Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow

To improve the performance of multilayer perceptron(MLP)neural networks activated by conventional activation functions,this paper presents a new MLP activated by univariate Gaussian radial basis functions(RBFs)with adaptive centers and widths,which is composed of more than one hidden layer.In the hidden layer of the RBF-activated MLP network(MLPRBF),the outputs of the preceding layer are first linearly transformed and then fed into the univariate Gaussian RBF,which exploits the highly nonlinear property of RBF.Adaptive RBFs might address the issues of saturated outputs,low sensitivity,and vanishing gradients in MLPs activated by other prevailing nonlinear functions.Finally,we apply four MLP networks with the rectified linear unit(ReLU),sigmoid function(sigmoid),hyperbolic tangent function(tanh),and Gaussian RBF as the activation functions to approximate the one-dimensional(1D)sinusoidal function,the analytical solution of viscous Burgers’equation,and the two-dimensional(2D)steady lid-driven cavity flows.Using the same network structure,MLP-RBF generally predicts more accurately and converges faster than the other threeMLPs.MLP-RBF using less hidden layers and/or neurons per layer can yield comparable or even higher approximation accuracy than other MLPs equipped with more layers or neurons.

Single cell RNA and immune repertoire prowling of COVID-19 patients reveal novel neutralizing antibody

There is no doubt that COVID-19 outbreak is currently the biggest public health threat,which has caused catastrophic con sequences in many countries and regions.As host immunity is key to fighting against virus infection,it is important to characterize the immunologic changes in the COVID-19 patients,and to explore potential therapeutic candidates.The most efficient ways to end this pandemic are to vaccinate the susceptible population,and to use specific drugs,such as monoclonal antibodies against the viral spike protein(S protein),to treat the affected individuals.Several promising neutralizing antibodies have recently been reported(Cao et al.,2020;Lv et al.,2020).

Complete cohomology for complexes with finite Gorenstein AC-projective dimension

We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC- projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.