Applications of Artificial Neural Networks for Periodic Structures Analysis

The paper presents the nondeterministic, based on artificial neural network application approach analysis of periodic structures. We can distinguish several examples where the problem may be observed: conventional and magnetic railways, high building constructions that consist of repeatable blocks, ship and aeroplane bodies, space-shuttle periodic designs, long-beam antenna structures or mistuned blade disks with friction damping elements. The scope of research is to examine possibilities of use the neural networks for mistuning parameters definition and also to denominate its possible causes. The results obtained via neural network simulator training process are compared with the calculations based on mathematical model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some New Approaches to the Construction and Learning of Artificial Neural Networks

We propose two new approaches to the construction of artificial neural networks: a Fourier neural network and a binary neural network. A distinctive feature of the approaches proposed is the availability of simple, linear, single-step learning algorithms, which enables one to apply them to the construction of networks with a fairly large number of neurons and weights.     

A Comparison of Discriminant Analysis versus Artificial Neural Networks

Artificial Neural Network (ANN) techniques have recently been applied to many different fields and have demonstrated their capabilities in solving complex problems. In a business environment, the techniques have been applied to predict bond ratings and stock price performance. In these applications, ANN techniques outperformed widely-used multivariate statistical techniques. The purpose of this paper is to compare the ANN method with the Discriminant Analysis (DA) method in order to understand the merits of ANN that are responsible for the higher level of performance. The paper provides an overview of the basic concepts of ANN techniques in order to enhance the understanding of this emerging technique. The similarities and differences between ANN and DA techniques in representing their models are described. This study also proposes a method to overcome the limitations of the ANN approach, Finally, a case study using a data set in a business environment demonstrates the superiority of ANN over DA as a method of classification of observations.     

几类微分-代数方程的神经网络求解法

在非线性科学中，寻求微分方程的近似解析解一直是重要的研究课题和研究热点.利用人工神经网络原理，结合最优化方法，研究了几类微分-代数方程的近似解析解，包括指标1，2，3型Hessenberg方程及指标3型Euler-Lagrange方程，得到了方程近似解析解的表达式.通过与精确解或Runge-Kutta(龙格-库塔)数值计算结果对比，表明神经网络方法的结果有很高的精度.     

人工神经网络在SARS疫情分析与预测中的应用

讨论人工神经网络在 SARS疫情分析与预测中的应用 .采用三层结构的反向传播网络 ( Backpropagation network,简称 BP网络 ) ,对 SARS在中国的传播与流行趋势及控制策略建立了网络模型 .并利用实际数据拟合参数 ,针对北京、山西的疫情进行了计算仿真 .结果表明 ,该网络模型算法收敛速度较快 ,预测精度很高     

Novel Algorithms for Noisy Minimization Problems with Applications to Neural Networks Training

The supervisor and searcher cooperation framework (SSC), introduced in Refs. 1 and 2, provides an effective way to design efficient optimization algorithms combining the desirable features of the two existing ones. This work aims to develop efficient algorithms for a wide range of noisy optimization problems including those posed by feedforward neural networks training. It introduces two basic SSC algorithms. The first seems suited for generic problems. The second is motivated by neural networks training problems. It introduces also inexact variants of the two algorithms, which seem to possess desirable properties. It establishes general theoretical results about the convergence and speed of SSC algorithms and illustrates their appealing attributes through numerical tests on deterministic, stochastic, and neural networks training problems.     

Traveling Wave Solutions for Planar Lattice Differential Systems with Applications to Neural Networks

We obtain some existence results for traveling wave fronts and slowly oscillatory spatially periodic traveling waves of planar lattice differential systems with delay. Our approach is via Schauder's fixed-point theorem for the existence of traveling wave fronts and via S¹-degree and equivarant bifurcation theory for the existence of periodic traveling waves. As examples, the obtained abstract results will be applied to a model arising from neural networks and explicit conditions for traveling wave fronts and global continuation of periodic waves will be obtained.     

On Fixed Points of Continuous Mappings Associated with Construction of Artificial Neural Networks

Doklady Mathematics - A general topological approach is proposed for the construction of converging artificial neural networks (ANN) by applying decision-making algorithms tuned on a sequence of...     

Applications of Hybrid Monte Carlo to Bayesian Generalized Linear Models: Quasicomplete Separation and Neural Networks

Abstract

The “leapfrog” hybrid Monte Carlo algorithm is a simple and effective MCMC method for fitting Bayesian generalized linear models with canonical link. The algorithm leads to large trajectories over the posterior and a rapidly mixing Markov chain, having superior performance over conventional methods in difficult problems like logistic regression with quasicomplete separation. This method offers a very attractive solution to this common problem, providing a method for identifying datasets that are quasicomplete separated, and for identifying the covariates that are at the root of the problem. The method is also quite successful in fitting generalized linear models in which the link function is extended to include a feedforward neural network. With a large number of hidden units, however, or when the dataset becomes large, the computations required in calculating the gradient in each trajectory can become very demanding. In this case, it is best to mix the algorithm with multivariate random walk Metropolis—Hastings. However, this entails very little additional programming work.     

人工神经网络在评定射击效率中的应用研究

将BP、RB、GRNN等人工神经网络引入火炮射击效率评定的计算中.通过实例运算,分析了各种神经网络在实际应用中各自的特点和需注意的问题,得到了有益的结论.     

An Approach to Modeling Artificial Gene Networks

We propose a new mathematical model of a repressilator, i.e., the simplest gene ring network consisting of three elements. The studied model is a three-dimensional system of ordinary differential equations depending on a single parameter. We study the existence and stability problems for relaxation periodic motion in this system.     

Optimal Stochastic Distribution of CNTS in a Cantilever Polymer Microbeam Using Artificial Neural Networks

Mechanics of Composite Materials - The optimal stochastic distribution of carbon nanotubes (CNTs) in nanoreinforced polymer composite of a cantilevered microbeam is investigated. Finite-element...     

基于灰色神经网络模型的水质预测应用研究

将灰色模型和神经网络模型进行组合建立灰色神经网络模型,分别用灰色模型、神经网络模型和组合模型对永定河流域官厅水库断面的水质检测指标DO的浓度值进行模拟预测.结果表明,组合预测模型的模拟预测精度高于两种单一模型的预测精度.     

Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

Deep neural network is a powerful tool for many tasks. Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past years. In the literature of mathematical analysis of deep neural networks, a lot of works is dedicated to establishing representation theories. How to make connections between deep neural networks and mathematical algorithms is still under development. In this paper, we give an algorithmic...     

Convergence of Solutions to Equations Arising in Neural Networks

We study polynomial ordinary differential systems whereQ0 is an n×n matrix and M(t) is an n×k matrix. It is proven that, as t grows to infinity, the solution M(t) tends to a limit BU, where U is a k×k orthogonal matrix and B is an n×k matrix whose columns are k pairwise orthogonal, normalized eigenvectors of Q. Moreover, for almost every M ₀, these eigenvectors correspond to the k maximal eigenvalues of Q; for an arbitrary Q with independent columns, we provide a procedure of computing B by employing elementary matrix operations on M ₀. This result is significant for the study of certain neural network systems, and in this context it shows that M() provides a principal component analyzer.     

正则模糊神经网络在Sugeno积分模意义下的泛逼近性

首先,给出了可加模糊测度空间上Sugeno积分模的定义。然后证明了正则模糊神经网络依Sugeno积分模对模糊值函数来讲具有泛逼近性。     

数学规划的求解与广义Hopfield神经网络

神经网络技术最为成功的应用领域之一是用于求解优化问题,本文就近年来的求解优化问题的神经网络方法进行了综述     

Harmonic Analysis of Neural Networks

It is known that superpositions of ridge functions (single hidden-layer feedforward neural networks) may give good approximations to certain kinds of multivariate functions. It remains unclear, however, how to effectively obtain such approximations. In this paper, we use ideas from harmonic analysis to attack this question. We introduce a special admissibility condition for neural activation functions. The new condition is not satisfied by the sigmoid activation in current use by the neural networks community; instead, our condition requires that the neural activation function be oscillatory. Using an admissible neuron we construct linear transforms which represent quite general functionsfas a superposition of ridge functions. We develop

• • • a continuous transform which satisfies a Parseval-like relation;
• • • a discrete transform which satisfies frame bounds.

Both transforms representfin a stable and effective way. The discrete transform is more challenging to construct and involves an interesting new discretization of time–frequency–direction space in order to obtain frame bounds for functions inL²(A) whereAis a compact set of Rⁿ. Ideas underlying these representations are related to Littlewood–Paley theory, wavelet analysis, and group representation theory.     

离散神经网络指数稳定的增强李亚普诺夫方法

This paper addresses the problem of robust stability for a class of discrete-time neural networks with time-varying delay and parameter uncertainties.By constructing a new augmented Lyapunov-Krasovskii function,some new improved stability criteria are obtained in forms of linear matrix inequality（LMI） technique.Compared with some recent results in the literature,the conservatism of these new criteria is reduced notably.Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.