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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.
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Almost every step during analysis and quantification requires the use of an often empirically determined threshold, which makes quantification of noise less accurate. In addition, each research group often develops their own data analysis pipeline making it impossible to compare data from different groups. To remedy this problem a streamlined and standardized scRNA-seq data analysis and normalization protocol was designed and developed. After analyzing multiple experiments we identified the possible pipeline stages, and tools needed. Our pipeline is capable of handling data with adapters and barcodes, which was not the case with pipelines from some experiments. Our pipeline can be used to analyze single experiment scRNA-seq data and also to compare scRNA-seq data across experiments. Various processes like data gathering, file conversion, and data merging were automated in the pipeline. The main focus was to standardize and normalize single-cell RNA-seq data to minimize technical noise introduced by disparate platforms.
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Neural progenitor cells (NPCs) derived from human pluripotent stem cells (hPSCs) are a multipotent cell population that is capable of nearly indefinite expansion and subsequent differentiation into the various neuronal and supporting cell types that comprise the CNS. However, current protocols for differentiating NPCs toward neuronal lineages result in a mixture of neurons from various regions of the CNS. In this study, we determined that endogenous WNT signaling is a primary contributor to the heterogeneity observed in NPC cultures and neuronal differentiation. Furthermore, exogenous manipulation of WNT signaling during neural differentiation, through either activation or inhibition, reduces this heterogeneity in NPC cultures, thereby promoting the formation of regionally homogeneous NPC and neuronal cultures. The ability to manipulate WNT signaling to generate regionally specific NPCs and neurons will be useful for studying human neural development and will greatly enhance the translational potential of hPSCs for neural-related therapies.