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Cellular Neural Networks: A Review
 Proc. 6th Italian Workshop on Parallel Architectures and Neural Networks, Vietri sul Mare, Italy
, 1993
"... A unified review of the Cellular Neural Network paradigm is attempted. First of all, general theoretical framework is stated, followed by description of particular models proposed in literature and comparison with other Neural Network and parallel computing paradigms. Theory of such systems, especia ..."
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A unified review of the Cellular Neural Network paradigm is attempted. First of all, general theoretical framework is stated, followed by description of particular models proposed in literature and comparison with other Neural Network and parallel computing paradigms. Theory of such systems, especially the issue of stability, is then resumed by listing main results available. Applications, design and learning follow. The paper is concluded by description of proposed and tested hardware realizations. 1. Cellular Neural Networks: spatially defined parallel analog computing for local and diffusionsolvable problems Problems defined in spacetime, e.g. image processing tasks, partial differential equations (PDE) systems, and so on, are often characterized by the fact that the information necessary to solve for the future or steady state of the system at a certain point is contained (from the start, or from a certain time on) within a finite distance of the same point. Therefore, these problems are solved by a relaxation and information diffusion process, which develops at the same time at all points of space domain.
An Exact and Direct Analytical Method for the Design of Optimally Robust CNN Templates
 IEEE TRANS. CIRCUITS & SYST.I
, 1999
"... 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 welldefined CNN tasks are characterized by a ..."
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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 welldefined 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.
Transactions Briefs Binary Output of Cellular Neural Networks with Smooth Activation
"... Abstract—An important property of cellular neural networks (CNN’s) is the binary output property, that, when the selffeedback is greater than one, the final activations are 61. This brief considers the generalization of this property to networks with sigmoidal output functions. It is shown that in ..."
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Abstract—An important property of cellular neural networks (CNN’s) is the binary output property, that, when the selffeedback is greater than one, the final activations are 61. This brief considers the generalization of this property to networks with sigmoidal output functions. It is shown that in this case the property cannot be stated without reference to the cross feedback, and conditions are found under which the property remains valid. I.
Complex
"... dynamic behavior of a CNN hardware system by an experimental and numerical analysis ..."
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dynamic behavior of a CNN hardware system by an experimental and numerical analysis
Complex dynamics in onedimensional CNNs
"... Abstract. The effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study onedimensional template CNNs are considered. It is shown that if the offdiagonal template elements have opposite sign, then the boundary conditions behave as bifu ..."
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Abstract. The effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study onedimensional template CNNs are considered. It is shown that if the offdiagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very rich and complex dynamic behavior. In particular they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractors and to the coexistence of several attractors. Then the influence of the number of cells on the global dynamics is studied, with particular reference to the occurrence of hyperchaotic behavior. 1.
Ethnic minorities and the planning system': a study revisited
 Town Planning Review
, 1997
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