In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

In [10] a theoretical framework for locally-adaptive smoothing of multidimensional data was presented. Based on this framework we introduce a hardware efficient architecture suitable for mixed-mode VLSI implementation. Substantial shortcomings of analogue implementations are overcome by connecting all cells in a circular structure: i) influence of process parameter deviation ii) limited number of cells iii) input/output bottleneck. The connections between the analogue cells and the cells themselves are dynamically reconfigured. This results in a non-linear adaptive filter kernel which is shifted virtually over the signal vector of infinite length. A 1-d prototype with 32 cells has been fabricated using 0.8¯m CMOS-technology. The chip is fully functional with an overall error less than 1%; experimental results are presented in this paper.

. In this article, we present a lattice differential equation model for a class of neural networks. We define a subset of the equilibrium solutions we call mosaic equilibrium solutions. Existence and stability theorems are proved for mosaic equilibrium solutions. Regions of stability are defined and spatial entropy calculations, as a measure of the complexity of the system, are presented that give insights in to the effects of spatial coupling. 1. Introduction. Neural networks are computational models characterized by patterns of weighted interconnections between neurons or cells. The method of determining the weights is called a training algorithm which resets the weights in accordance with some activation function. The result is a system which trains itself to recognize patterns or emulate functions. Traditional nets such as the Hopfield Net and the standard Backpropagation Neural Network have been intriguing to many disciplines. Although training can be slow, the resulting network ...