Assessment of the Information Sciences Directorate at the Army Research Office (2019) / Chapter Skim
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4 Mathematical Sciences Division
4 Mathematical Sciences Division
Pages 26-33
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From page 26... ...
Nonlinear structures and metrics for modeling and studying complex systems are sought, as is creating theory for the control of stochastic systems, spatial-temporal statistical inference, data classification and regression analysis, predicting and controlling biology through hierarchical and adaptive models, enabling new capabilities through bio-inspired techniques, creating high-fidelity computational principles for sharp-interface flows, solving inverse problems, deriving reduced-order methods, and developing computational linguistics." The programs are Modeling of Complex Systems, Probability and Statistics, Biomathematics, and Computational Mathematics.1 The division's budget of $20.2 million, including $7.5 million in core funding and $12.7 in leveraged funding, supports 156 current projects. COMPUTATIONAL MATHEMATICS PROGRAM Scientific Quality and Degree of Innovation The objectives of this program are to develop mathematical characterizations and computational models for (1)
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From page 27... ...
Consistent with this vision, the Biomathematics Program focuses on areas such as understanding circadian rhythm to improve sleep/alertness of soldiers in the field, and molecular interventions to improve healing of wounds. Scientific Quality and Degree of Innovation In general, the research funded under this program is of good scientific quality and is responsive to the scientific objectives of the program.
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From page 28... ...
The program manager provides ample opportunity for input to the Army at multiple phases of the research process. Multiple projects have resulted in outputs of interest to various government agencies, including the Defense Advanced Research Projects Agency's Defense Sciences Office, the Office of Naval Research, the Army Research Laboratory's (ARL)
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From page 29... ...
MODELING OF COMPLEX SYSTEMS PROGRAM Scientific Quality and Degree of Innovation Starting from a hypothesis that direct simulation approaches (e.g., computational partial differential equations) are insufficient for effective characterization of the systems of Army/DoD interest, this program has chosen to focus its activities on the nascent fields of geometric and topological analysis of complex systems.
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From page 30... ...
. Research on novel characterizations of stochastic differential equations and on insight into properties of random matrices are additional examples of an impressive portfolio of results from the funded research.
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From page 31... ...
But this is the nature of high-risk research: you never know until you try. The improved random matrix concentration bound is another primarily theoretical development, but it will lead directly to improved bounds on the convergence rates of various practical algorithms involving random matrices, and it thus gives better insights into the practical utility of those algorithms.
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From page 32... ...
Promising areas for the expansion of the scientific program include statistical methods and reinforcement learning in biology and learning combined with computational partial differential equations.
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From page 33... ...
In contrast with single investigator programs, the Multidisciplinary University Research Initiative programs at the ARO support centers whose efforts intersect more than one traditional research specialty, typically at $1.25 million per year for 5 years. Research topics increasingly benefit from such multidisciplinary participation, even in pairs or small sets of investigators and over shorter time periods.
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