for characterizing uncertainty in information created from the large volumes of data
arising from the smart grid. We also need new methods to enable the use of high-
bandwidth networks by dynamically identifying only the data relevant to the current
information need and discarding the rest.
Cyber attacks on the electric power grid are a major concern. “Cyberspace” is
insecure and faced with attacks by adversaries who wish to take advantage of our
dependence on it. Use of cyberspace subjects us to loss of information, loss of money,
and disruption, destruction, or interruption of critical services. Adversaries can launch
sophisticated “information warfare” (e.g., Russian cyberattacks on Estonia and “botnet”
attacks by North Korea on the South Korean government and private industry sites). We
need to find ways to protect against cyber attacks that take advantage of vulnerabilities
created by dependence on massive amounts of data generated through the smart grid.
Development of fast methods of anomaly detection, randomized algorithms for botnet
detection in order to confuse adversaries and increase the cost and risk of attacks, and
game-theoretic approaches to competition from smart adversaries are all important
mathematical sciences challenges in cyberdefense.
Research Challenge for the Mathematical Sciences: Find statistical and
algorithmic methods of data analysis, advanced computational tools, and new
cryptographic tools to aid us in making management and policy decisions about the
electric power grid; learn how to handle the massive amount of data that arise in
monitoring the grid to give us rapid awareness of anomalies so as to prevent cascading
failures; find ways to protect it against failures (deliberate and otherwise); and guide us
to efficient use of power while protecting the privacy of individuals.
- Concluding Remarks
As the examples given above show, the concept of human well-being is
multidimensional, depending on a number of factors, each depending on the local
environment. We may then represent the relationships between human systems and the
natural environment as a network whose nodes are the various factors by which we
measure this complex relationship. This network is dynamic, and the edges correspond
to evolving relationships that can be modeled by mathematical/statistical tools. Given
that what happens in one region of the world may affect what happens in other regions,
we may seek to understand human well-being and that of the natural environment of
planet Earth through understanding the whole as a network of networks. This network
consists of dynamically evolving networks, tied together in a network that itself is
changing over time and space. Sustainability can then be framed in terms of the long
term stability of networks over the local network and the network of networks. The study
of dynamically changing networks and the interplay of a complex web of such networks
presents a major set of challenges for the mathematical sciences.
We have focused on several examples that demonstrate how mathematical and
statistical methods can be used to provide new insight for challenging issues in
sustainability. However, we also articulate below a longer list of mathematical areas
which we believe can be transformative to the study of several research areas in
sustainability and also give a more extensive list of examples of sustainability issues that
seem amenable to analysis using methods of the mathematical sciences. Neither of the