By Xiaoming Huo, Jennifer Pearl, Henry Warchall, and Michael Vogelius
With this update on funding opportunities at the National Science Foundation, we draw readers’ attention to interdisciplinary programs and workforce-development programs of the Division of Mathematical Sciences that should be of particular interest to the mathematical sciences community. While the bulk (roughly 75%) of the DMS investment in mathematical sciences research is through the DMS Disciplinary Research Programs, DMS is also a partner in several crosscutting initiatives. Moreover, DMS itself has a significant workforce-development activity, encompassing four programs: Postdoctoral Research Fellowships (MSPRF), Enhanced Doctoral Training (EDT), Research Experiences for Undergraduates (REU), and Research Training Groups (RTG).
More information about any of these programs is available here.
Recognizing that the ideas, tools, and language of mathematics and statistics play important roles in every area of science and engineering research supported by NSF, the Division of Mathematical Sciences recently launched the MSII activity. It is widely acknowledged that interactions between the mathematical sciences and other fields catalyze developments in both. DMS wishes to foster the participation of more mathematical scientists, from every area of mathematics and statistics, in such important interdisciplinary work. In support of this goal, the MSII activity provides funding to catalyze the involvement of mathematical scientists in research areas in which the mathematical sciences do not yet play large roles.
MSII emphasizes scientific research areas of high national priority that would benefit from innovative developments in mathematics and statistics. For example, modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Success in meeting crucial challenges currently facing the nation in these areas will rest on advances in mathematical sciences research.
MSII provides support for collaborative research projects in these and other high-priority areas that are managed by NSF programs outside DMS and that involve mathematical scientists in the research. Mathematical scientists are encouraged to consider establishing research collaborations with researchers in other NSF-supported disciplines and to make collaborators aware of the possibility of MSII support for the activity. More information can be found on the MSII web page.
In addition to the MSII activity, DMS manages some special programs that support research in the mathematical sciences with direct applicability in other important areas of emphasis. We briefly describe here the newest of these programs, DMREF and CDS&E-MSS.
DMREF is the primary program through which NSF participates in the national Materials Genome Initiative (MGI) for Global Competitiveness. MGI recognizes the importance of materials science to the well-being and advancement of society and aims to “deploy advanced materials at least twice as fast as possible today, at a fraction of the cost.”
DMREF seeks to promote activities that significantly accelerate the discovery and development of materials by building the fundamental knowledge base needed to progress toward designing and making materials with specific and desired functions or properties from first principles. Also of interest is research that advances fundamental understanding of materials across length and time scales to elucidate the effects of microstructure, surfaces, and coatings on the properties and performance of materials and devices.
Controlling material properties through design requires an understanding of the interrelationships of composition, processing, structure, properties, performance, and process control. The approach envisioned in DMREF to achieve this goal involves modeling, analysis, and computational simulations, validated and verified through measurement, experimentation, or device demonstration. DMREF aims to support collaborative and iterative research wherein theory guides computational simulation, computational simulation guides experiments, and experiments further guide theory.
The topics span efforts in materials science, chemistry, mathematics, statistics, computer science, and engineering to develop new data analytic tools and statistical algorithms; advanced simulations of material properties; advances in predictive modeling that leverage machine learning, data mining, and sparse approximation; and software and data infrastructure that is accessible, extensible, reliable, interoperable, and reusable. The mathematical sciences community has a valuable role to play and much to contribute in these efforts. The recent DMREF program solicitation provides additional details. Readers may also be interested in a special NSF–SIAM minisymposium associated with DMREF that will be held in connection with the SIAM Conference on Computational Science and Engineering in Salt Lake City in March 2015.
The CDS&E-MSS program supports research confronting the host of mathematical and statistical challenges presented to the scientific and engineering communities by the ever-expanding role of computational modeling and simulation on the one hand, and the explosion in the production of digital and observational data on the other. The goal of the program is to promote the creation and development of the next generation of mathematical and statistical theories and methodologies that will be essential for addressing such issues. To this end, the program supports fundamental research in mathematics and statistics whose primary emphasis is on meeting these computational and data-related challenges.
In its first three years, CDS&E-MSS has made awards in a wide range of topics, including stochastic partial differential equations, Lie groups and representation theory, manifold learning, sparse optimization, data assimilation, partially observed Markov processes, and high-dimensional learning. Among the many emerging methodologies proposed are efficient parallel iterative Monte Carlo methods, accelerated Monte Carlo schemes, solution of large-scale eigenvalue problems, and measurement model specification search. Some projects deal with newly emerged datasets––for example, algebraic, geometric, and computational tools for data clouds and data arrays, LiDAR point cloud data, and data with network structure. The widely ranging application areas include tumor microenvironments, genetic association, brain connectivity, coastal ocean modeling, and subsurface imaging. The online award abstracts reflect the broad spectrum of research projects supported by the program.
CDS&E-MSS is part of the NSF-wide CDS&E program. There are differences: If the proposed work emphasizes mathematical or statistical foundations, CDS&E-MSS may be a fit. If the proposed work is driven more by particular scientific and/or engineering applications, the NSF-wide CDS&E program may be more suitable. The NSF-wide CDS&E program has varying proposal deadlines, depending on the NSF division to which the proposal is submitted; the next submission window for CDS&E-MSS is November 25–December 9, 2014. Investigators are encouraged to contact the cognizant program directors before preparing proposals.
The primary mission of DMS is the support of research in the mathematical sciences; students and postdoctoral associates receive training as frequent participants in these research projects. DMS also supports other activities by the community to enhance the training of the next generation of U.S. mathematical sciences researchers. Much of this additional support is provided through the DMS Workforce activity, which comprises the four programs centered on training through research involvement mentioned at the beginning of this article. Two of those programs––REU and Postdoctoral Research Fellowships––are of long standing and are not discussed further here. We briefly describe the new Enriched Doctoral Training in the Mathematical Sciences program and summarize updates to the long-running Research Training Groups in the Mathematical Sciences.
The EDT program supports efforts to enrich research training in the mathematical sciences at the doctoral level by preparing PhD students to recognize and find solutions to mathematical challenges arising in other fields and in areas outside today’s academic setting. Graduate research training activities supported by EDT will prepare participants for a broader range of mathematical opportunities and career paths than has been traditional in U.S. mathematics doctoral training.
The long-range goal of the EDT program is to strengthen the nation’s scientific competitiveness by increasing the number of well-prepared U.S. citizens, nationals, and permanent residents who pursue careers in the mathematical sciences and in other professions in which expertise in the mathematical sciences plays an increasingly important role. The program supports efforts by academic institutions or other qualified organizations to train doctoral students in the mathematical sciences who will be well equipped to recognize opportunities for the development of mathematics and statistics in problems from other disciplines, and who can effectively apply advanced mathematics and statistics to solve problems originating outside the traditional academic mathematical sciences setting. The program will support projects that include training in areas supplementary to students’ dissertation research themes and that are instrumental for connections with business, industry, government, and the non-profit sector; among such activities are internships, research projects, consulting, and participation in complementary courses or summer schools. Projects are expected to train students to work in teams to refine, attack, and solve problems that are open-ended, not initially sharply formulated, and that originate outside the academic mathematical realm.
DMS intends that the collection of projects funded will benefit students whose dissertation topics lie in all areas of the mathematical sciences, and we are hopeful that a wide spectrum of departments will submit proposals for this program. The intent is, funding permitting, to have fifteen or more EDT projects running by the third year of the program.
The REU, EDT, and postdoctoral fellowship programs support enhanced training through research involvement at the undergraduate, doctoral, and postdoctoral levels. The RTG program spans all these levels, supporting efforts to improve research training by involving undergraduate students, graduate students, postdoctoral associates, and faculty members in structured groups centered on a common research theme. Research groups supported by the RTG program must include vertically integrated activities that span this entire spectrum of educational levels.
The potential of such vertically integrated activities to enhance engagement, accelerate progress, and improve recruitment and retention in the discipline has been indicated by several reviews, as described in the RTG program solicitation. These observations reveal that well-implemented vertically integrated research groups can generate enormous enthusiasm, high motivation, and accelerated research progress among participants at all levels.
The RTG program aims to further the adoption of this research group model in mathematical sciences programs that conduct training spanning this entire spectrum of educational levels. The new RTG solicitation (re)-emphasizes the essential importance of vertical integration and strong training plans in successful RTG proposals.
We end this brief review of recent developments in the DMS portfolio by encouraging the mathematical sciences community to continue to submit strong proposals to the DMS Disciplinary Research Programs and to take advantage, when appropriate, of the additional opportunities outlined here. More information about all these opportunities is available through the program pages and program solicitations accessible via the DMS home page. As always, questions can be addressed to the program directors listed on the program pages for the various funding opportunities.
Xiaoming Huo and Jennifer Pearl are program directors in the Division of Mathematical Sciences (DMS) at the National Science Foundation. Henry Warchall and Michael Vogelius are deputy director and director, respectively, of the DMS.