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In this work, bilinear residual network method is proposed to solve nonlinear evolution equations. The activation function in final layer of deep neural network cannot interact with the neuron inside the deep neural network, but the residual network can transfer the input layer to the activation function in final layer to realize the interaction within the network. This reduces the complexity of the model and gives more interactive results. The steps of solving the exact analytical solution through the residual network are given. The rogue wave solution of Caudrey–Dodd–Gibbon–Kotera–Sawada-like equation is obtained by using the bilinear residual network method. Characteristic plots and dynamic analysis of these rogue waves are given.

A new method named bilinear neural network is introduced in this paper, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear partial differential equations (PDEs). This is the first time that the neural network model is used to find the exact analytical solution, and this method covers almost all methods of constructing a function after bilinearization to solve nonlinear PDEs. Furthermore, this method is most likely a universal method to obtain the exact analytical solutions of nonlinear PDEs. Abundant arbitrary functions solutions of the reduced p-gBKP equation are obtained by using this method. Various beautiful plots of the presented solutions, which show diversity of exact solutions to PDEs, are made. By choosing appropriate values and functions, the fractal solitons waves are obtained and the self-similar characteristics of these waves are observed by reducing the observation range and magnifying local images. Via various three-dimensional plots, the evolution characteristics of these waves are exhibited.

It is well known that most classical test functions to solve nonlinear partial differential equations can be constructed via single hidden layer neural network model by using Bilinear Neural Network Method (BNNM). In this paper, the neural network model of test function for the (3+1)-dimensional Jimbo–Miwa equation is extended to the “4-2-3” model. By giving some specific activation functions, new test function is constructed to obtain analytical solutions of the (3+1)-dimensional Jimbo–Miwa equation. Rogue wave solutions and the bright and dark solitons are obtained by giving some specific parameters. Via curve plots, three-dimensional plots, contour plots and density plots, dynamical characteristics of these waves are exhibited.

Manipulating valley-dependent Berry phase effects provides remarkable opportunities for both fundamental research and practical applications. Here, by referring to effective model analysis, we propose a general scheme for realizing topological magneto-valley phase transitions. More importantly, by using valley-half-semiconducting VSi2N4 as an outstanding example, we investigate sign change of valley-dependent Berry phase effects which drive the change-in-sign valley anomalous transport characteristics via external means such as biaxial strain, electric field, and correlation effects. As a result, this gives rise to quantized versions of valley anomalous transport phenomena. Our findings not only uncover a general framework to control valley degree of freedom, but also motivate further research in the direction of multifunctional quantum devices in valleytronics and spintronics.

Interference wave is an important research target in the field of navigation, electromagnetic and earth science. In this work, the nonlinear property of neural network is used to study the interference wave and the bright and dark soliton solutions. The generalized broken soliton-like equation is derived through the generalized bilinear method. Three neural network models are presented to fit explicit solutions of generalized broken soliton-like equations and Boiti–Leon–Manna–Pempinelli-like equation with 100% accuracy. Interference wave solutions of the generalized broken soliton-like equation and the bright and dark soliton solutions of the Boiti–Leon–Manna–Pempinelli-like equation are obtained with the help of the bilinear neural network method. Interference waves and the bright and dark soliton solutions are shown via three-dimensional plots and density plots.

Van der Waals heterostructures of transition metal dichalcogenides with interlayer coupling offer an exotic platform to realize fascinating phenomena. Due to the type II band alignment of these heterostructures, electrons and holes are separated into different layers. The localized electrons induced doping in one layer, in principle, would lift the Fermi level to cross the spin-polarized upper conduction band and lead to strong manipulation of valley magnetic response. Here, we report the significantly enhanced valley Zeeman splitting and magnetic tuning of polarization for the direct optical transition of MoS 2 in MoS 2 /WS 2 heterostructures. Such strong enhancement of valley magnetic response in MoS 2 stems from the change of the spin-valley degeneracy from 2 to 4 and strong many-body Coulomb interactions induced by ultrafast charge transfer. Moreover, the magnetic splitting can be tuned monotonically by laser power, providing an effective all-optical route towards engineering and manipulating of valleytronic devices and quantum-computation. Van der Waals heterostructures may offer a suitable platform for all-optical manipulation of valleytronic devices. Here, the authors observe a strong enhancement of the valley magnetic response in MoS 2 , and magnetic tuning of the polarization of MoS 2 direct optical transition

In this work, simple, rapid, and low-cost multiplexed detection of tumor-related micro-RNAs (miRNAs) was achieved based on multi-color fluorescence on a microfluidic droplet chip, which simplified the complexity of light path to a half. A four-T-junction structure was fabricated to form uniform nano-volume droplet arrays with customized contents. Multi-color quantum dots (QDs) used as the fluorescence labels were encapsulated into droplets to develop the multi-path fluorescence detection module. We designed an integrated multiplex fluorescence resonance energy transfer system assisted by multiple QDs (four colors) and one quencher to detect four tumor-related miRNAs (miRNA-20a, miRNA-21, miRNA-155, and miRNA-221). The qualitative analysis of miRNAs was realized by the color identification of QDs, while the quantitative detection of miRNAs was achieved based on the linear relationship between the quenching efficiency of QDs and the concentration of miRNAs. The practicability of the multiplex detection device was further confirmed by detecting four tumor-related miRNAs in real human serum samples. The detection limits of four miRNAs ranged from 35 to 39 pmol/L was achieved without any target amplification. And the linear range was from 0.1 nmol/L to 1 μmol/L using 10 nL detection volume (one droplet) under the detection speed of 320 droplets per minute. The multiple detection system for miRNAs is simple, fast, and low-cost and will be a powerful platform for clinical diagnostic analysis.

With the advancement of systems biology research, we have already seen great progress in pharmacology studies, especially in network pharmacology. Network pharmacology has been proven to be effective for establishing the “compounds-proteins/genes-diseases” network, and revealing the regulation principles of small molecules in a high-throughput manner, thus would be very effective for the analysis of drug combinations, especially for TCM preparations. In this work, we have proposed the TCM-Mesh system, which records TCM-related information collected from various resources and could serve for network pharmacology analysis for TCM preparations in a high-throughput manner (http://mesh.tcm.microbioinformatics.org/). Currently, the database contains 6,235 herbs, 383,840 compounds, 14,298 genes, 6,204 diseases, 144,723 gene-disease associations, 3,440,231 pairs of gene interactions, 163,221 side effect records and 71 toxic records, and web-based software construct a network between herbs and treated diseases, which will help to understand the underlying mechanisms for TCM preparations at molecular levels. We have used 1,293 FDA-approved drugs, as well as compounds from an herbal material Panax ginseng and a patented drug Liuwei Dihuang Wan (LDW) for evaluating our database. By comparison of different databases, as well as checking against literature, we have demonstrated the completeness, effectiveness, and accuracy of our database.

Separation of multi-component mixtures in an energy-efficient manner has important practical impact in chemical industry but is highly challenging. Especially, targeted simultaneous removal of multiple impurities to purify the desired product in one-step separation process is an extremely difficult task. We introduced a pore integration strategy of modularizing ordered pore structures with specific functions for on-demand assembly to deal with complex multi-component separation systems, which are unattainable by each individual pore. As a proof of concept, two ultramicroporous nanocrystals (one for C 2 H 2 -selective and the other for CO 2 -selective) as the shell pores were respectively grown on a C 2 H 6 -selective ordered porous material as the core pore. Both of the respective pore-integrated materials show excellent one-step ethylene production performance in dynamic breakthrough separation experiments of C 2 H 2 /C 2 H 4 /C 2 H 6 and CO 2 /C 2 H 4 /C 2 H 6 gas mixture, and even better than that from traditional tandem-packing processes originated from the optimized mass/heat transfer. Thermodynamic and dynamic simulation results explained that the pre-designed pore modules can perform specific target functions independently in the pore-integrated materials. Separation of multi-component mixtures is an extremely difficult task. Pore integration strategy offers an approach for assembling ordered pores with specific functions on demand to achieve the one-step separation of multi-component complex mixtures.

The g-C3N4 decorated magnesium ferrite (MgFe2O4) porous microspheres composites were successfully obtained via a one-step solvothermal method. The structure and morphology of the as-prepared MgFe2O4/g-C3N4 composites were characterized by the techniques of X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), thermal gravity and differential scanning calorimeter (TG–DSC) and N2-sorption. The gas sensing properties of the samples were measured and compared with a pure MgFe2O4-based sensor. The maximum response of the sensor based on MgFe2O4/g-C3N4 composites with 10 wt % g-C3N4 content to acetone is improved by about 145 times, while the optimum temperature was lowered by 60 °C. Moreover, the sensing mechanism and the reason for improving gas sensing performance were also discussed.