During liver development, hepatocytes and cholangiocytes are concurrently differentiated from common liver progenitor cells and are assembled into hepatobiliary architecture to perform proper hepatic function. However, the generation of functional hepatobiliary architecture from hepatocytes in vitro is still challenging, and the exact molecular drivers of hepatobiliary cell lineage determination is largely unknown. In this study, functional hepatobiliary organoids (HBOs) are generated from hepatocytes. These HBOs contain a bile duct network surrounded by mature hepatocytes and stably maintain hepatic characteristics and function in vitro and upon transplantation in vivo. Morphological transition and expression profile of hepatocyte-derived organoids recapitulate the process of liver development. Gene regulation landscape of hepatocyte-derived organoids reveal that Tead4 and Ddit3 promote the cell fate commitment of liver progenitors to functional cholangiocytes and hepatocytes, respectively. Liver cell fate determination is reversed by inhibiting Tead4 or increasing Ddit3 expression both in vitro and upon transplantation in vivo. Collectively, hepatocyte-derived HBOs reveal the essential transcription drivers of liver hepatobiliary cell lineage determination and represent powerful models for liver development and regeneration.
The stabilization problem of a 1D Schrödinger equation subject to boundary control is concerned in this paper. The control input is suffered from time delay. A "partial state" predictor is designed for the system and undelayed system is deduced. Based on the undelayed system, a feedback control strategy is designed to stabilize the original system. The exact observability of the dual one of the undelayed system is checked. Then it is shown that the system can be stabilized exponentially under the feedback control.
In this study, the stabilization problem for Schrödinger equation with distributed input time delay is considered. The main idea of solving the stabilization problem is transformation. The original time delay system is firstly transformed into the undelayed system, and then the feedback control law which can stabilize the undelayed system is found. Finally, we prove that the feedback control law can also exponentially stabilize the time delay system.
Design of controller subject to a constraint for a Schrödinger equation is considered based on the energy functional of the system. Thus, the resulting closed-loop system is nonlinear and its well-posedness is proven by the nonlinear monotone operator theory and a complex form of the nonlinear Lax-Milgram theorem. The asymptotic stability and exponential stability of the system are discussed with the LaSalle invariance principle and Riesz basis method, respectively. In the end, a numerical simulation illustrates the feasibility of the suggested feedback control law.
The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensional Logistic coupled map lattice, where any initial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact. The method utilized in the present paper could be applied to other discrete systems as well.
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