Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives
- 1Ming Hsieh Department of Electrical Engineering, University of Southern California, United States
Despite significant effort on understanding complex biological systems, we lack a unified theory for their modeling, inference, analysis and control in uncertain environments. This is made even more challenging when considering that only limited and noisy information is available for modeling. Missing information hampers the capabilities of analytical tools to uncover the true degrees of freedom and infer the model structure and parameters of complex systems. By understanding the universal laws characterizing the asymmetric statistics of magnitude increments and the complex space-time interdependency within one process and across processes, we can develop compact yet accurate mathematical models providing higher degree of predictability and efficient control strategies. To better predict the onset of disease and their root cause, as well as discover quality-of-life (QoL)-control strategies, we need mathematical strategies that discover the causal interactions and their corresponding mathematical expressions for space and time operators acting on biological processes and identify the number of unknown unknowns. Lastly, to improve the QoL of control strategies, the focus should not only be on specific values and ranges for biological processes, but also on optimizing / controlling knob variables that enforce a specific spatiotemporal multifractal behavior that corresponds to an initial healthy (patient specific) behavior. All in all, the modeling, analysis and control of complex biological collective systems requires a deeper understanding of multifractal properties of high dimensional heterogeneous and noisy data streams and new algorithmic tools that exploit geometric, statistical physics, and information theory concepts to deal with these data challenges.
Keywords: Fractals, time-varying complex networks, alpha stable distribution, complex collectives, Fractal control, Generalized master equations, Cyber-physical systems (CPS), Network physiology, multifractional differential equations, Multifractal profile optimal control, Unknown unknowns, Causality - Causal modelling, causal predictive modeling, compact mathematical modeling
Received: 01 Sep 2019;
Accepted: 08 Nov 2019.
Copyright: © 2019 Bogdan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Mr. Paul Bogdan, University of Southern California, Ming Hsieh Department of Electrical Engineering, Los Angeles, 90089-2562, CA, United States, firstname.lastname@example.org