SUMMARYRecent advances in shape optimization rely on free-form implicit representations, such as level sets, to support boundary deformations and topological changes. By contrast, parametric shape optimization is formulated directly in terms of meaningful geometric design variables, but usually does not support free-form boundary and topological changes. We propose a novel approach to shape optimization that combines and retains the advantages of the earlier optimization techniques. The shapes in the design space are represented implicitly as level sets of a higher-dimensional function that is constructed using B-splines (to allow free-form deformations), and parameterized primitives combined with R-functions (to support desired parametric changes).Our approach to shape design and optimization offers great flexibility because it provides explicit parametric control of geometry and topology within a large space of free-form shapes. The resulting method is also general in that it subsumes most other types of shape optimization as special cases. We describe an implementation of the proposed technique with attractive numerical properties. The explicit construction of an implicit representation supports straightforward sensitivity analysis that can be used with most gradient-based optimization methods. Furthermore, our implementation does not require any error-prone polygonization or approximation of level sets (isocurves and isosurfaces). The effectiveness of the method is demonstrated by several numerical examples

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Objective: To investigate the role of aerobic exercise in inhibiting chronic unpredictable mild stress (CUMS) depressed mice hippocampal inflammatory response and its potential mechanisms. Methods: Fifty-four male eight-week-old C57BL/6 mice were divided as control group (CG) (18 mice) and model group (36 mice). Model group mice were treated with 13 chronic stimulating factors for 28 days to set up the CUMS depression model. Neurobehavioral assessment was performed after modeling. The mice in the model group were randomly divided into the control model group (MG) and the aerobic exercise group (EG), with 18mice in each group. The EG group carried out the adaptive training of the running platform: 10 m/min, 0° slope, and increased by 10 minutes per day for 6 days. The formal training was carried for 8 weeks with 10 m/min speed, 0° slope, 60 min/d, 6 d/Week. After the training, a neurobehavioral assessment was performed, and hippocampus IL-1β and IL-10 protein levels were detected by ELISA. RT–PCR was used to detect the expression of miR-223 and TLR4, MyD88, and NF-κB in the hippocampus. Western blot was used to detect the expression of TLR4 and phosphorylated NF-κBp65 protein in the hippocampus. Results: The hippocampus function of CUMS depression model mice was impaired. The forced swimming and forced tail suspension time were significantly prolonged, and inflammatory factors IL-1β were significantly increased in the hippocampus. Aerobic exercise significantly improves CUMS-depressed mice hippocampal function, effectively reducing depressive behavior and IL-1β levels, and increasing IL-10 levels. Besides, aerobic exercise significantly upregulates the expression level of miR-223 and inhibits the high expression of TLR4, MyD88, and NF-κB. Conclusion: Aerobic exercise significantly increases the CUMS-depressed mice hippocampus expression of miR-223, and inhibits the downstream TLR4/MyD88-NF-κB signaling pathway and the hippocampal inflammatory response, which contributes to the improvement of the hippocampal function.

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