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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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Deposits of dark material appear on Vesta’s surface as features of relatively low-albedo in the visible wavelength range of Dawn’s camera and spectrometer. Mixed with the regolith and partially excavated by younger impacts, the material is exposed as individual layered outcrops in crater walls or ejecta patches, having been uncovered and broken up by the impact. Dark fans on crater walls and dark deposits on crater floors are the result of gravity-driven mass wasting triggered by steep slopes and impact seismicity. The fact that dark material is mixed with impact ejecta indicates that it has been processed together with the ejected material. Some small craters display continuous dark ejecta similar to lunar dark-halo impact craters, indicating that the impact excavated the material from beneath a higher-albedo surface. The asymmetric distribution of dark material in impact craters and ejecta suggests non-continuous distribution in the local subsurface. Some positive-relief dark edifices appear to be impact-sculpted hills with dark material distributed over the hill slopes.
Dark features inside and outside of craters are in some places arranged as linear outcrops along scarps or as dark streaks perpendicular to the local topography. The spectral characteristics of the dark material resemble that of Vesta’s regolith. Dark material is distributed unevenly across Vesta’s surface with clusters of all types of dark material exposures. On a local scale, some craters expose or are associated with dark material, while others in the immediate vicinity do not show evidence for dark material. While the variety of surface exposures of dark material and their different geological correlations with surface features, as well as their uneven distribution, indicate a globally inhomogeneous distribution in the subsurface, the dark material seems to be correlated with the rim and ejecta of the older Veneneia south polar basin structure. The origin of the dark material is still being debated, however, the geological analysis suggests that it is exogenic, from carbon-rich low-velocity impactors, rather than endogenic, from freshly exposed mafic material or melt, exposed or created by impacts.