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Mathematical and computationalmodeling enables biologists to integrate data from observations and experiments into a theoretical frame work. In this review, we describe how developmental processes associated with stemcelldriven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the singlecell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.

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Stabilization of turning processes with a digital proportionalderivative feedback controller is analyzed. A one-degree-offreedom model of the turning process is considered. The control force is assumed to be acting directly on the tool. The sampling effect and the delay of the digital controller are involved in the model. The governing equation is a periodic delaydifferential equation, which includes a continuous point delay due to the regenerative effect of the material removal process and a discrete delay (i.e., a term with piecewise constant argument) due to the sampling effect of the controller. The principal period of the system is the sampling period. The stability analysis is performed using different implementations of the semidiscretization method. A series of stability diagrams are presented for different proportional and derivative control gains.