Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

SIRENA: A CAD environment for behavioural modelling and simulation of VLSI cellular neural network chips

This paper presents SIRENA, a CAD environment for the simulation and modelling of mixed-signal VLSI parallel processing chips based on cellular neural networks. SIRENA includes capabilities for: (a) the description of nominal and non-ideal operation of CNN analogue circuitry at the behavioural level; (b) performing realistic simulations of the transient evolution of physical CNNs including deviations due to second-order effects of the hardware; and, (c) evaluating sensitivity figures, and realize noise and Monte Carlo simulations in the time domain. These capabilities portray SIRENA as better suited for CNN chip development than algorithmic simulation packages (such as OpenSimulator, Sesame) or conventional neural networks simulators (RCS, GENESIS, SFINX), which are not oriented to the evaluation of hardware non-idealities. As compared to conventional electrical simulators (such as HSPICE or ELDO-FAS), SIRENA provides easier modelling of the hardware parasitics, a significant reduction in computation time, and similar accuracy levels. Consequently, iteration during the design procedure becomes possible, supporting decision making regarding design strategies and dimensioning. SIRENA has been developed using object-oriented programming techniques in C, and currently runs under the UNIX operating system and X-Windows framework. It employs a dedicated high-level hardware description language: DECEL, fitted to the description of non-idealities arising in CNN hardware. This language has been developed aiming generality, in the sense of making no restrictions on the network models that can be implemented. SIRENA is highly modular and composed of independent tools. This simplifies future expansions and improvements.Comisión Interministerial de Ciencia y Tecnología TIC96-1392-C02-0

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Stability Analysis of Asynchronous States in Neuronal Networks with Conductance-Based Inhibition

Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations

Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attaining steady state solutions is pointed out. Various routes to chaos and existence of hyperchaos even for low values of time delay which is evidenced by multiple positive Lyapunov exponents are brought out. The study is extended to the case of two coupled systems, one with delay and the other one without delay.Comment: 34 Pages, 14 Figure

Comparison between Oja's and BCM neural networks models in finding useful projections in high-dimensional spaces

This thesis presents the concept of a neural network starting from its corresponding biological model, paying particular attention to the learning algorithms proposed by Oja and Bienenstock Cooper & Munro. A brief introduction to Data Analysis is then performed, with particular reference to the Principal Components Analysis and Singular Value Decomposition. The two previously introduced algorithms are then dealt with more thoroughly, going to study in particular their connections with data analysis. Finally, it is proposed to use the Singular Value Decomposition as a method for obtaining stationary points in the BCM algorithm, in the case of linearly dependent inputs

Second-order neural core for bioinspired focal-plane dynamic image processing in CMOS

Based on studies of the mammalian retina, a bioinspired model for mixed-signal array processing has been implemented on silicon. This model mimics the way in which images are processed at the front-end of natural visual pathways, by means of programmable complex spatio-temporal dynamic. When embedded into a focal-plane processing chip, such a model allows for online parallel filtering of the captured image; the outcome of such processing can be used to develop control feedback actions to adapt the response of photoreceptors to local image features. Beyond simple resistive grid filtering, it is possible to program other spatio-temporal processing operators into the model core, such as nonlinear and anisotropic diffusion, among others. This paper presents analog and mixed-signal very large-scale integration building blocks to implement this model, and illustrates their operation through experimental results taken from a prototype chip fabricated in a 0.5-μm CMOS technology.European Union IST 2001 38097Ministerio de Ciencia y Tecnología TIC 2003 09817 C02 01Office of Naval Research (USA) N00014021088

Design and development of an emulated human cognition using novel 3D neural networks

This paper describes the development of an Emulated Human Cognition (EHC) which is designed and based on a replicated human brain with a right- and a left- hand lobe, one a deductive side and the other a generic one. Right-hand lobe consists of a newly designed Artificial Neural Network (ANN) with a multi-hidden layer topology. Left-hand lobe is a newly designed 3-dimensional cellular neural network. The input variables presented to the EHC are immediately analysed for it to decide which lobe should be activated. The EHC, when fully developed, has almost an unlimited memory capacity and is capable of immediate recall of any data in its almost unlimited memory locations. EHC has been used in several applications where neural networks have been used to establish relationship between two or more sets of variables. In this paper the EHC has been used to forecast demand for a given product

Current-Mode Techniques for the Implementation of Continuous- and Discrete-Time Cellular Neural Networks

This paper presents a unified, comprehensive approach to the design of continuous-time (CT) and discrete-time (DT) cellular neural networks (CNN) using CMOS current-mode analog techniques. The net input signals are currents instead of voltages as presented in previous approaches, thus avoiding the need for current-to-voltage dedicated interfaces in image processing tasks with photosensor devices. Outputs may be either currents or voltages. Cell design relies on exploitation of current mirror properties for the efficient implementation of both linear and nonlinear analog operators. These cells are simpler and easier to design than those found in previously reported CT and DT-CNN devices. Basic design issues are covered, together with discussions on the influence of nonidealities and advanced circuit design issues as well as design for manufacturability considerations associated with statistical analysis. Three prototypes have been designed for l.6-pm n-well CMOS technologies. One is discrete-time and can be reconfigured via local logic for noise removal, feature extraction (borders and edges), shadow detection, hole filling, and connected component detection (CCD) on a rectangular grid with unity neighborhood radius. The other two prototypes are continuous-time and fixed template: one for CCD and other for noise removal. Experimental results are given illustrating performance of these prototypes