THEORETICAL ANALYSES ON DISCRETE FORMULAE OF DIRECTIONAL DIFFERENTIALS IN THE FINITE POINT METHOD

For the five-point discrete formulae of directional derivatives in the finite point method,overcoming the challenge resulted from scattered point sets and making full use of the explicit expressions and accuracy of the formulae,this paper obtains a number of theoretical results:(1)a concise expression with definite meaning of the complicated directional difference coefficient matrix is presented,which characterizes the correlation between coefficients and the connection between coefficients and scattered geometric characteristics;(2)various expressions of the discriminant function for the solvability of numerical differentials along with the estimation of its lower bound are given,which are the bases for selecting neighboring points and making analysis;(3)the estimations of combinatorial elements and of each element in the directional difference coefficient matrix are put out,which exclude the existence of singularity.Finally,the theoretical analysis results are verified by numerical calculations.The results of this paper have strong regularity,which lay the foundation for further research on the finite point method for solving partial differential equations.

Differential quadrature time element method for structural dynamics

An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.

Reliability of gas holdup measurements using the differential pressure method in a cyclone-static micro-bubble flotation column

Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expansion method. The errors were used to establish optimum measurement positions. The results show that the measurement position should be in the middle of the column and in the region half way from the center to the wall (the half-radius). The gas holdup along the axial direction is lower at the bottom and higher at the top of the floatation column. The gas holdup along the radial direction is lower near the wall and higher near the center of the flotation column. The average gas holdup measure- ment can be replaced by regional gas holdup values.

Integrated Organ-on-a-chip with Human-induced Pluripotent Stem Cells Directional Differentiation for 3D Skin Model Generation

Keratinocytes and fibroblasts,derived from hiPSCs,were used to construct the human epidermal model by a culture patch made by monolayer poly-(lactic-co-glycolic acid)(PLGA)nanofibers and a human skin-on-a-chip device.Unlike the conventional culture dish method,two different epidermal cells are successfully adhered to the front and back sides of the patch,which produces a three-dimensional nanofibrous scaffold similar to a natural extracellular matrix before the patch was cultured in the skin-on-a-chip device to mimic the physiological conditions of human skin.As expected,the differentiated hiPSCs show the expression of keratinocyte-and fibroblast-specific proteins on the patch,and the layering is found between these two kinds of cells,indicating that this approach creates a powerful in vitro system for modeling skin development and diseases.

In vitro derivation of functional insulin-producing cells from human embryonic stem cells

The capacity for self-renewal and differentiation of human embryonic stem （ES） cells makes them a potential source for generation of pancreatic beta cells for treating type I diabetes mellitus. Here, we report a newly developed and effective method, carried out in a serum-free system, which induced human ES cells to differentiate into insulin-producing cells. Activin A was used in the initial stage to induce definitive endoderm differentiation from human ES cells, as detected by the expression of the definitive endoderm markers Sox17 and Brachyury. Further, all-trans retinoic acid （RA） was used to promote pancreatic differentiation, as indicated by the expression of the early pancreatic transcription factors pdxl and hlxb9. After maturation in DMEM/F12 serum-free medium with bFGF and nicotinamide, the differentiated cells expressed islet specific markers such as C-peptide, insulin, glucagon and glut2. The percentage of C-peptide-positive cells exceeded 15%. The secretion of insulin and C-peptide by these cells corresponded to the variations in glucose levels. When transplanted into renal capsules of Streptozotocin （STZ）-treated nude mice, these differentiated human ES cells survived and maintained the expression of beta cell marker genes, including C-peptide, pdxl, glucokinase, nkx6.1, lAPP, pax6 and Tcfl. Thirty percent of the transplanted nude mice exhibited apparent restoration of stable euglycemia; and the corrected phenotype was sustained for more than six weeks. Our new method provides a promising in vitro differentiation model for studying the mechanisms of human pancreas development and illustrates the potential of using human ES cells for the treatment of type I diabetes mellitus.

Neurotoxic role of interleukin-17 in neural stem cell differentiation after intracerebral hemorrhage

Interleukin 17(IL-17)and its main producer,T cell receptorγδcells,have neurotoxic effects in the pathogenesis of intracerebral hemorrhage(ICH),aggravating brain injuries.To investigate the correlation between IL-17 and ICH,we dynamically screened serum IL-17 concentrations using enzyme-linked immunosorbent assay and explored the clinical values of IL-17 in ICH patients.There was a significant negative correlation between serum IL-17 level and neurological recovery status in ICH patients(r=–0.498,P<0.01).To study the neurotoxic role of IL-17,C57 BL/6 mice were used to establish an ICH model by injecting autologous blood into the caudate nucleus.Subsequently,the mice were treated with mouse neural stem cells(NSCs)and/or IL-17 neutralizing antibody for 72 hours.Flow cytometry,brain water content detection,Nissl staining,and terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling results indicated that NSC transplantation significantly reduced IL-17 expression in peri-hematoma tissue,but there was no difference in T cell receptorγδcells.Compared with the ICH group,there were fewer apoptotic bodies and more Nissl bodies in the ICH+NSC group and the ICH+NSC+IL-17 group.To investigate the potential effect of IL-17 on directional differentiation of NSCs,we cultured mouse NSCs(NE-4 C)alone or co-cultured them with T cell receptorγδcells,which were isolated from mouse peripheral blood mononuclear cells,for 7 days.The results of western blot assays revealed that IL-17 secreted by T cell receptorγδcells reduced the differentiation of NSCs into astrocytes and neurons,while IL-17 neutralization relieved the inhibition of directional differentiation into astrocytes rather than neurons.In conclusion,serum IL-17 levels were elevated in the early stage of ICH and were negatively correlated with outcome in ICH patients.Animal experiments and cytological investigations therefore demonstrated that IL-17 probably has neurotoxic roles in ICH because of its inhibitory effects on the directional differentiation of NSCs.The application of IL-17 neutralizing antibody may promote the directional differentiation of NSCs into astrocytes.This study was approved by the Clinical Research Ethics Committee of Anhui Medical University of China(For human study:Approval No.20170135)in December 2016.All animal handling and experimentation were reviewed and approved by the Institutional Animal Care and Use Committee of Anhui Medical University(approval No.20180248)in December 2017.

Finite element response sensitivity analysis of three-dimensional soil-foundation-structure interaction (SFSI) systems

The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method（DDM） has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction（SFSI） models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method（FFD）.The relative importance（RI） of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM（e.g.,accurate,efficient,insensitive to numerical noise）.Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.

THE TANGENT CONES ON CONSTRAINT QUALIFICATIONS IN OPTIMIZATION PROBLEMS

This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.

Sensitivity Analysis Approach to Multibody Systems Described by Natural Coordinates

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.

Correlation between receptor-interacting protein 140 expression and directed differentiation of human embryonic stem cells into neural stem cells

Overexpression of receptor-interacting protein 140（RIP140） promotes neuronal differentiation of N2 a cells via extracellular regulated kinase 1/2（ERK1/2） signaling.However,involvement of RIP140 in human neural differentiation remains unclear.We found both RIP140 and ERK1/2 expression increased during neural differentiation of H1 human embryonic stem cells.Moreover,RIP140 negatively correlated with stem cell markers Oct4 and Sox2 during early stages of neural differentiation,and positively correlated with the neural stem cell marker Nestin during later stages.Thus,ERK1/2 signaling may provide the molecular mechanism by which RIP140 takes part in neural differentiation to eventually affect the number of neurons produced.

Alpha-actinin expression at different differentiating time points from temporal lobe cerebral cortex neural stem cells to neuron-like cells using energy dispersive X-ray analysis

BACKGROUND： Alpha-actinin （ a -actinin） plays a key role in neuronal growth cone migration during directional differentiation from neural stem cells （NSCs） to neurons. OBJECTIVE： To detect in situ microdistribution and quantitative expression of a -actinin during directional differentiation of NSCs to neurons in the temporal lobe cerebral cortex of neonatal rats. DESIGN, TIME AND SETTING： Between January 2006 and December 2008, culture and directional differentiation of NSCs were performed at Department of Histology and Embryology, Preclinical Medical College, China Medical University. Immune electron microscopy was performed at Department of Histology and Embryology and Department of Electron Micrology, Preclinical Medical College, China Medical University. Spectrum analysis was performed at Laboratory of Electron Microscopy, Mental Research Institute, Chinese Academy of Sciences. MATERIALS： Basic fibroblast growth factor, epidermal growth factor, brain-derived nerve growth factor, type-1 insulin like growth factor, and a -actinin antibody were provided by Gibco BRL, USA; rabbit-anti-rat nestin monoclonal antibody, rabbit-anti-rat neuron specific enolase polyclonal antibody, and EDAX-9100 energy dispersive X-ray analysis were provided by PHILIPS Company, Netherlands. METHODS： NSCs, following primary and passage culture, were differentiated with serum culture medium （DMEM/F12 ＋ 10% fetal bovine serum ＋ 2 ng/mL brain-derived nerve growth factor ＋ 2 ng/mL type-1 insulin like growth factor）. MAIN OUTCOME MEASURES： Expression of a -actinin in neuron-like cells was quantitatively and qualitatively detected with immunocytochemistry using energy dispersive X-ray analysis. RESULTS： Immunocytochemistry, combined with electron microscopy, indicated that positive α -actinin expression was like a spheroid particle with high electron density. In addition, the expression was gradually concentrated from the nuclear edge to the cytoplasm and expanded into developing neurites, during differentiation of neural stem cells to neurons. Conversely, energy dispersive X-ray analysis indicated that the more mature the neural differentiation was, and the greater the expression of α -actinin. CONCLUSION： The gradual increase of α -actinin expression is related to growth, development, and maturity of differentiated neuron-like cells, in neonatal rat frontal lobe cortex, at different differentiating time points of NSCs to neurons.

Promotion of Chondrogenesis of Marrow Stromal Stem Cells by TGF-β3 Fusion Protein In Vitro

The purpose of this study was to investigate the repair of the osteoarthritis（OA）-induced car- tilage injury by transfecting the new TGF-β3 fusion protein （LAP-MMP-mTGF-β3） with targeted ther- apy function into the bone marrow-derived mesenchymal stem cells （MSCs） in rats. The recombinant of plRES-EGFP-MMP was constructed by combination of DNA encoding MMP enzyme cutting site and eukaryotic expression vector plRES-EGFP. LAP and mTGF-β3 fragments were obtained from rat em- bryos by RT-PCR and inserted into the upstream and downstream of MMP from plRES-EGFP-MMP respectively, so as to construct the recombinant plasmid ofplRES-EGFP-LAP-MMP-mTGF-β3, plRES- EGFP-LAP-MMP-mTGF-β3 was transfected into rat MSCs. The genetically modified MSCs were cul- tured in medium with MMP-1 or not. The transfected MSCs were transplanted in the rat OA models. The OA animal models were surgically induced by anterior cruciate ligament transaction （ACLT）. The pathological changes were observed under a microscope by HE staining, Alcian blue, Safranin-fast Gre- en and graded by Mankin＇s scale, plRES-EGFP-LAP-MMP-mTGF-β3 was successfully constructed by means of enzyme cutting and sequencing, and the mTGF-β3 fusion protein （39 kD） was certified by Western blotting. Those genetically modified MSCs could differentiate into chondrocytes induced by MMP and secrete the relevant-matrix. The transfected MSCs could promote chondrogenesis and matrix production in rat OA models in vivo. It was concluded that a new fusion protein LAP-MMP-mTGF-β3 was constructed successfully by gene engineering, and could be used to repair the OA-induced cartilage injury.

Improvement of neurological function in rats with spinal cord injury after the transplantation of neural stem cells directly differentiated from bone marrow mesenchymal stem cells

Objective To study the effect and mechanism of neurological function recovery in rats with spinal cord injury ( SCI) rats after transplantation of neural stem cells which are directly differentiated from bone marrow mesenchymal stem cells ( BMSC ) ,and to investigate the suitable engraftment time. Methods BMSC at 3rd passage were differentiated into neural stem cells ( NSC) , and immunofluorescence staining was used to

Singular Directions and Differential Polynomials of Meromorphic Functions

We prove the existance of a kind of singular directions concerning the differentialpolynomials f（k）+sum from j=0 to k-1 ajfj-afn

Eigenvalue sensitivity analysis based on the transfer matrix method

For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues.Therefore,classical strategies for sensitivity analysis of eigenvalues w.r.t.system parameters cannot be applied.The paper develops two specific strategies for this situation,a direct differentiation strategy and an adjoint variable method,where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems.Like the system analysis itself,it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure.Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation.The obtained procedure may support gradient‐based optimization and robust design by delivering exact sensitivities.