simulator. While we have analyzed many configurations for their foldability and found that the number of vertex connections on a Dürer net is well correlated to self-foldability, there is considerable variation within vertex connections subgroups. If you enjoy three dimensional puzzles and visualization, learning about 3D printing and laser cutting, and mathematical problem solving, please consider coming to our lab at the Delaware Biotechnology Institute at the University of Delaware.
Mentor: John R. Jungck
Mentors are selected from SIAM’s experienced and highly qualified member base to work closely with the student participants and SIAM. While mentors do oversee the research activities of the participants, they also serve as a primary connection between the participants and the applied math community broadly, helping them feel connected and welcomed.
Applications to be a mentor for summer 2024 are closed. Applications for summer 2025 will open in summer 2024.
The Simons Foundation, co-founded in 1994 by Jim and Marilyn Simons, works to advance the frontiers of research in basic science and mathematics. The foundation provides grants to individual investigators and their projects through academic institutions and conducts in-house scientific research supporting teams of top computational scientists through its Flatiron Institute. Jim and Marilyn Simons co-chair the foundation’s board.
SIAM is incredibly grateful to the Simons Foundation for funding this important program (award number 1036702) that will provide support and career advancement opportunities for undergraduate students who are historically underrepresented in the mathematical and computational sciences.
Computational Methods for Inverse Problems in Imaging In this project, we will work on developing computational methods for solving inverse problems arising from imaging systems. Most of these problems are ill-posed, which means, in most cases, that the solution is very sensitive to the data. Since the data usually contain errors produced by the different imaging systems (e.g., cameras, sensors, etc.), robust and reliable regularization methods need to be developed for computing meaningful solutions. Furthermore, in most imaging systems, massive amounts of data are produced which makes the acquisition and the storage of data and the computational cost of the inversion process intractable. To deal with these issues, we will investigate the algebraic tensor structure of the data, apply dimension reduction techniques and study its impact in the inversion process.
Participants: Kelsi Anderson and Ashley Ramsay-Allison
Mentor: Malena Español
Program MASTER: Modeling, Analysis and Simulation for the grand challenges through innovative Training, Education and Research Over the years, the importance of mathematical modeling and its applications to solve real-world challenges has been rapidly increasing. Also, there is a great demand for combining modeling with multidisciplinary problem-solving competencies and life-long learning skills for addressing the global challenges such as, understanding the dynamics of COVID-19 epidemic to impact of Domestic Violence. This program will expose two motivated undergraduate students to advanced topics in mathematics, problem-solving, data driven approaches, computing, visualization techniques and multidisciplinary applications. The program will also greatly enhance the awareness of the ever-increasing utility of mathematical approaches in understanding biological, engineering and bio-inspired systems and how they can help contribute to the scientific and professional development of students at all levels.
Participants: Adan Baca and Diego Gonzalez
Mentor: Dr. Padmanabhan (Padhu) Seshaiyer
Identifying Novel Biomarkers for Cancer Treatment Personalization This project will focus on analyzing clinical data and developing mathematical models to identify novel biomarkers for cancer treatment personalization. We are situated in the unique Integrated Mathematical Oncology (IMO) department at Moffitt Cancer Center, the only math department within an NCI-designated cancer center. The IMO is a highly interdisciplinary and collaborative department with researchers from various backgrounds.
Participants: Moriam Animashaun and Layla Montemayor
Mentors: Dr. Heiko Enderling and Dr. Renee Brady-Nicholls
Minimum Cycle Basis for Pose Graph Optimization Pose graph optimization (PGO) is a fundamental problem that arises in various research disciplines, like simultaneous localization and mapping (SLAM), structure from motion, calibration of multi-camera rig, and sensor network localization. For this project, we will focus on the minimum cycle basis problem and its usage for pose graph optimization.
Participants: Rachel Ahumada and Drake Lewis
Mentor: Dr. Illya V. Hicks
Cost/benefit analysis of yearly mammograms: a social justice approach to individualized medicine The current U.S. guidelines state that women over 40 need to get a mammogram every year. Some researchers claim that the recent decrease in breast cancer deaths can be attributed to this recommendation. However, mammograms are invasive and known to have a high rate of false positive diagnosis. Other countries have piloted different requirements depending on family history, breast density, among other factors. In this project we will take a data driven approach to propose personalized testing protocols that will take to account factors such as family history and breast density while trying to offer solutions that take into account access to health care, economic background, race and other markers that have a significant impact on health outcomes.
Participants: Amira Claxton and America Jarillo-Montero
Mentor: Dr. Alicia Prieto-Langarica
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