正则模糊神经网络对一类连续模糊值函数的普遍近似性

本文讨论了正则模糊神经网络于对定义于区间［０，Ｔ０］上连续可减模糊值函数的普遍近似性，在此基础上，证明了［０，Ｔ０］上取值为三角形模糊连续递增函数可用正则模糊神经网络逼近到任意精度。     

An approximation by neural networkswith a fixed weight

Neural networks are widely used in many applications including astronomical physics,image processing, recognition, robotics, and automated target tracking, etc. Their ability to approximate arbitrary functions is the main reason for this popularity. In this paper, we discuss the constructive approximation on the whole real line by a neural networks with a sigmoidal activation function and a fixed weight. Using the convolution method, we show neural network approximation with a fixed weight to a continuous function on a compact interval. Also, we demonstrate a computational work that shows good agreement with theory.     

Application of Sequential Learning Neural Networks to Civil Engineering Modeling Problems

A sequential orthogonal approach to the building and training of a single hidden layer neural network is presented in this paper. The Sequential Learning Neural Network (SLNN) model proposed by Zhang and Morris [1]is used in this paper to tackle the common problem encountered by the conventional Feed Forward Neural Network (FFNN) in determining the network structure in the number of hidden layers and the number of hidden neurons in each layer. The procedure starts with a single hidden neuron and sequentially increases in the number of hidden neurons until the model error is sufficiently small. The classical Gram–Schmidt orthogonalization method is used at each step to form a set of orthogonal bases for the space spanned by output vectors of the hidden neurons. In this approach it is possible to determine the necessary number of hidden neurons required. However, for the problems investigated in this paper, one hidden neuron itself is sufficient to achieve the desired accuracy. The neural network architecture has been trained and tested on two practical civil engineering problems – soil classification, and the prediction o strength and workability of high performance concrete.     

Design of multi-layer coated particles with sigmoidal release pattern

In order to design and control the release pattern of an active solid component, we investigated the release characteristics of core particles coated with multiple layers of fine permeable particles surrounding soluble particles dispersed in layers of impermeable wax. We examined the effect of operational conditions on the parameters of the release profile by multivariate analysis, and obtained simplified correlations for the maximum release rate and the lag time of the release curve as a function of the volume fraction of permeable particles and the thickness of the permeable- and soluble-particle layers. The results confirmed that the desired release rate could be obtained in the first place by adjusting the volume fraction and the thickness of the permeable-particle layer, while it was also possible to attain the required lag time by changing the thickness of the soluble layer. Finally, the calculation examples successfully illustrated the possibility of our being able to design the controlled-release particles with a prescribed sigmoidal release.     

Influence of the swelling history on the swelling kinetics of stimuli-responsive poly[(N-isopropylacrylamide)-co-(methacrylic acid)] hydrogels

The influence of the swelling history on the swelling behavior of poly[(N-isopropylacrylamide)-co-(methacrylic acid)] P[(N-iPAAm)-co-(MAA)] random copolymers hydrogels synthesized by free radical polymerization in solution of N-iPAAm and MAA comonomers crosslinked with tetraethylene glycol dimethyl acrylate (TEGDMA) has been studied. The swelling behavior under pH 7 at 18, 29, 39 and 49 °C of this series of copolymers, previously soaked either at pH 2 or 7 has been investigated. The swelling kinetics of these two series of samples displays different behavior as function of the composition and temperature. However, the equilibrium swelling values only show slight dependences on the previous soaking pH and temperature. When samples are soaked at pH 7, then the swelling at pH 7 follows a first order kinetics, irrespective of the copolymer composition or the temperature at which the experiment has been carried out. In this case, the swelling process is very fast and depends only slightly on temperature. The first order rate constant increases with the MAA content in the hydrogel. Furthermore, the swelling rate of copolymer hydrogels soaked at pH 2, show strong dependence on composition and temperature. They follow an autocatalytic swelling kinetics due to the disruption of hydrogen bond arrangements. An initial slow water uptake is followed by an acceleration process, in which water molecules inside the gel help the next water molecules to come in. Two rate constants, a first-order rate constant and an autocatalytic one have been obtained from the kinetics analysis. They have revealed different temperature dependence which may be due to a balance between hydrophobic and hydrogen bond interactions. The temperature dependence of the swelling kinetics is stronger and more complex for copolymers treated under pH 2 than for copolymers soaked under pH 7.     

Proteomic waves in networks of transcriptional regulators

The protein production for a gene regulatory network model with activation–repression links (cascade) is analysed. In these networks this production depends on how proteins induce or repress the genes. Experiments show that networks of inducers or repressors exhibit bistability or oscillatory behaviour of protein production. Here we report a completely novel aspect, namely for different promoter activity functions, protein production (initially localised on a certain number of genes) can propagate to the others in a “solitonic” way. In particular, the chemical rate equation for the cascade can be solved exactly and in the case of big number of operator sites the proteomic signal along the gene network is given by a superposition of perturbed dark solitons of defocusing semidiscrete modified Korteweg de Vries equation.     

Artificial wavelet neural network and its application in neuro-fuzzy models

In the proposed work, two types of artificial neural networks are proposed by using well-known advantages and valuable features of wavelets and sigmoidal activation functions. Two neurons are derived by adding and multiplying the outputs of the wavelet and the sigmoidal activation functions. These neurons in a feed-forward single hidden layer network result summation wavelet neural network (SWNN) and multiplication wavelet neural network (MWNN). An algorithm is introduced for structure determination of the proposed networks. Approximation properties of SWNN and MWNN have been evaluated with different wavelet functions. The above networks in the consequent part of the neuro-fuzzy model result summation wavelet neuro-fuzzy (SWNF) and multiplication wavelet neuro-fuzzy (MWNF) models. Different types of wavelet function are tested with the proposed networks and fuzzy models on four different dynamical examples. Convergence of the learning process is also guaranteed by adaptive learning rate and performing stability analysis using Lyapunov function.     

Measuring sigmoidality

Several new shape measures are proposed for measuring the sigmoidality (i.e. S-shapedness) of a curve or a region's axis. The correctness of the measures are verified on synthetic data, and then tested quantitatively on several classification tasks.     

The <Emphasis Type="Italic">p</Emphasis>-recursive piecewise polynomial sigmoid generators and first-order algorithms for multilayer tanh-like neurons

This paper demonstrates how the p-recursive piecewise polynomial (p-RPP) generators and their derivatives are constructed. The feedforward computational time of a multilayer feedforward network can be reduced by using these functions as the activation functions. Three modifications of training algorithms are proposed. First, we use the modified error function so that the sigmoid prime factor for the updating rule of the output units is eliminated. Second, we normalize the input patterns in order to balance the dynamic range of the inputs. And third, we add a new penalty function to the hidden layer to get the anti-Hebbian rules in providing information when the activation functions have zero sigmoid prime factor. The three modifications are combined with two versions of Rprop (Resilient propagation) algorithm. The proposed procedures achieved excellent results without the need for careful selection of the training parameters. Not only the algorithm but also the shape of the activation function has important influence on the training performance.