Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives.

Paul Bogdan

doi:10.3389/fphys.2019.01452

Abstract

Despite significant effort on understanding complex biological systems, we lack a unified theory for modeling, inference, analysis, and efficient control of their dynamics in uncertain environments. These problems are made even more challenging when considering that only limited and noisy information is accessible for modeling, which can prove insufficient for explaining, and predicting the behavior of complex systems. For instance, missing information hampers the capabilities of analytical tools to uncover the true degrees of freedom and infer the model structure and parameters of complex biological systems. Toward this end, in this paper, we discuss several important mathematical challenges that could open new theoretical avenues in studying complex systems: (1) By understanding the universal laws characterizing the asymmetric statistics of magnitude increments and the complex space-time interdependency within one process and across many processes, we can develop a class of compact yet accurate mathematical models capable to potentially providing higher degree of predictability, and more efficient control strategies. (2) In order to better predict the onset of disease and their root cause, as well as potentially discover more efficient quality-of-life (QoL)-control strategies, we need to develop mathematical strategies that not only are capable to discover causal interactions and their corresponding mathematical expressions for space and time operators acting on biological processes, but also mathematical and algorithmic techniques to identify the number of unknown unknowns (UUs) and their interdependency with the observed variables. (3) Lastly, to improve the QoL of control strategies when facing intra- and inter-patient variability, 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 the multifractal properties of high dimensional heterogeneous and noisy data streams and new algorithmic tools that exploit geometric, statistical physics, and information theoretic concepts to deal with these data challenges.

Highlights

Genomic, proteomic, and physiological processes are generally used for medical diagnosis because they encompass the complex dynamics and multi-scale interactions between the chemical, electrical, and mechanical components of the human body
Toward achieving the design of these genomic, proteomic, and physiological complexity-aware medical cyber-physical systems (MCPS) architectures, in this paper, we briefly review a list of urgent mathematical challenges and advocate for (1) a comprehensive understanding of individual complexity of genomic, proteomic and physiological processes in order (2) to establish compact yet accurate mathematical models (Xue and Bogdan, 2017) to predict abnormal behavior corresponding to disease precursor patterns, and (3) to optimize the dynamics of human physiology in accordance with observed complexity and improve the patients QoL
Relying on simplifying assumptions such as memoryless dynamics for either modeling biological processes or linearity for inferring the directionality of causal interactions can provide inaccurate inference strategies of the time-varying complex networks that govern the healthy dynamics of anatomical systems, which in turn can derail medical therapies

Summary

Introduction

Proteomic, and physiological processes are generally used for medical diagnosis because they encompass the complex dynamics and multi-scale interactions between the chemical, electrical, and mechanical components of the human body. They exhibit higher-order statistical variability from person to person due to individual biological features (e.g., body mass and height) while being highly influenced by a wide web of environmental factors (e.g., temperature, noise pollution, cultural traits, and social anxiety levels). Mathematical investigations of physiological processes collected from the individuals suffering from various diseases revealed specific patterns, for example, a decrease in correlation in both temporal and fractal behavior (Ivanov et al, 1999; Stanley et al, 1999; Kotani et al, 2005; Gierałtowski et al, 2012). Fractal scaling has been demonstrated to be capable to discriminate between type 1, type 2 diabetes, and non-diabetic subjects, and identify the dynamical instabilities in the glucoregulation (Kohnert et al, 2018)

Objectives

Conclusion