Nonlinear functions can be approximated by the linear combination of base functions, which provides a road towards the analog synthesis. An improved Simulated Annealing Algorithm(SA) for nonlinear function approximation and a universal implementation of analog circuits are presented in this paper. Synthesis results demonstrate the validity and efficiency of the proposed approach.

The Hamming distance of a Boolean function to the functions having many linear structures is an important cryptographic parameter. Most notably, the accuracy of the approximation of the combining function by a function of fewer variables is a major issue in most attacks against combination generators. Here, we show that the distance of a function to the functions having a k-dimensional linear s...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this brief note we make three remarks concerning adaptive implementations of neural networks and fuzzy systems. First, we bring to the readers attention the fact that the potential power of these systems as function approximators is lost when, as done in recently published work, the adjustable parameters are only the linear combination weights of the basis functions. Second, we show that the...

We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of L p and Besov spaces. We...

Neural Networks are widely noticed to provide a nonlinear function approximation method. In order to make its approximation ability clear, a new theorem on an integral transform of ridge functions is presented. By using this theorem, an approximation bound, which clari es the quantitative relationship between the approximation accuracy and the number of elements in the hidden layer, can be obta...

We derive Monte Carlo-amenable solutions to the problem of unbiased estimation of a nonlinear function of the mean of a normal distribution. For most nonlinear functions the maximum likelihood estimator is biased. Our method yields a Monte Carlo approximation to the uniformly minimum variance unbiased estimator for a wide class of nonlinear functions. Applications to problems arising in the ana...

Generalized Regression Neural Network (GRNN) is usually applied to the Function approximation. This paper, based on the principle of GRNN, presents a method for the predictive model of nonlinear complex system. The presented algorithm is applied to the learning and predicting process for the system modeling. The simulations show the described method has good effects on predicting the dynamic pr...

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which ...

When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear statespace models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The key idea in this paper is to run a particle filter based on a current parameter estimate, but then use the output from this particle filter to re-evaluate the l...