According to the National Research Council report *Network Science* (2006),

"[Despite] society's profound dependence on networks, fundamental knowledge about them is primitive. [G]lobal communication ... networks have quite advanced technological implementations but their behavior under stress still cannot be predicted reliably.... There is no science today that offers the fundamental knowledge necessary to design large complex networks [so] that their behaviors can be predicted prior to building them."

As a result, such systems are highly vulnerable to instabilities and failure resulting either as an inherent function of their design, or as a response to unexpected external stimulus (e.g. attack).

There is a long history of scientific theories and mathematical models which enables a fundamental understanding of physical systems. Such understanding is a prerequisite for the development of a true measurement science. In contract, computing technology, while quite sophisticated, is at a much less mature stage. Hence, the mathematical foundations necessary for the development of a rigorous measurement science for information systems remain very weak. We intend to develop a research focus within ITL which seeks to develop the mathematical foundations which can ultimately provide a sound basis for the measurement science work of ITL.

*Goal.* We seek to develop mathematical models, techniques, and tools which facilitate fundamental understanding of information systems. In particular, we seek to

- Develop mathematical foundations needed to characterize the macro-scale structure and dynamics of large-scale interconnected systems.
- Identify and characterize fundamental measurable properties of complex information systems that are indicators of the systems' inherent level of security and reliability.
- Assess the applicability of mathematical models and metrics to the prediction of security and reliability during all stages of a system's life cycle, i.e., initial design, operational monitoring, and long-term planning.

*Expected Impact.* Increased understanding of mathematical foundations will lead to metrics for assessing critical properties of information systems. Ultimately, such metrics can be used both to design more reliable and secure systems, as well as to enable effective real-time control of deployed systems.

*Most of the work associated with this effort takes place under the aegis of the following ITL Programs: Complex Systems, Trustworthy Information Systems*