Special Seminar: Embracing Complexity

Embracing Complexity: A Fractal Calculus Approach to the Modeling and Optimization of Cyber-Physical Systems
Wednesday, February 17, 2016 - 3:00pm to 4:00pm
Gates 463A
Paul Bodgan (USC)
Abstract / Description: 

Cyber-physical systems (CPS) constitute a new generation of networked embedded systems that interweave computation, communication and control to facilitate our interaction with the physical world. They will stand among other application domains at the foundation of novel smart healthcare systems, which monitor individual physiological process across time and enable accurate disease prediction and health assessment. However, existing approaches to their modeling and optimization ignore important mathematical characteristics (e.g., non-stationarity, fractality). To face these challenges, we embrace the complexity of biological systems: instead of skirting around their non-linear variability. We propose a statistical physics inspired approach to CPS by encapsulating the observed mathematical characteristics of cyber and physical processes via a dynamical master equation. The first part of the talk is dedicated to explaining the benefits of this new approach, which facilitates a more accurate state-space modeling of Networks-on-Chip workloads, contributes to power savings and opens new possibilities for the dynamic optimization of large-scale systems. The second part focuses on a concrete example of a mathematical model based on fractional calculus concepts, which takes into account the dynamics of blood glucose characteristics (e.g., time dependent fractal behavior) and can be used to design an artificial pancreas that regulates insulin injection. Finally, the benefits of this mathematical framework will be also demonstrated in the context of interdependent networks by elucidating the brain-muscle interdependency with applications to brain-machine-body-interfaces and the brain functional connectivity.


Paul Bogdan is an Assistant Professor in the Ming Hsieh Department of Electrical Engineering at University of Southern California. He received his Ph.D. degree in Electrical and Computer Engineering from Carnegie Mellon University. His work has been recognized with a number of distinctions, including the 2015 NSF CAREER Award, the 2012 A.G. Jordan Award from the Electrical and Computer Engineering Department, Carnegie Mellon University for outstanding Ph.D. thesis and service, the 2012 Best Paper Award from the Networks-on-Chip Symposium (NOCS), the 2012 D.O. Pederson Best Paper Award from IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, the 2012 Best Paper Award from the International Conference on Hardware/Software Codesign and System Synthesis (CODES+ISSS), the 2013 Best Paper Award from the 18th Asia and South Pacific Design Automation Conference, and the 2009 Roberto Rocca Ph.D. Fellowship. His research interests include the theoretical foundations of cyber-physical systems, modeling and analysis of biological systems and swarms, understanding of neural and cognitive systems via new mathematical models, development of new control algorithms for dynamical systems exhibiting multi-fractal characteristics, modeling biological / molecular communication, development of fractal mean field games to model and analyze biological, social and technological system-of-systems, performance analysis and design methodologies for many core systems.