Grants & Awards
Research in the Mathematical Sciences at WPI is well funded, thanks to numerous grants and awards. Find out more about our faculty’s most recent grants and awards below.
Collaborative Research: A Predictive Theory of Muscle Energy Consumption
National Institutes of Health
The NIH award is titled Collaborative Research: A Predictive Theory of Muscle Energy Consumption. This work will develop mathematical models to predict the amount of chemical energy that muscles need to contract, an advance that could lead to improved medical treatments and the creation of better prosthetic devices. This is in collaboration with Walter Herzog at the University of Calgary, Manoj Srinivasan at The Ohio State University, and Edward Debold at the University of Massachusetts, Amherst.
For more information, please see: https://www.wpi.edu/news/wpi-researcher-awarded-14-million-develop-model-predicts-energy-needed-muscle-movement
Award Amount: $1.4 Million
New Techniques to Combine Measures of Statistical Significance from Heterogeneous Data Sources with Application to Analysis of Genomic Data
National Science Foundation
This project is motivated by integrative analysis of large-scale genomic data, where an important question is how to effectively combine statistical significances, or p-values, from heterogeneous data sources. Despite recent advances in theoretical and applied studies, statistical and computational challenges remain in addressing critical data features, such as complex correlations, discreteness of data, and availability of prior knowledge that could have been utilized to boost signal detection. This project will develop novel statistical methods to address the challenges and increase the statistical power for detecting valid signals. The research will facilitate innovations in statistical theory and methodology as well as in broad applications. The research activities will leverage project-oriented education, promote multi-disciplinary interactions, and benefit STEM education for the next generation of engineers and scientists, especially members of minorities underrepresented in the statistics field.
For more information, please see: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113570&HistoricalAwards=false
Award Period: August 2021 - July 2024 Award Amount: $200,000
Collaborative Research: Multiscale Simulations and Imaging of Viscoelastic Media in Reduced Order Model Framework
National Science Foundation
The 3-year NSF award is titled “Collaborative Research: Multiscale Simulations and Imaging of Viscoelastic Media in Reduced Order Model Framework” and is joint with Elena Cherkaev (University of Utah) and Murthy Guddati (NCSU). Vladimir is the PI on the WPI part of the award ($159,552). In Vladimir's own words: The foundation of this project is the Stieltjes-Krein (elastic) network realization of data-driven reduced order models that we previously developed for imaging in oil exploration and defense applications. We plan to extend this approach to non-Stieltjes viscoelastic networks and apply it to non-destructive testing and medical imaging.
For more information, please see:
Award Period: August 2021 - July 2024 Award Amount: $159,552
Direct adjustment in combination with robust or nonlinear regression: software and methods for RDDs, RCTs and matched observational studies
Department of Education/Institute of Education Sciences (IES)
Sales, A., (Co-PI, WPI PI), Hansen, B (PI) (University of Michigan), Bowers, J., (Co-PI), Errickson, J., (Co-PI)
Adam is a co-PI (WPI PI) with a team of researchers (Profs. Hansen, Bowers, and Errickson) on this grant funded through the Department of Education by the Institute of Education Sciences (IES). In Adam's own words: This grant is to develop a suite of methods and software for estimating treatment effects in a wide range of randomized experimental designs and observational studies common in education research. The tools we develop will allow researchers to separate covariate models--models of outcomes and treatment assignment, conditional on covariates--from effect estimation, while ensuring that standard errors are valid. For more information, please see:
Award Period: March 2021 - February 2024 Award Amount: $785,482
Improving the Power of Education Experiments with Auxiliary Data
Department of Education/Institute of Education Sciences (IES)
Sales, A., (Co-PI), Gagnon-Bartsch, J. (University of Michigan), Heffernan, N. (WPI).
Professor Sales is a co-PI with a team of researchers (Prof. Gagnon-Bartsch at University of Michigan and Prof. Neil Heffernan at WPI). This is a three-year grant funded through the Department of Education by the Institute of Education Sciences (IES). In Adam's own words: Data for analyzing randomized experiments are often drawn from larger databases, such as state longitudinal data systems for educational experiments or log data for A/B tests run on technology platforms. This project investigates ways to incorporate covariate and outcome data from outside the randomized experiment to improve the power and precision of experimental causal estimates, without sacrificing the advantages of experimentation. For more information, please see:
Award Period: March 2021 - February 2024 Award Amount: $576,429
Bayesian Models for Cash Rents of U.S. Counties
National Agricultural Statistics Service (NASS, USDA)
In Professor Nandram's own words: This work at NASS is to develop Bayesian small area models to get reliable estimates of cash rental rates. I also advise researchers at NASS on the use of these small area models, which use Markov chain Monte Carlo methods extensively and routinely. NASS informs many crop insurance and agricultural support programs administered by other agencies such as the Farm Service Agency (FSA) and the Risk Management Agency (RMA). Many farmers rent their lands to other farmers, and it is useful to know annually what a fair price is by practice (irrigated, non-irrigated, and pasture land) for each of 49 states consisting of nearly 3000 counties with nearly two million operations. Data are collected in the annual Cash Rent Survey and other sources of information (e.g., the Census of Agriculture) are also used, particularly last year's data. Models must be operationalized to provide fast analysis and precise positive estimates of cash rental rates with standard errors. This is a very important on-going activity at NASS because NASS is responsible to the US government to perform this research activity.
Award Period: 2021-2022 Award Amount: $262,000
Cargo Transport by Myosin Va and Kinesin-1 Molecular Motors: In Vitro Model Systems that Build Complexity in 3-Dimensions
Walcott, S., (co-PI), Warshaw, D. (Pi)
In Sam's own words: The Warshaw lab performs molecular-scale biophysical measurements, and my group develops multi-scale mathematical models. The overall objective of this project is to build a mechanistic understanding of how molecular motor-based intracellular transport is both achieved and regulated. My role is to build predictive mathematical models of the experimental system developed by the Warshaw lab, including myosin Va and kinesin molecular motors, actin and microtubule protein filaments, liposome cargos, adapter proteins and microtubule- and actin-binding proteins.
For more information, please see: https://reporter.nih.gov/project-details/10204620
Award Period: May 2021 - April 2022
Fully Latent Principal Stratification: A New Framework for Big, Complex Implementation Data from Education RCTs
Department of Education by the Institute of Education Sciences (IES)
Sales, A. (co-PI), Khang, H, (co-PI), Whittaker, T., (PI)
In Adam's own words: Randomized field trials of interventions in education, health, and other areas often gather complex, rich data on how the intervention is carried out. For instance, in interventions involving educational technology, researchers gather computer log data of students' actions within the program. There is broad agreement that implementation data is important, but little guidance on how best to use it to understand treatment effects. This project develops a framework for using modern measurement models to summarize complex implementation data, and then to estimate different average treatment effects for groups of subjects who implement (or would implement) the intervention in different ways.
For further information on this award, please visit https://ies.ed.gov/funding/grantsearch/details.asp?ID=4544
Award Period: 2021-2024 Award Amount: $891,895
Synoptic Engineering (Prime: DARPA)
In this project WPI is working with Synoptics Engineering (Prime: DARPA) on using machine learning to study electromagnetic scattering problems. The key idea is to train deep neural networks on far-field scattering patterns and use these deep neural networks to infer properties of the scattering medium.
Award Date: May 2021
CRII: AF: Optimization and sampling algorithms with provable generalization and runtime guarantees, with applications to deep learning
Division of Computing and Communication Foundations (CCF) at the National Science Foundation
In Professor Mangoubi's own words: "The aim of this project is to design novel optimization and sampling algorithms for training deep learning and other machine learning models, and to prove guarantees on the running time, generalization error and related robustness properties of these algorithms. Training algorithms with good generalization properties can lead to machine learning models which are more robust to changes in the dataset, allow for robust predictions, and help mitigate algorithmic bias when the training dataset may not be fully representative of the diversity of the population dataset. Guaranteeing a low generalization error is especially challenging in deep learning, since the number of trainable parameters is oftentimes much larger than the size of the dataset, and the loss function used to train the model is nonconvex. To prove stronger generalization and related robustness guarantees, we will use ideas from manifold learning and differential geometry to model the low-dimensional structure of datasets which arise in many machine learning applications."
For more information, please see:
Award Period: 2021-2023 Award Amount: $174,187
Bayesian Models for Cash Rents by Agricultural Practice
IPA Agreement with USDA
US Dept. of Agriculture
Award Period: 2020-2021 Award Amount: $149,574
Bayesian nonignorable nonresponse and selection models for small areas
Award Period: 2015-2021 Award Amount: $35,000
Data Sciences, AI and Machine Learning for Army Applications
Army Research Lab (ARL)
This project is focused on research in several disciplines from material science to data science and statistics to support the missions of the Aviation & Missile Center Technology Development Directorate. Our aim is to provide sound statistical and data science methodologies and data analysis for their research development and applications. The project is a two-year grant totaling $854,000 awarded to PI Prof. Rundensteiner, and Co-PIs Profs. Zou, Emdad, Zhang, and Kong.
Award Period: 2019-2021 Award Amount: $854,000
NRT-HDR: Data Driven Sustainable Engineering for a Circular Economy
National Science Foundation
This project is focused on training graduate students in disciplines from chemical science to data sciences to advance and support the future of circular economies. Our aim is to produce students versed in data-driven sustainable engineering that can have an impact on society. The project is a five-year traineeship grant totaling $2,999,289 awarded to PI Prof. Rundensteiner, and Co-Pis Profs. Paffenroth, Titova, Timko, and Deskins. For more information on this award, please visit https://www.nsf.gov/awardsearch/showAward?AWD_ID=2021871
Award Period: 9/1/2020 - 8/31/2025 Award Amount: $2,999,289
Modeling the dynamics of spindle behavior in cells with supernumerary centrosomes
NIH (R01 GM140465-01)
In Professor Olson's own words: Mitosis is the process of cell division, involving an intricate balance of forces to ensure a successful result—two genetically identical daughter cells. In normal cells, the mitotic spindle contains two spindle poles (bipolar), each having microtubules nucleated from a centrosome. Cells in disease states may have extra centrosomes, leading to either formation of a multipolar spindle and multiple daughter cells with poor viability, or formation of a pseudo-bipolar spindle with daughter cells that are viable. A hallmark of cancer cells is the ability to successfully divide with extra centrosomes. Through a combination of live-cell imaging and model simulations, we will provide new fundamental knowledge and insight into how the normal mitotic machinery has been co-opted to allow for bipolar division in cells with extra centrosomes. The developed modeling frameworks for fluid-structure interactions will lead to new computational methods that will leverage high performance computing architectures to simulate centrosome movement and stochastic MT dynamics.
Award Period: 9/5/2020 - 6/30/2023 Award Amount: $916,956
Valid time-series analyses of satellite data to obtain statistical inference about spatiotemporal trends at global scales
NASA/University of Wisconsin-Madison
Start Date: 2/21/2020 (2 years). Amount: $174,762.00
As remote sensing has matured, there is a growing number of datasets that have both broad spatial extent and repeated observations over decades. These datasets provide unprecedented ability to detect broad-scale changes in the world through time and to forecast changes into the future. However, rigorously testing for patterns in these datasets, and confidently making forecasts, require a solid statistical foundation that is currently lacking. The challenge presented by remotely sensed data is the same as its remarkable value: remotely sensed datasets consist of potentially millions of time series that are non-randomly distributed in space. We propose to develop new statistical tools to analyze big, remotely sensed datasets that will add rigor to the conclusions about patterns of past changes and confidence to forecasts of future trends. Our focus is providing statistical tests for regional scale hypotheses using pixel-scale data, thereby harnessing the statistical power contained within all of the information in remotely sensed time series.
Portable multiplexed chemical agent sensor for detection in obscurant-heavy environments
DTRA and CCDC-SC
Start Date: 2020 (3 years).
This project is focused on combining machine learning with chemical sensor arrays to reduce false alarm rates in challenging environments. The project leverages our groups recent work in applying machine learning techniques to problems from the physical sciences. The project is a multi-party effort between WPI, CCDC-SC, Seiksui Chemical Co., and UMass Amherst. The project is an up to $1.8 million award to the team, and up to $249,000 of that amount is expected to support our group’s work on the project over the next three years.
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DeepM&Mnet: A General Framework for Building Multiphysics & Multiscale Models using Neural Network Approximation of Functions, Functionals, and Nonlinear Operators
Brown University (Prime: Defense Advanced Research Projects Agency)
Start Date: June 15, 2020 (3 years). Amount: $149,854
The proposal focuses on mathematical analysis for the neural network approximation (NNA) as well as the design of efficient deep learning algorithms for multiphysics and multiscale systems. The key idea is to train NNA for separated systems offline and then combine all the trained networks to solve multiphysics systems online. The research will result in fast and reliable solvers for multiphysics and multiscale systems. The main goal of the WPI investigator is to analyze and to improve the performance of the NNA as universal approximations in learning functions, functionals, and nonlinear operators and fusion of all pre-trained networks to solve multiphysics systems.The project is collaborative with Brown University and John Hopkins University
Simulating Large-Scale Morphogenesis in Planar Tissues
National Science Foundation, DMS 2012330
Start Date: 6/15/2020 (3 years). Amount: $200,000
Cutting-edge developments in biotechnology and medicine involve reconstructing large-scale tissues and organs. This work can be limited by lack of knowledge in tissue morphogenesis, the process by which living tissues develop their size-and-shape characteristics. Though live-imaging techniques have enabled the observation of morphogenetic processes, progress in fundamental understanding has been slow. This project aims to improve tools for modeling a wide range of living tissues that are relatively planar and have been extensively studied experimentally. The project will develop methods for numerical simulation of morphogenesis processes and attempt to reproduce the observed large-scale morphogenesis structures in planar tissues. The project provides graduate student training through involvement in the research.
This project concerns numerical simulation of large-scale continuum models for tissue morphogenesis that involve free boundaries, bulk-interface coupling, and highly nonlinear interactions. The work centers on a new mathematical model in which the field variables are nonlinearly coupled via reaction-convection equations and non-standard spatial partial differential equations. The project will develop semi-implicit and fully implicit time-stepping methods to avoid a potential time-step restriction for explicit time-stepping methods. Due to the high nonlinearity of the system, the boundary configuration must be updated together with the velocity field as well as other field variables. For this purpose, a novel interface-tracking method based on reference-map techniques will be investigated. Linear analysis close to trivial solutions will be conducted to assist the design of fast-converging iterative methods for solving the nonlinear system derived from the implicit time-stepping discretization of the original model. Simulations to understand in vitro micro-tissue and in vivo epithelial-tissue morphogenesis from live-imaging data will be carried out.
For more information on this grant, please visit https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012330&HistoricalAwards=false
Applications of Quasiconformal Geometry and Partial Differential Equations
National Science Foundation, DMS 1955992
Start Date: 7/1/2020 (3 years). Amount: $187,987
Partial Differential Equations (PDE) are used to model real life systems, and in particular, subelliptic PDE are helpful in settings where there is a constrained dynamics. Examples of such systems include the motion of robot arms, structural functions of the first layer of the mammalian visual cortex, the Black-Scholes model for financial markets and quantum computing. Geometric and analytic properties of such spaces are captured in a quantitative fashion by studying the behavior of certain families of transformations of the space into itself. This project aims at studying fine properties of such transformations. In terms of broader impacts, the PI will involve graduate and undergraduate students in several aspects of the research and design outreach activities to attract K12 students to mathematics.
The technical focus of the proposed research addresses a curve shrinking flow in Carnot groups, the study of harmonic extensions of quasiconformal mappings between boundaries of certain Gromov hyperbolic spaces, and regularity of certain nonlinear, degenerate parabolic PDE.
For more information on this grant, please visit https://www.nsf.gov/awardsearch/showAward?AWD_ID=1955992&HistoricalAwards=false
Vladimir Druskin receives $200,000 award from Air Force Research Laboratories for “Active Array Imaging in Complex Media in the Presence of Losses and Dispersion Effects”
In Vladimir’s own words: This project is focusing on extension to the air force imaging applications of the novel data-driven model reduction approach introduced earlier by the PI and his collaborators. The scope includes algorithmic development and mathematical justification of this approach for radar imaging in strongly inhomogeneous media with multiple scattering (echoes) effects, losses and dispersion.
Learn more about Vladimir Druskin
Total award period: July 2020 - June 2023 Award amount: $200,000
Christopher Larsen receives $250,000 award from the Division of Mathematical Sciences (DMS) at the National Science Foundation "New Mathematical Methods for Dynamic Fracture Evolution"
In Professor Larsen's own words: "For a large range of applications, from civil infrastructure to national defense, understanding the failure of materials is critical. Yet, our ability to predict this failure is limited by both modeling, which is somewhat ad hoc, and the mathematics available to formulate and analyze models, as well as to justify numerical methods. These issues are most severe in dynamic problems, such as impacts, when loading changes quickly. The main goal of this project is the development of new mathematical methods for dynamic fracture evolution. In particular, the principal investigator (PI) will extend methods for regular crack paths to more realistic paths, with kinking and branching. A second goal is to address fundamental mathematical issues that are necessary for further progress in completely general settings. Finally, the PI will study phase-field approximations of fracture, which have become very popular tools in the engineering community but remain poorly understood.
The ability to accurately predict failure depends on the quality of the underlying mathematical models of defects as well as on understanding fundamental properties of solutions. When crack paths are regular, mathematical methods are available to study these evolutions. However, when they are not, the only methods so far involve considering the paths to be limits of more regular paths. The main technical issue here is that strong convergence of the corresponding elastodynamics is necessary for energy balance, as well as for other properties of solutions, but this convergence remains open in many situations. Another fundamental issue is uniqueness of elastodynamic solutions for a given crack path. The investigator will show uniqueness in certain settings, and explore general consequences, such as bounds on crack speed. The final goal of the project is to analyze phase-field models for fracture. While very popular in the engineering community, a number of properties, including whether they approximate the correct surface energy, or satisfy a maximal dissipation condition, remain open questions."
For more information please see https://www.nsf.gov/awardsearch/showAward?AWD_ID=1909991&HistoricalAwards=false
Total award period: 2019-2022 Award Amount: $250,000
Further Advancing the Northeast Combinatorics Network
National Science Foundation
Martin, W., (Co-PI), Ellis-Monaghan, J., (PI)
Start Date: 3/1/2019 (3 years). Amount: $39,000
The Northeast Combinatorics Network (NCN) will host several events including Spring and Fall Discrete Math Day (DMD) conferences and a Summer Combo conference as well as a Virtual Combinatorics Colloquium series in each year of the three-year project. The Spring 2018 DMD will be hosted at UMass Amherst, https://sites.google.com/view/umass-dms/dmdspring19, and universities in the region are being given the opportunity to host the remaining five DMD meetings. This project aims to further cultivate and enhance a network of students, post-doctoral researchers, faculty and industry mathematicians spread across the institutions in New England and New York working in the area of combinatorics (discrete mathematics), which is a thriving and rapidly advancing mathematical discipline.
Further information on this grant can be found at https://www.nsf.gov/awardsearch/showAward?AWD_ID=1853455&HistoricalAwards=false
Andrea Arnold receives 2019 Women's Impact Network (WIN Impact) Grant
Assistant Professor Andrea Arnold has received the 2019 Women’s Impact Network (WIN Impact) Grant “Sonia Kovalevsky Day: Math Outreach Initiative for Female Middle-School Students”. The grant will support Andrea’s initiative in organizing SK days at WPI. In her words:
Sonia Kovalevsky Days (SK Days) are nationally-held, locally-organized outreach events with the aim of supporting and encouraging young women to continue their study of mathematics (https://awm-math.org/programs/math-outreach/). The recently-formed WPI Chapter of the Association of Women in Mathematics (AWM) is planning to host an SK Day outreach event on campus this spring, specifically targeting the participation of local female middle school students. The day's events will include math activities and problems for the students, as well as a keynote talk from Dr. Misha Kilmer (Tufts), with volunteers from the WPI community. This year's inaugural event is scheduled for Saturday, March 23, 2019, with plans to host subsequent events annually each spring. This award will support the funding of SK Days at WPI for the next two years, to be held in Spring 2019 and Spring 2020
Total award period: 07/01/2019 - 06/30/21 Award Amount: $10,500
Professor Suzanne Weekes named winner of prestigious Humphreys Award
The Executive Committee of the Association for Women in Mathematics has established this prize in memory of M. Gweneth Humphreys to recognize outstanding mentorship activities. The prize is awarded annually to a mathematics teacher (female or male) who has encouraged female undergraduate students to pursue mathematical careers and/or the study of mathematics at the graduate level
This award is named for M. Gweneth Humphreys (1911–2006). Professor Humphreys earned her master’s degree from Smith College and her PhD at age 23 from the University of Chicago in 1935. She taught mathematics to women for her entire career, at Mount St. Scholastica College, Sophie Newcomb College, and for over thirty years at Randolph-Macon Woman's College. This award, funded by contributions from her former students and colleagues at Randolph-Macon Woman's College, recognizes her commitment to and her profound influence on undergraduate students of mathematics.
Professor Suzanne Weekes exemplifies fully the tradition of Gweneth Humphreys. Through her research, her project advising, her REU leadership, her CIMS activities and more, she has contributed significantly to our mission, as few others have. Dr. Weekes’ track record in mentoring students (and faculty!) is superb and extends well beyond WPI, to her work with PIC math, and includes her impactful service in MSRI-UP.
For more information about the Humphreys Award, please see https://www.wpi.edu/news/wpi-mathematician-receives-prestigious-teaching-award
Burt Tilley and Vadim Yakovlev receive $775,336 award from AFOSR titled ``Permittivity Gradients, Polarization, and Gas Dynamics in Composite Electromagnetic Heat Exchangers’
In Professor Tilley's and Professor Yakovlev's own words, the project consists of a five-year research program to quantify the fundamental heat-transfer processes in the conversion efficiency from incoming electromagnetic radiation into elevated internal energy of a compressible coolant. The idea is to use electromagnetic-radiation absorbing materials, either porous or designed with channels through which a coolant can flow, that can withstand temperature up to 2000 K, heat these materials through the application of electromagnetic waves, and then run coolant through the material to harness the desired energy. Since electrical conductivity of these materials depends on temperature, multiple steady temperatures are possible at the same input power. The research program centers on using asymptotic multiscale methods including homogenization to formulate an effective medium theory to describe the energy conservation and electric field propagation through this medium, for incompressible and compressible coolants. The spatial variation of loss factor will be examined in order to compensate for conduction losses found at higher temperatures, and as a simple model for metal-ceramic composites. These results depend on the examination of the energy transfer between the composite and the coolant, and we shall consider these modes for incompressible and compressible coolants. Three-dimensional electric field amplitude equations, developed in our current award using high-frequency homogenization, will be extended to incorporate heat transfer, viscous fluid flow spatial dimensions, and comparisons with solutions using finite-difference time-domain and with finite-element methods will be performed. The goal is to develop a systematic method to better understand wave propagation, heat transfer and power delivery to the coolant for a general three-dimensional spatially-periodic microstructure.
Award period: September 2018 - August 2023 Award amount: $775,336
Luca Capogna Receives Five-Year Grant to Use Mathematics to Classify and Understand the Nature of Shapes
Luca Capogna, professor and head of the Department of Mathematical Sciences, has received a five-year, $42,000 grant from the Simons Foundation, a 24-year-old organization that funds research into mathematics and the sciences. The project being funded is titled “Topics in Nonlinear PDE and in Quasiconformal Mappings.”
The goal of Capogna’s research is to classify all possible shapes—whether the curls of a lettuce leaf shape or the space swept up by a robot arm as it moves through all of its possible configurations—using a mix of geometry and analysis methods. By better classifying and understanding shapes, scientists will better understand their nature and how they behave.
The research should enable Capogna to determine whether or not two spaces are similar. For instance, two shapes may look very different but have hidden similarities, from a mathematical perspective.
Capogna’s project, which is a continuation of research he’s been conducting for the past 10 years, could ultimately be applied to the study of cloud computing or even social networks. For instance, he is using mathematical models that relate to curved spaces, such as a curling lettuce leaf, to understand spaces that expand very quickly, a technique that connects a leaf that takes up more space as it uncurls to a cloud of data or a social network that rapidly expand in size.
Award Date: July 31, 2018 Total Award Amount: $42,000
Research Experiences for Undergraduates in Industrial Mathematics and Statistics
National Science Foundation
The Worcester Polytechnic Institute (WPI) REU in Industrial Mathematics and Statistics provides a distinctive educational experience for students in the mathematical sciences by introducing them to the ways in which mathematicians and statisticians use math in the "real world". Students work in teams on research problems of industrial and mathematical significance that come directly from industry and that are of immediate interest to the companies involved in the program. Students work closely with company representatives to define the problem and to develop solutions. They work closely with faculty advisors to maintain a clear focus on the mathematics and statistics at the core of the project. This summer research provides challenges not faced in traditional undergraduate programs and helps to develop skills usually not addressed in academic programs. It also provides a glimpse of some of the many career possibilities that are open to students with a strong mathematical background. For further information on this grant, please visit https://www.nsf.gov/awardsearch/showAward?AWD_ID=1757685
Total Award Period: February, 2018 to January 31, 2022 (estimated) Total Award Amount: $299,606
William Martin Receives $150,000 NSF Grant to Further Our Understanding of Association Schemes
William Martin, professor of mathematical sciences, has received a three-year, $150,000 grant from the National Science Foundation for a research project titled, “Association Schemes and Configurations in Real and Complex Space.”
The project is aimed at taking on questions that have stumped the best mathematical minds in the world for decades. Martin is looking to advance mathematicians’ understanding of association schemes, which are finite combinatorial structures that can be viewed algebraically, geometrically, or as highly symmetric networks.
Finding new association schemes, or even better understanding them, could enable researchers to use one quantum computer to simulate another. They also could be used to discover new error-correcting codes for digital communications, new spherical designs for estimating solutions to calculus problems in high-dimensional space, or new secure scrambling components for symmetric key encryption.
Martin is working on underlying algebraic theorems that will lead to a stronger mathematical theory, though he said he is focused on making advances that other researchers can then use in their own work, to solve problems in various applied areas.
At least one PhD student and multiple MQP teams will be working on the project.
Further information on this award can be found at https://www.nsf.gov/awardsearch/showAward?AWD_ID=1808376&HistoricalAwards=false
Total Award Period: 2018 - 2022
Zheyang Wu Receives NSF Award for Work Related to ALS
Zheyang Wu, associate professor of mathematical sciences, has received a three-year, $150,000 award from the National Science Foundation for a project titles, “Optimal and Adaptive p-Value Combination Methods with Application to ALS Exome Sequencing Study.” The project is focused on developing tests that will give scientists a better understanding of which DNA segments are related to ALS susceptibility. Using ALS exome-sequence data, researchers will develop better data analysis methodology to paint a clearer picture of how genes influence ALS.
ALS, or amyotrophic lateral sclerosis, is a progressive neurodegenerative disease that affects nerve cells in the brain and spinal cord, affecting one’s speech and ability to swallow and to control the muscles. Ultimately, it causes paralysis and death. Each year, more than 5,000 people in the United States are diagnosed with ALS, which is also known as Lou Gehrig's disease.
Genetics plays a critical role in ALS. Despite numerous advances in recent years, doctors still cannot trace the genetic cause of a significant amount of ALS cases. This research project is taking on the “missing heritability” problem, using innovative genetic data analysis algorithms and more powerful p-value combination tests to analyze large exome sequencing data for detecting novel ALS genes. The methodology being developed in this project has broad applications and could be used to better understand other diseases, as well. A WPI graduate student will work on this research with Wu. For more information on this grant please visit https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812082
Total award period: July 1, 2018 - June 30, 2022
Andrea Arnold Receives NSF Award to Develop Computational Filtering Methods
August 16, 2018
Andrea Arnold, assistant professor of mathematical sciences, has receives a three-year, $220,458 award from the National Science Foundation for a project titled “Computational Filtering Methods for Time-Varying Parameter Estimation in Nonlinear Systems. ” The aim of the study is to design and analyze novel computational methods for estimating time-varying parameters through use of nonlinear filtering. The research has applications in the life sciences, such as modeling the spread of infectious diseases, determining the optimal treatment strategy for HIV drug therapy, and modeling tissue response to laser-based microsurgery.
Arnold’s research in applied mathematics focuses on inverse problems and uncertainty quantification, which involves estimating unknown system parameters using indirect observations and analyzing the changes in predicted outcomes due to changes in the inputs. Many applications in modern science involve system parameters that are estimated using little prior information. This poses a challenge in applied and computational mathematics, particularly for problems where knowledge of parameters is crucial in obtaining trustworthy model output.
The study will develop mathematically sound and computationally efficient systematic approaches for estimating time-varying parameters with unknown dynamics. This work also will involve developing models for parameter evolution that take into account any prior knowledge relating to the structure or behavior of the parameter over time without defining explicit functions to describe the dynamics. Arnold will include WPI undergraduates and graduate students on the project team starting in the summer of 2019. Learn more about this grant.
Total Award period: 07/012018-06/30/2022 Award amount: $220,458
CAREER: Numerical Methods and Biomechanical Models for Sperm Motility
National Science Foundation
Mammalian sperm must navigate the female reproductive tract, swimming a distance greater than 1000 times their own length to reach and fertilize the egg. In order to aid in the treatment of reduced sperm motility, it is important to understand interactions of the sperm flagellum with different regions of the reproductive tract. In particular, fluid flow helps bring the egg to the uterus (in the opposite direction of sperm progression). Recent experiments have shown that a large percentage of sperm exhibit positive rheotaxis, the ability to reorient and swim against a background flow. Additionally, sperm will bind and unbind to the oviductal wall and the role of a background flow on sperm detachment is not known. The main scientific goals of this project include further analyzing existing experimental data (through image processing techniques) and developing new computational models to understand the clinical importance of migration through the female reproductive tract and sperm binding and detachment from walls in a background flow. Several new computational modeling frameworks will be developed to allow simulations of sperm in the presence of a background flow and a wall. The PI will provide interdisciplinary training for several students (undergraduate and graduate) as well as one postdoc in the areas of computational biofluids, image processing of experimental movies, and model development. In addition, the PI will work to develop image processing and modeling modules to be used in area High Schools and at summer programs for High School students at WPI. Learn more about the grant.