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- All Subjects: nonlinear dynamics
- All Subjects: Biomanufacturing
- Creators: Wang, Xiao
- Status: Published
First, in existing linear controllability frameworks, the ability to steer a network from any initiate state toward any desired state is measured by the minimum number of driver nodes. However, the associated optimal control energy can become unbearably large, preventing actual control from being realized. Here I develop a physical controllability framework and propose strategies to turn physically uncontrollable networks into physically controllable ones. I also discover that although full control can be guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control energy to achieve actual control, and my work provides a framework to address this issue.
Second, in spite of recent progresses in linear controllability, controlling nonlinear dynamical networks remains an outstanding problem. Here I develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another. I introduce the concept of attractor network and formulate a quantifiable framework: a network is more controllable if the attractor network is more strongly connected. I test the control framework using examples from various models and demonstrate the beneficial role of noise in facilitating control.
Third, I analyze large data sets from a diverse online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors: linear, “S”-shape and exponential growths. Inspired by cell population growth model in microbial ecology, I construct a base growth model for meme popularity in OSNs. Then I incorporate human interest dynamics into the base model and propose a hybrid model which contains a small number of free parameters. The model successfully predicts the various distinct meme growth dynamics.
At last, I propose a nonlinear dynamics model to characterize the controlling of WNT signaling pathway in the differentiation of neural progenitor cells. The model is able to predict experiment results and shed light on the understanding of WNT regulation mechanisms.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
Regenerative medicine utilizes living cells as therapeutics to replace or repair damaged or diseased tissue, but the manufacturing processes to produce cell-based tissue products require customized biounit operations that do not currently exist as conventional biochemical and biopharma manufacturing processes. Living cells are constantly changing and reacting to their environment, which in the case of cells isolated from their hosts, are utilized as living bioreactor components that, by themselves, are manipulated to biomanufacturer selected tissue products. Therefore, specialized technology is required to assure that cellular products produce the phenotypical tissue characteristics that the final product is designated to have, while also maintaining sterility of the culture. Because of this, FDA guidelines encourage the use of Process Analytical Technology (PAT – see Ref ) to be integrated into manufacturing systems of biologics to ensure quality and safety. To address the need for evaluation of sensor technologies for potential use in PAT, a literature review of both existing sensing technologies and biomarkers was conducted. After a thorough assessment of the sensor technologies that were most applicable to biomanufacturing, spectrophotometry was selected to monitor the metabolic components glucose and lactate of living cells in culture in real time. Initially, spectrophotometric measurements were taken of mock solutions of glucose and lactate solutions at concentrations relevant to human cell culture and physiology. With that data, a mathematical model was developed to predict a solution’s glucose and lactate concentration. This model was then integrated into a Matlab program that was used to continuously monitor and estimate solutions of glucose and lactate concentrations in real time. After testing the accuracy of this program in different solutions, it was determined that calibration curves and models must be made for each media type and estimates of glucose and lactate were found accurate only at higher concentrations. This program was successfully utilized to monitor in real time glucose and lactate production and consumption trends of Mesenchymal Stem Cells (MSCs) in culture, demonstrating proof-of-concept of the proposed bioprocess monitoring schema.