Adversarial Training for Physics-Informed Neural Networks

Physics-informed neural networks have shown great promise in solving partial differential equations. However, due to insufficient robustness, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behaviors or solutions with sharp or oscillatory characteristics. To address these issues, based on the projected gradient descent adversarial attack, we proposed an adversarial training strategy for PINNs termed by AT-PINNs. AT-PINNs enhance the robustness of PINNs by fine-tuning the model with adversarial samples, which can accurately identify model failure locations and drive the model to focus on those regions during training. AT-PINNs can also perform inference with temporal causality by selecting the initial collocation points around temporal initial values. We implement AT-PINNs to the elliptic equation with multi-scale coefficients, Poisson equation with multi-peak solutions, Burgers equation with sharp solutions and the Allen-Cahn equation. The results demonstrate that AT-PINNs can effectively locate and reduce failure regions. Moreover, AT-PINNs are suitable for solving complex PDEs, since locating failure regions through adversarial attacks is independent of the size of failure regions or the complexity of the distribution

Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation

Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function, and thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design scalar auxiliary variable (SAV) scheme coupled with fast Fourier transform (FFT), which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, retain fine segmentation targets and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency

Synthesis and biological evaluation of pentacyclic triterpenoid derivatives as potential novel antibacterial agents

A series of ursolic acid (UA), oleanolic acid (OA) and 18β-glycyrrhetinic acid (GA) derivatives were synthesized by introducing a range of substituted aromatic side-chains at the C-2 position after the hydroxyl group at C-3 position was oxidized. Their antibacterial activities were evaluated in vitro against a panel of four Staphylococcus strains. The results revealed that the introduction of aromatic side-chains at the C-2 position of GA led to the discovery of potent triterpenoid derivatives for inhibition of both drug sensitive and resistant S. aureus, while the other two series derivatives of UA and OA showed no significant antibacterial activity even at high concentrations. In particular, GA derivative showed good potency against all four strains of Staphylococcus (MIC = 1.25 - 5 μmol/L) with acceptable pharmacokinetics properties and low cytotoxicity in vitro. Molecular docking was also performed using S. aureus DNA gyrase structure to rationalize the observed antibacterial activity. Therefore, this series of GA derivatives have strong potential for the development of a new type of triterpenoid antibacterial agent

A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise

Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative is imposed due to its textural detail enhancing capability. We also introduce the gray level indicator, which fully considers the gray level information of multiplicative noise images, so that the model can effectively remove high level noise and protect the details of the structure. The well-posedness of the proposed fractional-order telegraph diffusion model is presented by applying the Schauder’s fixed-point theorem. To solve the model, we develop an iterative algorithm based on the discrete Fourier transform in the frequency domain. We give various numerical results on despeckling natural and real SAR images. The experiments demonstrate that the proposed method can remove multiplicative noise and preserve texture well

Novel Natural Glycyrrhetinic Acid-Derived Super Metal Gel and Its Highly Selective Dyes Removal

Hydrogels play important roles in function materials, especially in wastewater treatment, that could solve the problems of microbial infections and dye pollutions. Herein, a natural glycyrrhetinic acid-derived gel was successfully constructed by forming hierarchical assemblies of the glycyrrhetinic acid derivatives (GA-O-09) with Cu2+. Interestingly, the GA-O-09/Cu2+ gel exhibited Cu2+-triggered shrinkage, which was helpful for spontaneous self-demolding through the shrinkage process with a precise amount of Cu2+. Moreover, the gel showed excellent antimicrobial activity against Staphylococcus aureus and methicillin-resistant Staphylococcus aureus (MRSA) with minimum inhibitory concentrations (MICs) at 2.5 μg/mL and 5.0 μg/mL, respectively. Furthermore, the resultant GA-O-09/Cu2+ gel showed an excellent performance in dyes removal; the adsorption capacity at equilibrium (qe) could reach 82.91 mg/g according to a pseudo-second-order model, and it was better than most reported dye adsorbent materials. The experimental result suggested that the electrostatic interactions of the hydrogel with the cationic dyes and the hydrogel swelling were responsible for the possible dye removal mechanism of GA-O-09/Cu2+ gel. Therefore, our study holds the promise of a better future, for such a hydrogel could be used as an antibacterial and dye removal material

Neutral Möbius [5]helicene-embedded Cycloparaphenylene Nanohoops: Synthesis, [4n]Möbius Topology and Hückel Aromaticity

The relationship between Möbius topology and aromaticity and topological chirality is still elusive to date, which is, to a large extent, due to the related synthetic challenges and, further, the scarcity in both the quantity and the diversity of the con-structed Möbius systems. In this work, we reported the synthesis of [4n]Möbius conjugated all-carbon nanohoops ([5]H-[7,8]CPPs) by utilizing a [5]helicene unit as a hidden writhe and a masked aromatic unit to overcome the strain inherited from Möbius topology. X-ray analysis revealed that [5]H-[7,8]CPPs contain a [5]helicene moiety and an oligoparaphenylene unit, and display a Möbius topology. Photophysical investigations demonstrated that [5]H-[7,8]CPPs exhibited moderately high fluorescence quantum yields, which are significantly higher than those of pristine [5]helicene and [7,8]CPPs. Chiropti-cal studies revealed that [5]H-[7,8]CPPs displayed an obvious Cotton effect in circular dichroism and bright circularly polar-ized luminescence, indicating that the chirality of [5]helicene was efficiently transferred to the overall carbon nanohoops. Importantly, theoretical investigations reveal that, though possessing a 4n π-electron array, such all-carbon nanohoops are fully conjugated systems with Hückel aromaticity. The results may help us to better understand the relationship between Möbius topology and aromaticity

18β-Glycyrrhetinic acid derivative-based metallo-hydrogels with highly selective and sensitive for histidine detection

Quantitative detection of His has aroused great interest in disease diagnosis since abnormal histidine (His) metabolism would cause a variety of serious diseases. However, exploiting a strategy with facile, highly selective, sensitive sensing and low-cost to monitor His remains a challenge. In this study, a series of novel metallo-hydrogels were successfully constructed, which were composed of 18β-glycyrrhetinic acid (GA) derivative (GA-O-09) with rare earth metal ions (Ce3+, Tb3+, Eu3+ and La3+). In addition, these metallo-hydrogels possessed excellent thermodynamics stability with the gel melting temperature (Tgel) ranging from 62.4 ± 0.49 °C to 67.4 ± 0.49 °C and remarkable pH stability over a range of pH values of 3–10. Interestingly, the Histidine (His)-loaded GA-O-09/Eu3+ hydrogel and the His-loaded GA-O-09/La3+ hydrogel displayed extraordinary fluorescence enhancement, in which the lowest fluorescence response concentrations (LODs) of the His-loaded GA-O-09/Eu3+ hydrogel and the His-loaded GA-O-09/La3+ hydrogel were 1.14 × 10-8 and 1.07 × 10-8 M, respectively. Therefore, the result showed that the study of the GA-O-09/Eu3+ and GA-O-09/La3+ hydrogels could provide a potential application for highly selective and sensitive detection for His

High-throughput fabrication of soft magneto-origami machines

Machines capable of magnetically controllable shape morphing and locomotion have diverse promising applications. Here, authors propose a scalable fabrication strategy that transforms 2D magnetic sheets into 3D soft magneto-active machines with customized geometries by incorporating origami folding

Oleanolic acid indole derivatives as novel α-glucosidase inhibitors: Synthesis, biological evaluation, and mechanistic analysis

Research efforts have been directed to the development of oleanolic acid (OA) based α-glucosidase inhibitors and various OA derivatives showed improved anti-α-glucosidase activity. However, the inhibitory effects of indole infused OA derivatives on α-glucosidase is unknown. Herein, we synthesized a series of indole-OA (2a-2o) and -OA methyl ester (3a-3 l) derivatives with various electron withdrawing groups inducted to indole benzene ring and evaluated their anti-α-glucosidase activity. Indole OA derivatives (2a-2o) exhibited superior α-glucosidase inhibitory effects as compared to OA methyl ester derivatives (3a-3l) and OA (with IC50 values of 4.02 μM-5.30 μM v.s. over 10 μM and 5.52 µM, respectively). In addition, mechanistic studies using biochemical (kinetic assay), biophysical (circular dichroism), and computational (docking) methods revealed that OA-indole derivatives (2a and 2f) are mixed type of α-glucosidase inhibitors and their inhibitory effects were attributed to their capacity of forming the ligand-enzyme complex with α-glucosidase enzyme. Findings from this study support that OA indole derivatives are promising α-glucosidase inhibitors as a potential management of diabetes mellitus