The complex hyperbolic form as a Weil-Petersson form

For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the K\"ahler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form.Comment: 29 pages, all comments are welcome

On a relation between the K\mathrm{K}-cowaist and the A^\hat{\mathsf{A}}-cowaist

The $\mathrm{K}$-cowaist $\text{K-cw}_2 (M)$ and the $\hat{\mathsf{A}}$-cowaist $\hat{\mathrm{A}}$-$\mathrm{cw}_2 (M)$ are two interesting invariants on a manifold $M$, which are closely related to the existence of the positive scalar curvature metric on $M$. In this note, we give a detailed proof of the following inequality due to Gromov: $\text{K-cw}_2 (M) \le c \hat{\mathrm{A}}$-$\mathrm{cw}_2 (M)$, where $c$ is a dimensional constant.Comment: 8 pages, comments are welcom

A note on the generalized Geroch conjecture for complete spin manifolds

Let $W$ be a closed area enlargeable manifold in the sense of Gromov-Lawson and $M$ a noncompact spin manifold, we show that the connected sum $M\# W$ admits no complete metric of positive scalar curvature. When $W=T^n$, this provides a positive answer to the generalized Geroch conjecture in the spin setting.Comment: 4 pages, comments are welcome

Nonlinear dynamic characteristic of the spindle-cutter system

A nonlinear dynamic model of spindle-cutter coupling system under cutting force, which takes into account the cutter stiffness and the nonlinearity of bearing clearance, is established. Analysis of the cross-section of a two-flute end mill is conducted to determine cutter stiffness. Then, the calculated cutter stiffness is introduced into the nonlinear dynamic model of coupling system. In the modeling of cutting force, the cutting width takes into account the cutter tip displacement. Moreover, nonlinear dynamic characteristics of spindle-cutter coupling system are studied and the effects of bearing clearance on the response of cutter tip are discussed as well, considering unbalanced force. The numerical results show that the bearing clearance strongly affects the equilibrium position. With different values of bearing clearance and rotation speed, the responses of cutter tip exhibit periodic, quasi-periodic and chaotic characteristics. Dynamic characteristics of spindle-cutter system depends on the bearing clearance and rotation speed. The proper bearing clearance and rotation speed should be chosen to ensure a stable cutting and high cutting rate according to the bifurcation diagram. The response of the cutter tip is a quasi-periodic motion when the cutting force is considered. The time-domain response of cutter tip predicted by nonlinear dynamic analysis can provide the basis for machining error prediction

Human posture recognition based on multiple features and rule learning

The use of skeleton data for human posture recognition is a key research topic in the human-computer interaction field. To improve the accuracy of human posture recognition, a new algorithm based on multiple features and rule learning is proposed in this paper. Firstly, a 219-dimensional vector that includes angle features and distance features is defined. Specifically, the angle and distance features are defined in terms of the local relationship between joints and the global spatial location of joints. Then, during human posture classification, the rule learning method is used together with the Bagging and random sub-Weili Ding space methods to create different samples and features for improved classification of sub-classifiers for different samples. Finally, the performance of our proposed algorithm is evaluated on four human posture datasets. The experimental results show that our algorithm can recognize many kinds of human postures effectively, and the results obtained by the rule-based learning method are of higher interpretability than those by traditional machine learning methods and CNNs

Parametric Design of Femoral Implant with Gradient Porous Structure

Patients who has been implanted with hip implant usually undergo revision surgery. The reason is that high stiff implants would cause non-physiological distribution loadings, which is also known as stress shielding, and finally lead to bone loss and aseptic loosening. Titanium implants are widely used in human bone tissues; however, the subsequent elastic modulus mismatch problem has become increasingly serious, and can lead to stress-shielding effects. This study aimed to develop a parametric design methodology of porous titanium alloy hip implant with gradient elastic modulus, and mitigate the stress-shielding effect. Four independent adjustable dimensions of the porous structure were parametrically designed, and the Kriging algorithm was used to establish the mapping relationship between the four adjustable dimensions and the porosity, surface-to-volume ratio, and elastic modulus. Moreover, the equivalent stress on the surface of the femur was optimized by response surface methodology, and the optimal gradient elastic modulus of the implant was obtained. Finally, through the Kriging approximation model and optimization results of the finite element method, the dimensions of each segment of the porous structure that could effectively mitigate the stress-shielding effect were determined. Experimental results demonstrated that the parameterized design method of the porous implant with gradient elastic modulus proposed in this study increased the strain value on the femoral surface by 17.1% on average. Consequently, the stress-shielding effect of the femoral tissue induced by the titanium alloy implant was effectively mitigated

Theoretical modeling approach for adsorption of fibronectin on the nanotopographical implants

The success of orthopedic implants depends on the sufficient integration between tissue and implant, which is influenced by the cellular responses to their microenvironment. The conformation of adsorbed extracellular matrix is crucial for cellular behavior instruction via manipulating the physiochemical features of materials. To investigate the electrostatic adsorption mechanism of fibronectin on nanotopographies, a theoretical model was established to determine surface charge density and Coulomb’s force of nanotopography – fibronectin interactions using a Laplace equation satisfying the boundary conditions. Surface charge density distribution of nanotopographies with multiple random fibronectin was simulated based on random number and Monte Carlo hypothesis. The surface charge density on the nanotopographies was compared to the experimental measurements, to verify the effectiveness of the theoretical model. The model was implemented to calculate the Coulomb’s force generated by nanotopographies to compare the fibronectin adsorption. This model has revealed the multiple random quantitative fibronectin electrostatic adsorption to the nanotopographies, which is beneficial for orthopedic implant surface design. Significance: The conformation and distribution of adsorbed extracellular matrix on biomedical implants are crucial for directing cellular behaviors. However, the Ti nanotopography-ECM interaction mechanism remains largely unknown. This is mostly because of the interactions that are driven by electrostatic force, and any experimental probe could interfere with the electric field between the charged protein and Ti surface. A theoretical model is hereby proposed to simulate the adsorption between nanotopographies and fibronectin. Random number and Monte Carlo hypothesis were applied for multiple random fibronectin simulation, and the Coulomb’s force between nanoconvex and nanoconcave structures was comparatively analyzed