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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.

A significant increase in the information processing abilities of CNN's demands powerful information processing at the cell level. In this paper, the defining formula, the main properties, and several applications of a novel coupling cell are presented. Since it is able to implement any Boolean function, its functionality expands on those of digital RAM's by adding new capabilities such as learning and interpolation. While it is able to embed all previously accumulated knowledge regarding useful binary information processing tasks performed by standard CNN's, the pyramidal universal cell provides a broader context for defining other useful processing tasks, including extended gray scale or color image processing as well. Examples of applications in image processing are provided in this paper. Implementation issues are also considered. Assuming some compromise between area and speed, a VLSI implementation of CNN's based on pyramidal cells offers a speedup of up to one million times when compared to corresponding software implementations.

A novel image scanning and transmission system is proposed, where the traditional raster scan is replaced with a new one, called a chaotic scan. The result is a low complexity image transmission system with encryption and spread spectrum capabilities well suited for compressed sensing applications. Due to the uncorrelated nature of the consecutively scanned pixels, it allows a form of progressive compression and fast discovery of the relevant image features using only a small fraction of the transmitted pixels. The key ingredient of the proposed system is a chaotic counter addressing the sensor array, based on a cellular automaton exhibiting a pseudo-random chaotic behavior and binary synchronization property. [ABSTRACT FROM AUTHOR]

It is shown that 8 of all 256 elementary cellular automata have the property of chaos synchronization using a binary driving sequence. The binary synchronization signal ensures good noise robustness. A simple measure for characterizing long periodic cycles as being "chaotic" was introduced. It is also shown that certain relations between the profile of attractors shaped by the local rule in the finite state space and the property of chaos synchronization exists. A simple modulation–demodulation scheme is proposed allowing to build spread spectrum communication links at low implementation costs while the cellular automata state space (number of cells) can be taken as large as required by cryptographic reasons. [ABSTRACT FROM AUTHOR]

This paper proposes a compact neural classifier, based on the theory of simplicial decomposition and approximation, with a very convenient hardware or software implementation. It can learn arbitrary n-inputs patterns with O(n) time complexity. There are no multipliers required, and the learned knowledge is stored in a general purpose RAM with a size ranging from O(n) to O(n2). The proposed architecture is composed only of four building blocks, an iterative nonlinear expander, a sorter, a RAM memory, and an accumulator, all of them readily available in either digital hardware or software technology. Simulation results indicate good accuracy for a wide variety of benchmark problems. © 2008 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This tutorial provides a nonlinear dynamics perspective to Wolfram's monumental work on A New Kind of Science. By mapping a Boolean local Rule, or truth table, onto the point attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram's empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenomena is that it is based on concepts from nonlinear dynamics and attractors where many fuzzy concepts introduced by Wolfram via brute force observations can be defined and justified via mathematical analysis. The main result of Part I is the introduction of a fundamental concept called linear separability and a complexity index κ for each local Rule which characterizes the intrinsic geometrical structure of an induced "Boolean cube" in three-dimensional Euclidean space. In particular, Wolfram's seductive idea of a "threshold of complexity" is identified with the class of local Rules having a complexity index equal to 2. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for studying the relationship between the properties of isolated cells and the emergent behavior that occurs in cellular systems formed by coupling such cells. The novelty of our approach consists of a method for precisely partitioning the cell parameter space into subdomains via the failure boundaries of the piecewise-linear CNN (cellular neural network) cells [Dogaru & Chua, 1999a] of a generalized cellular automata [Chua, 1998]. Instead of exploring the rule space via statistically defined parameters (such as λ in [Langton, 1990]), or by conducting an exhaustive search over the entire set of all possible local Boolean functions, our approach consists of exploring a deterministically structured parameter space built around parameter points corresponding to "interesting" local Boolean logic functions. The well-known "Game of Life" [Berlekamp et al., 1982] cellular automata is reconsidered here to exemplify our approach and its advantages. Starting from a piecewise-linear representation of the classic Conway logic function called the "Game of Life", and by introducing two new cell parameters that are allowed to vary continuously over a specified domain, we are able to draw a "map-like" picture consisting of planar regions which cover the cell parameter space. A total of 148 subdomains and their failure boundaries are precisely identified and represented by colored paving stones in this mosaic picture (see Fig. 1), where each stone corresponds to a specific local Boolean function in cellular automata parlance. Except for the central "paving stone" representing the "Game of Life" Boolean function, all others are mutations uncovered by exploring the entire set of 148 subdomains and determining their dynamic behaviors. Some of these mutations lead to interesting, "artificial life"-like behavior where colonies of identical miniaturized patterns emerge and evolve from random initial conditions. To classify these... [ABSTRACT FROM AUTHOR]

The goal of this letter is to report a novel class of dynamical behaviors observed from a generalized cellular automata CNN [Chua, 1998] with piecewise-linear (PWL) cells. Starting from an almost homogeneous initial condition, self-making (autopoietic in the sense of [Varela et al., 1974]) patterns, reminiscent of simple living systems, emerge as a result of the nonlinear coupling among cells. Similar to patterns of organization characterizing living systems, our patterns display features such as growth, maturity and death. The discovery of such patterns was made possible via mutations in several piecewise-linear CNN cell realizations of the "Game of Life" [Conway, 1982]. [ABSTRACT FROM AUTHOR]

A cellular neural/nonlinear network (CNN) [Chua, 1998] is a biologically inspired system where computation emerges from a collection of simple nonlinear locally coupled cells. This paper reviews our recent research results beginning from the standard uncoupled CNN cell which can realize only linearly separable local Boolean functions, to a generalized universal CNN cell capable of realizing arbitrary Boolean functions. The key element in this evolutionary process is the replacement of the linear discriminant (offset) function w(σ) = σ in the "standard" CNN cell in [Chua, 1998] by a piecewise-linear function defined in terms of only absolute value functions. As in the case of the standard CNN cells, the excitation σ evaluates the correlation between a given input vector u formed by the outputs of the neighboring cells, and a template vector b, which is interpreted in this paper as an orientation vector. Using the theory of canonical piecewise-linear functions [Chua & Kang, 1977], the discriminant function w(cr): z + z[sub 0]σ - s ∑[sub k=1][sup m] (-l)[sup k]σ -z[sub k] is found to guarantee universality and its parameters can be easily determined. In this case, the number of additional parameters and absolute value functions m is bounded by m < 2[sup n] - 1, where n is the number of all inputs (n: 9 for a 3 x 3 template). An even more compact representation where m < n - 1 is also presented which is based on a special form of a piecewise-linear function; namely, a multi-nested discriminant: w(σ) = s(z[sub m] + |z[sub m-1] + … |z[sub 1] + |z[sub 0] + σ|||). Using this formula, the "benchmark" Parity function with an arbitrary number of inputs n is found to have an analytical solution with a complexity of only m = O(log[sub 2](n)). [ABSTRACT FROM AUTHOR]