An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional treatment accounting for the jump discontinuities must be employed. Here, we aim to elevate such an extra effort to ease our implementation by machine learning methodology. The key idea is to decompose the solution into singular and regular parts. The neural network learning machinery incorporating the given jump conditions finds the singular solution, while the standard finite difference method is used to obtain the regular solution with associated boundary conditions. Regardless of the interface geometry, these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation, making the hybrid method easy to implement and efficient. The two- and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives, and it is comparable with the traditional immersed interface method in the literature. As an application, we solve the Stokes equations with singular forces to demonstrate the robustness of the present method

A cusp-capturing PINN for elliptic interface problems

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find such a solution using neural network representation, we introduce a cusp-enforced level set function as an additional feature input to the network to retain the inherent solution properties; that is, capturing the solution cusps (where the derivatives are discontinuous) sharply. In addition, the proposed neural network has the advantage of being mesh-free, so it can easily handle problems in irregular domains. We train the network using the physics-informed framework in which the loss function comprises the residual of the differential equation together with certain interface and boundary conditions. We conduct a series of numerical experiments to demonstrate the effectiveness of the cusp-capturing technique and the accuracy of the present network model. Numerical results show that even using a one-hidden-layer (shallow) network with a moderate number of neurons and sufficient training data points, the present network model can achieve prediction accuracy comparable with traditional methods. Besides, if the solution is discontinuous across the interface, we can simply incorporate an additional supervised learning task for solution jump approximation into the present network without much difficulty

Effect of urban innovation on land finance dependence: evidence from 233 Chinese cities

Unlike most studies on urban innovation, which focus on the effects of land-use policies, this study investigates the effect of urban innovation (UI) on land finance dependence (LFD). In China, innovation-related policies are intended to create a shared business environment where new entrepreneurs can contribute to achieving sustainable economic growth. This study analyzes the spatiotemporal dynamics of LFD and UI from 2005 to 2019 using the spatial autocorrelation model and dynamic spatial Durbin model. It finds a positive spatial association between LFD and UI throughout the studied regions during the study period. It also reveals a significant inhibitory effect of UI on LFD and a negative impact on the LFD of neighbouring cities. Moreover, the inhibitory effects will increase over time. Lastly, this study shows varied impacts of UI on LFD in different regions, especially in eastern China. Important policy recommendations for high-quality development in China are provided

Neel tensor torque at the ferromagnet/antiferromagnet interface

Antiferromagnets (AFMs) exhibit spin arrangements with no net magnetization, positioning them as promising candidates for spintronics applications. While electrical manipulation of the single-crystal AFMs, composed of periodic spin configurations, is achieved recently, it remains a daunting challenge to characterize and to manipulate polycrystalline AFMs. Utilizing statistical analysis in data science, we demonstrate that polycrystalline AFMs can be described using a real, symmetric, positive semi-definite, rank-two tensor, which we term the Neel tensor. This tensor introduces a unique spin torque, diverging from the conventional field-like and Slonczewski torques in spintronics devices. Remarkably, Neel tensors can be trained to retain a specific orientation, functioning as a form of working memory. This attribute enables zero-field spin-orbit-torque switching in trilayer devices featuring a heavy-metal/ferromagnet/AFM structure and is also consistent with the X-ray magnetic linear dichroism measurements. Our findings uncover hidden statistical patterns in polycrystalline AFMs and establishes the presence of Neel tensor torque, highlighting its potential to drive future spintronics innovations.Comment: main text 18 pages, supplementary information 10 page

MG63 Osteoblast-Like Cells Exhibit Different Behavior when Grown on Electrospun Collagen Matrix versus Electrospun Gelatin Matrix

Electrospinning is a simple and efficient method of fabricating a non-woven polymeric nanofiber matrix. However, using fluorinated alcohols as a solvent for the electrospinning of proteins often results in protein denaturation. TEM and circular dichroism analysis indicated a massive loss of triple-helical collagen from an electrospun collagen (EC) matrix, and the random coils were similar to those found in gelatin. Nevertheless, from mechanical testing we found the Young's modulus and ultimate tensile stresses of EC matrices were significantly higher than electrospun gelatin (EG) matrices because matrix stiffness can affect many cell behaviors such as cell adhesion, proliferation and differentiation. We hypothesize that the difference of matrix stiffness between EC and EG will affect intracellular signaling through the mechano-transducers Rho kinase (ROCK) and focal adhesion kinase (FAK) and subsequently regulates the osteogenic phenotype of MG63 osteoblast-like cells. From the results, we found there was no significant difference between the EC and EG matrices with respect to either cell attachment or proliferation rate. However, the gene expression levels of OPN, type I collagen, ALP, and OCN were significantly higher in MG63 osteoblast-like cells grown on the EC than in those grown on the EG. In addition, the phosphorylation levels of Y397-FAK, ERK1/2, BSP, and OPN proteins, as well as ALP activity, were also higher on the EC than on the EG. We further inhibited ROCK activation with Y27632 during differentiation to investigate its effects on matrix-mediated osteogenic differentiation. Results showed the extent of mineralization was decreased with inhibition after induction. Moreover, there is no significant difference between EC and EG. From the results of the protein levels of phosphorylated Y397-FAK, ERK1/2, BSP and OPN, ALP activity and mineral deposition, we speculate that the mechanism that influences the osteogenic differentiation of MG63 osteoblast-like cells on EC and EG is matrix stiffness and via ROCK-FAK-ERK1/2

Metabolic labelling of cholesteryl glucosides in Helicobacter pylori reveals how the uptake of human lipids enhances bacterial virulence.

Helicobacter pylori infects approximately half of the human population and is the main cause of various gastric diseases. This pathogen is auxotrophic for cholesterol, which it converts upon uptake to various cholesteryl α-glucoside derivatives, including cholesteryl 6'-acyl and 6'-phosphatidyl α-glucosides (CAGs and CPGs). Owing to a lack of sensitive analytical methods, it is not known if CAGs and CPGs play distinct physiological roles or how the acyl chain component affects function. Herein we established a metabolite-labelling method for characterising these derivatives qualitatively and quantitatively with a femtomolar detection limit. The development generated an MS/MS database of CGds, allowing for profiling of all the cholesterol-derived metabolites. The subsequent analysis led to the unprecedented information that these bacteria acquire phospholipids from the membrane of epithelial cells for CAG biosynthesis. The resulting increase in longer or/and unsaturated CAG acyl chains helps to promote lipid raft formation and thus delivery of the virulence factor CagA into the host cell, supporting the idea that the host/pathogen interplay enhances bacterial virulence. These findings demonstrate an important connection between the chain length of CAGs and the bacterial pathogenicity

Finding a Fair Land Dispute Settlement Mechanism Between Adat Law Community Vs. Investor

Land utilization for investment in local areas raises various land related problems that ends with conflicts within the community. A conflict that occurs, usually begins with the management of communal land “tanah ulayat” within the adat law community environment, and in this case, land utilization that is managed by the third party (investors). The basic problem is the difference of perception and expectations toward the company that exists in the land which is claimed by the community. Both parties have their own claim on the land based on each legal systems, in this situation adat law or local law faced with state law which is used by investors. So far, the Indonesian government has yet to have legal grounds in giving a directions for land dispute/conflict settlement mechanism. This paper attempts to give an input regarding a land dispute settlement mechanism that can be accepted for all disputing parties. The paper features critical analysis using legal pluralism approach towards related government policies and technical regulations in the ministerial level. These regulations, among others are, Minister of Agrarian Regulation No. 5 of 1999 on the Guidance for Dispute Settlement of Communal Land Rights, and Ministry of Agrarian and Spatial Affairs Regulation No. 9 of 2015 on Procedures of Appointment of Communal Land Rights for Adat Law Community and Communities Located in certain regions, also the draft of Law regarding Recognition and Protection of Adat Law Community

Urodynamic and Bladder Diary Factors Predict Overactive Bladder-wet in Women: A Comparison With Overactive Bladder-dry

Purpose To identify factors predicting the presence of overactive bladder syndrome (OAB)-wet, compared with OAB-dry. Methods Between September 2007 and September 2013, the medical records of 623 women with OAB who completed a 3-day bladder diary and underwent urodynamic studies in a medical center were retrospectively reviewed. OAB-wet was diagnosed in patients who complained of at least one episode of urgency incontinence in the previous month; otherwise, OAB-dry was diagnosed. Multivariable logistic regression analysis was used to predict the presence of OAB-wet. Results Age (odds ratio [OR], 1.05; P<0.001), maximal flow rate (Qmax) (OR,1.06; P<0.001), voided volume (OR, 0.996; P=0.001), detrusor pressure at maximal flow rate (PdetQmax) (OR, 1.02; P=0.003), urgency episodes (OR, 1.04; P<0.001) and urodynamic stress incontinence (OR,1.78; P=0.01) were independent predictors for the presence of OAB-wet vs. OAB-dry. If we use bladder contractility index as a variable for multivariable logistic regression analysis, bladder contractility index (OR, 1.012; P<0.001) become an independent predictor for OAB-wet. Conclusions A smaller bladder capacity and more frequent urgency episodes were predictors of OAB-wet, and the above findings indicate that OAB-wet and OAB-dry might be a continuum of OAB. Old age, high Qmax, high PdetQmax and urodynamic stress incontinence were also predictors for OAB-wet, and the above results reveal that OAB-wet and OAB-dry have partially different clinical and urodynamic features. Further studies might be performed to elucidate whether different treatment strategies between OAB-dry and OAB-wet can improve treatment efficacy

Local synergetic collaboration between Pd and local tetrahedral symmetric Ni oxide enables ultra-high-performance CO2 thermal methanation

Tetrahedral symmetric NiO2 and Pd respectively facilitate H2 splitting and CO2 to CO reduction and thus enable an ultra-high CH4 production yield performance in the epitaxial interfaces in the bimetallic NiO2@Pd NPs.</p