The Army relies on the Army Research Laboratory (ARL) to provide the
critical links between the scientific and military commu
|
Mathematical
Research Contacts
|
|
NOTE: The email link provides a
response through the receptionist. The individual's name in the subject
line will identify the desired addressee. If you do not wish to go through
the receptionist, you may construct your own email address by using the
Email Userid provided and arl.army.mil as the email suffix.
|
|
Cooperative
Systems
|
|
Dr. David (Chris) Arney,
Division Chief
919.549.4254
david.arney1
The goal of this work package is to exploit the power of collaboration
and cooperation in complex intelligent systems to enhance Army systems
and operations. Research areas include the mathematical foundations of
system theory, communication, networking, language, learning, swarming,
game theory, decision-making, and information processing related to
autonomous intelligent systems. This program involves innovative,
mathematics-based research to study and advance the understanding and
utility of multi-component, adaptive intelligent systems (e.g.,
multi-robot systems, human-machine systems, groups of pursuers and
evaders, self-optimizing communication or transportation systems, sensor
networks, and expert AI systems). These systems can originate from
applications in any form (i.e., physical, informational, social,
behavioral, or life sciences) and are often multi-scaled and complex
(systems of systems). While multi-component, information-rich systems
can utilize centralized management, this research program seeks to
replace centralized organization with distributed cooperation (component
collaboration) through the development of structures and processes for
communication, adaptation, learning, reasoning, and decision-making by
many, if not all, components of the system. Principal research areas
include the mathematical foundations for and the qualitative and
quantitative analysis of: distributed system theory; measures of system
complexity; measures of the value of system information and intelligence;
models for the transfer of data into information and information into
intelligence (text exploitation); interoperability and connectivity of
communication/transportation/logistics nets; power and limitation of swarming
phenomena; multi-player/multi-objective game theory; information
processing and data fusion for decision-making; adaptive data structures
for intelligent and dynamic systems; applications of cellular automata to
problems in distributed control; development of methodology for language
(formal and natural) and cognition for autonomous systems; metrics and
theories related to networks of various types; and new architectures and
processes for streamlined command, control, computer, communication, intelligence,
surveillance, and reconnaissance (C4ISR) systems. Major objectives of
the program are to develop new mathematical language, theories,
structures, and processes for the development of fundamental principles
to understand information science, network science, cognitive science,
decision science, and intelligent cooperation and to apply the principles
to science and technology for effective C4ISR systems. The program also
supports mathematical development to enhance and employ cooperation into
existing systems with naturally different or conflicting components or
structures (e.g., hybrid, multi-disciplinary, multi-scale, or
multi-perspective mathematics such as discrete/continuous,
linear/nonlinear, deterministic/stochastic).
<<back to top>>
|
|
Computational
Mathematics
|
|
Dr. Janet Spoonamore
919.549.4284
janet.spoonamore
Numerical computation has become an essential part of engineering design
and scientific investigation. It is now possible to simulate potential
designs and analyze failures after they have occurred. Such simulations
often require considerable effort to set up, considerable computer time
on large scale parallel systems and considerable effort to distill useful
information from the massive data sets which result. In addition, it is
not often possible to quantify how well the models simulate the real
problem or how accurate the simulation is. This problem is especially
acute for simulations of failure processes. Data has become ubiquitous
but mathematically sound methods for incorporating the data into accurate
simulations are lacking. Finally, simulations are not timely. The most
recent example of this was the fact that the Corps of Engineers was not
able to determine with enough reliability that the levees in New Orleans would fail before they did. The emphasis in the Computational
Mathematics program is on mathematical research directed towards
overcoming these and related shortcomings.
<<back
to top>>
|
|
|
Discrete Mathematics and Computer Science
|
|
Dr. Janet Spoonamore
919.549.4284
janet.spoonamore
Discrete mathematics and computer science play key roles in the effective
implementation of the digital battlefield. Research in these areas is also
crucial in providing tools to dominate information warfare and determine
and analyze alternatives for battle strategies. The main goals of this
program are to enhance the understanding of discrete phenomena and digital
information environments, provide rigorous algorithmic foundations and
better modeling tools, as well as advance the underpinnings of the
mathematics and enabling technology for distributed interactive simulation
for both physically based and non-physically based models. (Training
simulation is an example of a non-physically based model. Imagery for
automatic target recognition is a physically based model.) The major
thrusts in this program are targeted to address the Army's and DoD's
interests in training, war-gaming, reconnaissance, surveillance imaging,
battlefield management, large scale information and data management, and
virtual environments and prototyping.
<<back to top>>
|
|
Modeling of
Complex Systems
|
|
Dr. John
Lavery
919.549.4253
john.lavery2
The Modeling of Complex Systems Program involves fundamental
mathematics-oriented research with objectives to develop quantitative
models of complex phenomena of interest to the Army, especially those for
which current models are not based on first/basic principles, and to
develop new metrics, preferably those based on first/basic principles, for
these models. The complex phenomena of interest to the Modeling of Complex
Systems Program are mainly human-made phenomena (information, wireless
networks, geometric modeling) and human cognitive and behavioral phenomena.
Complete and consistent mathematical analytical frameworks for the modeling
effort are the preferred context for the research, but research that does
not take place in such frameworks can be considered if the phenomena are so
complex that such frameworks are not feasible. Metrics are part of the
mathematical framework and are of great interest. Traditional metrics, when
they exist, often do not measure the characteristics in which observers in
general and the Army in particular are interested. For many complex
phenomena, new metrics need to be developed at the same time as new models.
Just as is the case for the modeling effort, these metrics should
preferably be in a complete mathematical analytical framework. The research
in modeling of and metrics for complex phenomena supported by the Modeling
of Complex Systems Program may include numerical/computational work as a
subordinate component. However, research that focuses mainly on
numerical/computational issues should be directed to the Computational
Mathematics Program in the Mathematics Division of the Army Research
Office.
<<back to top>>
|
|
|
|
|
|
|
Stochastic
Analysis, Applied Probability, and Statistics
|
|
Dr. Mou-Hsiung (Harry) Chang
919.549.4229
mouhsiung.chang
The Stochastic Analysis, Applied
Probability and Statistics Program support critical Army needs in weapon
system developments and decision making under uncertainty.
Stochastic Analysis and Applied
Probability. Army research and development (R&D) programs directed
toward system design, development, testing and evaluation problems generate a
need for research in the field of stochastic processes, including stochastic
differential equations. Special emphasis is placed on research into methods
for the analysis of observations from phenomena modeled by such processes and
to numerical methods for stochastic delay and partial differential equations
that have Army relevant applications in life, physical, and information
sciences. Research areas of importance to the Army in probability and its
applications include: 1) stochastic modeling, analysis and control of complex
multi-scale networks; 2) theory of spatial-temporal random fields and
nonlinear filtering that are applicable to automatic target recognition (ATR), information assurance, anomaly detection, and antiterrorism in real time; 3) stochastic
optimization and approximation in mathematics of operations research,
manufacturing systems, and supply chain management; 4) optimal control of
stochastic delay and partial differential equations driven by Levy processes
or fractional Brownian motion; and 5) stochastic analysis and control of
fluid turbulence (especially turbulence in helicopter aerodynamics) and
complex physical and biological systems that exhibit the properties of long
range dependence and self-similarity. Ideas are needed from Markov random
fields, stochastic systems with memory, nonlinear stochastic analysis, and
infinite-dimensional stochastic differential equations. The techniques
required include large deviations, heavy traffic analysis, interacting
particle systems, Pontryagin maximum principle for non-Markovian processes,
infinite-dimensional Hamilton-Jacobi-Bellman equations and inequalities,
stochastic attractors and semi-flows.
Statistical Methods. There is
great interest in statistical methods for very large data sets or very small
data sets, sampled from nonstandard, poorly understood distributions. The
extraction of more information from small data sets requires improved methods
for combining information from disparate sets, as in meta-analysis. Useful
statistical models should be based on a thorough understanding of physical
processes combined with sound statistical theory. Thus, it is important to
integrate statistical procedures with scientific and engineering information
about mechanisms as exemplified by a probabilistic methodology that describes
the nature of the growth of cracks in different media and the associated
statistical analysis. More research is required in several statistical areas
including text data mining, Bayesian methods, Markov random fields, cluster
analysis, change point methods, and Markov chain Monte Carlo methods. It is
important to bring novel statistical thinking into resource management and
optimization in very large communication and logistics networks.
<<back to top>>
|
|
|
Electronics 
