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Recently, a novel structure called the simplicial cellular neural network (CNN) has been introduced [1], which permits to implement any Boolean/Gray-level function of any number of variables. This paper is devoted to explore novel circuit architectures for the implementation of the simplicial CNN based on resonant tunneling diodes. The final objective is to implement a fully programmable CNN in a hardware platform based on nanoelectronic devices. Index Terms--Cellular neural networks (CNNs), piecewise-linear (PWL) approximation, resonant tunneling diodes. (RTDs).

This paper introduces a novel neural architecture which is capable of similar performance to any of the 'classic' neural paradigms while having a very simple and efficient mixed-signal implementation which makes it a valuable candidate for intelligent signal processing in portable multimedia applications. The architecture and its realization circuit are described and the functional capabilities of the novel neural architecture called a simplicial neural cell are demonstrated for both regression and classification problems including nonlinear image filtering. Index Terms--Cellular neural networks, feedforward neural networks, image reconstruction, mixed analog-digital integrated circuits, pattern classification, piecewise linear (PWL) approximation.

In this paper, we propose a universal piecewise-linear (PWL) CNN coupling cell, the simplicial cell, which is intended to work with binary as well as gray-level inputs. The construction of the cell is based on the theory of canonical simplicial PWL representations. As a consequence, the coupling function is endowed with important numerical features, namely: the representation of the characteristic cell function is sparse; the familiy of coupling functions constitutes a Hilbert space; powerful solution algorithms have been developed for the approximation of nonlinear functions, which is particularly useful when the CNN parameters need to be tuned from examples; the parameters can be extracted from a truth table when the CNN is specified analytically. Index Terms--Cellular neural networks, image processing, piecewise-linear approximation.

A synaptic operator based on multiplication requires a large amount of hardware, particularly in digital implementations. In this brief, we introduce an extended class of synaptic operators which includes the standard multiplication as a particular case. The properties of the extended class of operators are established. Among these, it was found that the global stability theorem of cellular neural networks (CNN's) is applicable to the extended class of synaptic operator as well as for the multiplier-based synapse. This is an important property which allows for the replacement of the multiplication-based synaptic operator with another specific member of the extended class, here referred to as a comparative synapse, without changing the functionality of the overall CNN system. Instead of multiplication, which has an implementation complexity of O([n.sup.2]), the comparative synapse has a complexity of only O(n) in a digital implementation (where n is the resolution of the fixed-point implementation). The effectiveness of this new operator is demonstrated by a few examples of discrete-time CNN operating in all possible dynamic modes (equilibrium, periodic and chaotic).

This paper introduces a novel synaptic model called a comparative synapse. Compared with traditional synapses, the new model is multiplication free, being thus attractive for digital implementations. Our results suggests that in an adaptive layer with binary outputs, the synaptic model does not significantly affect the system performances, provided that the input data is properly projected via a nonlinear preprocessor into a separable space. A set of benchmark classification problems were considered to illustrate this property for the case of the comparative synapse and a nonlinear preprocessor defined by fuzzy membership functions. Index Terms--Adaptive signal processing, fuzzy logic, neural networks, neural network hardware, pattern classification, piecewise linear approximation.