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.
Long noncoding RNAs (lncRNAs) play roles in the development and progression of many cancers; however, the contributions of lncRNAs to human gallbladder cancer (GBC) remain largely unknown. In this ...study, we identify a group of differentially expressed lncRNAs in human GBC tissues, including prognosis-associated gallbladder cancer lncRNA (lncRNA-PAGBC), which we find to be an independent prognostic marker in GBC. Functional analysis indicates that lncRNA-PAGBC promotes tumour growth and metastasis of GBC cells. More importantly, as a competitive endogenous RNA (ceRNA), lncRNA-PAGBC competitively binds to the tumour suppressive microRNAs miR-133b and miR-511. This competitive role of lncRNA-PAGBC is required for its ability to promote tumour growth and metastasis and to activate the AKT/mTOR pathway. Moreover, lncRNA-PAGBC interacts with polyadenylate binding protein cytoplasmic 1 (PABPC1) and is stabilized by this interaction. This work provides novel insight on the molecular pathogenesis of GBC.
Synopsis
Long noncoding RNAs play roles in the development and progression of many cancers. In this study the lncRNA PAGBC is identified as promoting tumorigenesis in human gallbladder cancer by competitive binding to the tumour suppressive microRNAs miR-133b and miR-511.
LncRNA-PAGBC is up-regulated in GBC and increased levels associate with poor prognosis.
LncRNA-PAGBC promotes tumour growth and metastasis, and activates AKT/mTOR signaling by competitively binding to mirR-133b and mirR-511.
LncRNA-PAGBC interacts with and is stabilized by the polyadenylate binding protein PABPC1.
Graphical Abstract
Long noncoding RNAs play roles in the development and progression of many cancers. In this study the lncRNA PAGBC is identified as promoting tumorigenesis in human gallbladder cancer by competitive binding to the tumour suppressive microRNAs miR-133b and miR-511.
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.
•The lump solution method is generalized.•The CDGKS-like equation is derived through the generalized bilinear method.•The new rogue wave solution is constructed by using “3-2-2” neural network model.
...Under investigation in this paper is the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like (CDGKS-like) equation. Based on bilinear neural network method, the generalized lump solution, classical lump solution and the novel analytical solution are constructed by giving some specific activation functions in the single hidden layer neural network model and the “3-2-2” neural network model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. These results fill the blank of the CDGKS-like equation in the existing literature. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are exhibited. The effective methods used in this paper is helpful to study the nonlinear evolution equations in plasmas, mathematical physics, electromagnetism and fluid dynamics.
The Fokker–Planck equation has significant applications in dynamical systems. In recent years, some neural network methods have been used in combination with physical models to obtain its numerical ...solutions. However, it is also appealing if the analytical solution of the physical model can be obtained. This paper proposes a neural network-based method for the analytical solution of the FP equation. It relies on neural networks and uses their explicit model as the trial function for the FP equation. The trial function contains the weights and biases in the neural network. Therefore, the solving of the FP equation is converted into the calculation of the weights and biases. In the proposed method, the FP equations are first reduced to a set of easily solvable nonlinear algebraic equations using some trial functions, and then the corresponding weights and biases are determined using the method of pending coefficients. In this paper, linear and nonlinear numerical examples were used to verify the effectiveness of the proposed method. The results demonstrated that the proposed method can obtain the exact solution of the FP equations without data samples. Finally, the proposed method is compared in detail with physics-informed neural networks in terms of computational theory and computational effectiveness.
In this paper, we study a secure cooperative transmission system in which a transmitter (Alice) intends to send a secret message to an authorized receiver (Bob), with the aid of a friendly private ...cooperative jammer (Oscar), in the presence of a malicious eavesdropper (Eve). Specifically, artificial noise (AN) assisted secrecy beamforming is utilized for secure transmission. Under the imperfect channel state information (CSI) of legitimate channels and the statistic CSI of illegitimate channels, the optimal power allocation ratio between the information-bearing signal and the AN signal for maximizing secrecy rate is derived. Through mathematical analysis, we notice that the high channel estimation error is greatly detrimental to the realization of the positive secrecy rate in secure system. For overcoming this drawback, back propagation neural network (BPNN) is employed for a high accuracy channel estimation to simulate a realistic security communication scenario. The numerical results show that the channel estimation errors result in a decrease in secrecy rate, but the BPNN channel estimator still can guarantee secure transmission that verifies the feasibility of the application of physical layer security. Analytical derivations and numerical simulations are presented to validate the correctness of obtained expressions and our analysis.
Baicalein, a widely used Chinese herbal medicine, has multiple pharmacological activities. However, the precise mechanisms of the anti-proliferation and anti-metastatic effects of baicalein on ...gallbladder cancer (GBC) remain poorly understood. Therefore, the aim of this study was to assess the anti-proliferation and anti-metastatic effects of baicalein and the related mechanism(s) on GBC. In the present study, we found that treatment with baicalein induced a significant inhibitory effect on proliferation and promoted apoptosis in GBC-SD and SGC996 cells, two widely used gallbladder cancer cell lines. Additionally, treatment with baicalein inhibited the metastasis of GBC cells. Moreover, we demonstrated for the first time that baicalein inhibited GBC cell growth and metastasis via down-regulation of the expression level of Zinc finger protein X-linked (ZFX). In conclusion, our studies suggest that baicalein may be a potential phytochemical flavonoid for therapeutics of GBC and ZFX may serve as a molecular marker or predictive target for GBC.
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