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We address the prescribed-time stability of a class of nonlinear system with uncertainty/disturbance. With the help of the parametric Lyapunov equation (PLE), we designed a state feedback control to regulate the full-state of a controlled system within prescribed time, independent of initial conditions. The result illustrated that the controlled state converges to zero as $t$ approaches the settling time and remains zero thereafter. It was further proved that the controller is bounded by a constant that depends on the system state. A numerical example is presented to verify the validity of the theoretical results.

Abstract Adipose tissue development begins in the fetal period, and continues to expand after birth. Dysregulation of adipose tissue during weaning may predispose individuals to lifelong metabolic disorders. However, the developmental remodeling of adipose tissue during weaning remains largely unexplored. Here we comprehensively compare the changes in mouse subcutaneous white adipose tissue from 7 days after birth to 7 days after weaning using single-cell RNA sequencing along with other molecular and histologic assays. We characterize the developmental trajectory of preadipocytes and indicate the commitment of preadipocytes with beige potential during weaning. Meanwhile, we find immune cells unique to weaning period, whose expression of extracellular matrix proteins implies potential regulation on preadipocyte. Finally, the strongest cell-cell interaction during weaning determined by the TGFβ ligand-receptor pairs is between preadipocytes and endotheliocytes. Our results provide a detailed and unbiased cellular landscape and offer insights into the potential regulation of adipose tissue remodeling during weaning.

Introduction: Paclitaxel (PTX) cannot effectively treat glioma because it cannot cross the bloodbrain barrier (BBB). A specific mode electroacupuncture stimulation (SMES) can temporarily open the BBB, thereby improving drug delivery to the brain. This study aimed to observe SMES-mediated accumulation of PTX in the brain and its anti-glioma effect and explore the role of the Hedgehog pathway. Methods: The acupoint selectivity of SMES in opening the BBB was examined in normal rats. The penetration and anti-glioma activity were determined in a C6-Luc glioma rat model. SMES was performed using 2/100 Hz, 3 mA, 6–6 s, and 40 min The survival curve was analysed by the KaplanMeier method, brain tumour pathology and size was observed by HE staining, and in vivo imaging system respectively. Results: SMES-induced BBB opening had acupoint selectivity. SMES could improve PTX accumulation in brain and SMES-mediated PTX delivery showed enhanced anti-glioma activity due to better brain penetration. Hedgehog pathway was involved in SMES-mediated PTX delivery by regulating Occludin expression. Conclusion: SMES at the head acupoints to deliver PTX is a feasible and effective method for treating glioma. The Hedgehog pathway may play a key role in SMES-mediated PTX delivery across the BBB.