Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives
Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives
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DOI：
10.3389/fphys.2019.01452
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发表时间：
2019-12-03
影响因子：
4
通讯作者：
Bogdan, Paul
中科院分区：
文献类型：
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作者：
Bogdan, Paul
尽管在理解复杂的生物系统方面做出了巨大的努力，但我们缺乏一个统一的理论来建模，推理，分析和有效控制不确定环境中的动态。当考虑到只有有限和嘈杂的信息可用于建模时，这些问题变得更具挑战性，这可能不足以解释和预测复杂系统的行为。例如，信息缺失阻碍了分析工具揭示真实自由度和推断复杂生物系统的模型结构和参数的能力。为此，在本文中，我们讨论了几个重要的数学挑战，这些挑战可能为研究复杂系统开辟新的理论途径：（1）通过理解一个过程内和许多过程之间的震级增量的不对称统计和复杂的时空相互依赖性的普遍规律，我们可以开发出一类紧凑而精确的数学模型，能够潜在地提供更高程度的可预测性和更有效的控制策略。(2)为了更好地预测疾病的发作及其根本原因，以及潜在地发现更有效的生活质量（QoL）控制策略，我们需要开发数学策略，不仅能够发现因果相互作用及其相应的数学表达式，用于作用于生物过程的空间和时间算子，还包括数学和算法技术，以识别未知的未知数（UU）的数量及其与观测变量的相互依赖性。(3)最后，为了提高控制策略的生活质量，当面对患者内和患者间的变异性时，重点不仅应该放在生物过程的特定值和范围上，而且还应该放在优化/控制旋钮变量上，这些变量强制执行对应于初始健康（患者特定）行为的特定时空多重分形行为。总而言之，复杂生物集体系统的建模，分析和控制需要更深入地了解高维异构和噪声数据流的多重分形特性，以及利用几何，统计物理和信息理论概念来处理这些数据挑战的新算法工具。
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.