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AFIT Researcher Discusses Mathematical Approaches to Protect Cyber Networks

Posted Thursday, August 06, 2015

 

 

In a recent department seminar, Dr. Parisa Fatheddin, a Research Assistant Professor within the Air Force Institute of Technology (AFIT) Graduate School of Engineering and Management's Department of Mathematics and Statistics, presented a talk titled " Branching Stochastic Processes, Large Deviations and Anomalous Information Flow in Cyber Systems" .  Cyber security is considered a critical defense capability by the U. S. Air Force and AFIT is a national leader in the education and research of cyber related disciplines for the Air Force officers and the U. S. defense enterprise.

The presentation described certain novel mathematical approaches to describe malicious viruses and worm flows in cyber networks using advanced probabilistic methods called branching stochastic processes. She also described methods to estimate the probability of anomalous network activities separating them from normal activities using the theory of rare events which is a branch of probability theory called large deviations. This research has the potential to aide agile secure network designs of future cyber networks and also rapid detection and propagation of malicious intrusions.

Branching stochastic processes have striking properties that can be utilized in a variety of applications including virus and worm flow in cyber networks. They also provide a fascinating probabilistic representation of solutions to certain classes of semi-linear partial differential equations. Dr. Fatheddin began by discussing related research at Oak Ridge National Laboratory (ORNL) and shared some thoughts on describing anomalous information and virus/worm flow in cyber systems using branching stochastic processes and large deviations theory.

Two classes of Stochastic Partial Differential Equations that are used to characterize two well studied population models, super-Brownian motion and Fleming-Viot Process, were described and results on large and moderate deviations and central limit theorem for these classes were given. Dr. Fatheddin also provided an introduction to large deviations theory and branching process, the discrete version of super-Brownian motion population model, and discussed ways that they can be used in the study of virus/worm flow cyber networks.
 

 

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