Optimal control of a nonconvex perturbed sweeping process

The paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the Moreau sweeping process with control functions acting in both nonconvex moving sets and additive perturbations. This is a new class of optimal control problems in comparison with previously considered counterparts where the controlled sweeping sets are described by convex polyhedra. Besides a theoretical interest, a major motivation for our study of such challenging optimal control problems with intrinsic state constraints comes from the application to the crowd motion model in a practically adequate planar setting with nonconvex but prox-regular sweeping sets. Based on a constructive discrete approximation approach and advanced tools of first-order and second-order variational analysis and generalized differentiation, we establish the strong convergence of discrete optimal solutions and derive a complete set of necessary optimality conditions for discrete-time and continuous-time sweeping control systems that are expressed entirely via the problem data.     

Modulation of the functions of osteoblast-like cells on poly(allylamine hydrochloride) and poly(acrylic acid) multilayer films

Deposition of layer-by-layer polyelectrolyte multilayer (PEM) films has been a widely applied surface modification technique to improve the biocompatibility of biomaterials. The objective of this study was to investigate the impact of the deposition of poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA) multilayer films on adhesion, growth and differentiation of osteoblasts-like MG63 cells. PAH and PAA were deposited sequentially onto tissue culture polystyrene at either pH 2.0 or pH 6.5 with 4-21 layers. While the MG63 cells attached poorly on the PAH/PAA multilayer films deposited at pH 2.0, while the cells adhered to the PEM films deposited at pH 6.5, depending on layer numbers. Cell adhesion, proliferation and osteogenic activities (alkaline phosphatase activity, expression of osteogenic marker genes and mineralization) were highest on the 4-layer PAH/PAA film and decreased with increasing layer numbers. On the other hand, the behavior of MG63 cells did not show any difference on the adjacent even and odd layers, except PEM4 and PEM5, i.e. the surface charges of the PAH/PAA multilayer films with over ten layers seem indifferent to osteoblastic functions. The results in this study suggested that the mechanical properties of PEM films may play a critical role in modulating the behavior of osteoblasts, providing guidance for application of PEM films to osteopaedic implants.     

Influence of 40 Hz and 100 Hz Vibration on SH-SY5Y Cells Growth and Differentiation—A Preliminary Study

(1) Background: A novel bioreactor platform of neuronal cell cultures using low-magnitude, low-frequency (LMLF) vibrational stimulation was designed to discover vibration influence and mimic the dynamic environment of the in vivo state. To better understand the impact of 40 Hz and 100 Hz vibration on cell differentiation, we join biotechnology and advanced medical technology to design the nano-vibration system. The influence of vibration on the development of nervous tissue on the selected cell line SH-SY5Y (experimental research model in Alzheimer’s and Parkinson’s) was investigated. (2) Methods: The vibration stimulation of cell differentiation and elongation of their neuritis were monitored. We measured how vibrations affect the morphology and differentiation of nerve cells in vitro. (3) Results: The highest average length of neurites was observed in response to the 40 Hz vibration on the collagen surface in the differentiating medium, but cells response did not increase with vibration frequency. Also, vibrations at a frequency of 40 Hz or 100 Hz did not affect the average density of neurites. 100 Hz vibration increased the neurites density significantly with time for cultures on collagen and non-collagen surfaces. The exposure of neuronal cells to 40 Hz and 100 Hz vibration enhanced cell differentiation. The 40 Hz vibration has the best impact on neuronal-like cell growth and differentiation. (4) Conclusions: The data demonstrated that exposure to neuronal cells to 40 Hz and 100 Hz vibration enhanced cell differentiation and proliferation. This positive impact of vibration can be used in tissue engineering and regenerative medicine. It is planned to optimize the processes and study its molecular mechanisms concerning carrying out the research.     

近似已知函数求导方法的改进

本文研究了近似已知函数求导方法的改进.利用Lagrange乘数法对罗方法中的系数进行了优化,得到了更快的收敛速度,并给出了相关的数值试验.     

Enhancing endothelial differentiation of human mesenchymal stem cells by culture on a nanofibrous polycaprolactone/(poly-glycerol sebacate)/gelatin scaffold

Cardiovascular diseases have always been one of the main causes of death worldwide and eventually one of the major medical concerns. Tissue engineering is promising strategies of treating cardiovascular, which can be an effective approach with the design of appropriate scaffold. In this study, to develop engineering basement membrane for endothelial differentiation with good cell attachment, we produced polycaprolactone (PCL)/poly (glycerol sebacate) (PGS)/gelatin nanofibrous scaffold via electrospinning. Attenuated total reflectance-Fourier transform infrared and the proton nuclear magnetic resonance results confirmed the chemical structure of synthesized PGS. Scanning electron microscope images of the electrospun scaffold revealed that the nanofibers are smooth, continues and uniform. Moreover, due to the presence of hydrophilic functional groups in the scaffold, the contact angle is in the appropriate range for cell adhesion especially endothelial cells. The elastic modulus and ultimate tensile stress of electrospun scaffold were calculated 1.32 ± 0.27 MPa and 1.23 ± 0.18 MPa respectively. Quantitative polymerase chain reaction was performed for evaluation of endothelial differentiation of mesenchymal stem cells cultured on standard plate and fibrous scaffold under chemical stimulation with growth factor. Specific endothelial gene expression results postulated that our modified scaffold could support and significantly promote endothelial differentiation of MSCs.     

Stiffness-Tunable Hydrogel-Sandwich Culture Modulates the YAP-Mediated Mechanoresponse in Induced-Pluripotent Stem Cell Embryoid Bodies and Augments Cardiomyocyte Differentiation

Microenvironmental factors, including substrate stiffness, regulate stem cell behavior and differentiation. However, the effects of substrate stiffness on the behavior of induced pluripotent stem cell (iPSC)- derived embryoid bodies (EB) remain unclear. To investigate the effects of mechanical cues on iPSC-EB differentiation, a 3D hydrogel-sandwich culture (HGSC) system is developed that controls the microenvironment surrounding iPSC-EBs using a stiffness-tunable polyacrylamide hydrogel assembly. Mouse iPSC-EBs are seeded between upper and lower polyacrylamide hydrogels of differing stiffness (Young's modulus [E’] = 54.3 ± 7.1 kPa [hard], 28.1 ± 2.3 kPa [moderate], and 5.1 ± 0.1 kPa [soft]) and cultured for 2 days. HGSC induces stiffness-dependent activation of the yes-associated protein (YAP) mechanotransducer and actin cytoskeleton rearrangement in the iPSC-EBs. Moreover, moderate-stiffness HGSC specifically upregulates the mRNA and protein expression of ectoderm and mesoderm lineage differentiation markers in iPSC-EBs via YAP-mediated mechanotransduction. Pretreatment of mouse iPSC-EBs with moderate-stiffness HGSC promotes cardiomyocyte (CM) differentiation and structural maturation of myofibrils. The proposed HGSC system provides a viable platform for investigating the role of mechanical cues on the pluripotency and differentiation of iPSCs that can be beneficial for research into tissue regeneration and engineering.     

Laponite–Gelatin Nanofibrous Microsphere Promoting Human Dental Follicle Stem Cells Attachment and Osteogenic Differentiation for Noninvasive Stem Cell Transplantation

Nanofibrous microspheres (NFM) are emerging as prominent next-generation biomimetic injectable scaffold system for stem cell delivery and different tissue regeneration where nanofibrous topography facilitates ECM-like stem cells niches. Addition of osteogenic bioactive nanosilicate platelets within NFM can provide osteoconductive cues to facilitate matrix mediated osteogenic differentiation of stem cells and enhance the efficiency of bone tissue regeneration. In this study, gelatin nanofibrous microspheres are prepared containing fluoride-doped laponite XL21 (LP) using the emulsion mediated thermal induce phase separation (TIPS) technique. Systematic studies are performed to understand the effect of physicochemical properties of biomimicking NFM alone and with different concentrations of LP on human dental follicle stem cells (hDFSCs), their cellular attachment, proliferation, and osteogenic differentiation. The study highlights the effect of LP nanosilicate with biomimicking nanofibrous injectable scaffold system aiding in enhancing stem cell differentiation under normal physiological conditions compared to NFM without LP. The laponite–NFM shows suitability as excellent injectable biomaterials system for stem cell attachment, proliferation and osteogenic differentiation for stem cell transplantation and bone tissue regeneration.     

Solving Schrodinger equations using a physically constrained neural network

Deep neural networks (DNNs) and auto differentiation have been widely used in computational physics to solve variational problems. When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization, various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency. We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function (CDF) \begin{document}$F(x) = \int_{-\infty}^{x} \psi^*\psi {\rm d}x'$\end{document}. Using this constrained neural network to represent the variational wave function, we solve Schrodinger equations using auto-differentiation and stochastic gradient descent (SGD) by minimizing the violation of the trial wave function \begin{document}$ \psi(x) $\end{document} to the Schrodinger equation. For several classical problems in quantum mechanics, we obtain their ground state wave function and energy with very low errors. The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.     

Generalization of Hardy–Littlewood maximal inequality with variable exponent

Let $p(·)$ be a measurable function defined on ${\mathbb{R}}^d$ and $p_{-}:={inf}_{x\in {\mathbb{R}}^d}p(x)$. In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the $L_{q(·)}$-means. Let $p(·)$ and $q(·)$ satisfy the log-Hülder condition and $p(·)=q(·)r(·)$. Then, we prove that the maximal operator is bounded on $L_{p(·)}$ if and is bounded from $L_{p(·)}$ to the weak $L_{p(·)}$ if $1\le r_{-}\le \infty$. We generalize also the theorem about the Lebesgue points.