Basic dynamics from a pulse-coupled network of autonomous integrate-and-fire chaotic circuits

This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena and their existence regions can be elucidated in the parameter space. We then construct a ring-type PCN and elucidate that the PCN exhibits interesting grouping phenomena based on the chaos synchronization patterns. Using a simple test circuit, some of typical phenomena can be verified in the laboratory.

Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators

This paper studies a pulse-coupled network consisting of simple chaotic spiking oscillators (CSOs). If a unit oscillator and its neighbor(s) have (almost) the same parameter values, they exhibit in-phase synchronization of chaos. As the parameter values differ, they exhibit asynchronous phenomena. Based on such behavior, some synchronous groups appear partially in the network. Typical phenomena are verified in the laboratory via a simple test circuit. These phenomena can be evaluated numerically by using an effective mapping procedure. We then apply the proposed network to image segmentation. Using a lattice pulse-coupled network via grouping synchronous phenomena, the input image data can be segmented into some sub-regions.

Sigma-delta cellular neural network for 2D modulation

Although sigma-delta modulation is widely used for analog-to-digital (A/D) converters, sigma-delta concepts are only for 1D signals. Signal processing in the digital domain is extremely useful for 2D signals such as used in image processing, medical imaging, ultrasound imaging, and so on. The intricate task that provides true 2D sigma-delta modulation is feasible in the spatial domain sigma-delta modulation using the discrete-time cellular neural network (DT-CNN) with a C-template. In the proposed architecture, the A-template is used for a digital-to-analog converter (DAC), the C-template works as an integrator, and the nonlinear output function is used for the bilevel output. In addition, due to the cellular neural network (CNN) characteristics, each pixel of an image corresponds to a cell of a CNN, and each cell is connected spatially by the A-template. Therefore, the proposed system can be thought of as a very large-scale and super-parallel sigma-delta modulator. Moreover, the spatio-temporal dynamics is designed to obtain an optimal reconstruction signal. The experimental results show the excellent reconstruction performance and capabilities of the CNN as a sigma-delta modulator.

Estimating nonlinear interdependences in dynamical systems using cellular nonlinear networks

We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.

Stability Analysis of Takagi–Sugeno Fuzzy Cellular Neural Networks With Time-Varying Delays

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results.

Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli

This paper presents new theoretical results on the global exponential stability of recurrent neural networks with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. As special cases, the Hopfield neural network and the cellular neural network are examined in detail. In addition, it is shown that criteria herein, if partially satisfied, can still be used in combination with existing stability conditions. Simulation results are also discussed in two illustrative examples.

Advanced fuzzy cellular neural network: application to CT liver images

OBJECTIVE

To achieve better boundary integrities and recall accuracies for segmented liver images, use of the advanced fuzzy cellular neural network (AFCNN), as a variant of the fuzzy cellular neural network (FCNN), is proposed to effectively segment CT liver images.

MATERIALS AND METHODS

In order to better utilize relevant contour and gray information from liver images, we have improved the FCNN [Wang S, Wang M. A new algorithm NDA based on fuzzy cellular neural networks for white blood cell detection. IEEE Trans Inform Technol Biomed, in press], which proved to be very effective for the segmentation of microscopic white blood cell images, to create the novel neural network, AFCNN. Its convergent property and global stability are proved. Based on the FCNN-based NDA algorithm [Wang S, Wang M. A new algorithm NDA based on fuzzy cellular neural networks for white blood cell detection. IEEE Trans Inform Technol Biomed, in press], we developed the AFCNN-based NDA algorithm, which we used to segment 5 CT liver images. For comparison, we also segmented the same 5 CT liver images using the FCNN-based NDA algorithm.

RESULTS AND CONCLUSION

: AFCNN has distinct advantages over FCNN in both boundary integrity and recall accuracy. In particular, the performance index Binary_rate is generally much higher for AFCNN than for FCNN when applied to CT liver images.

Training cellular automata for image processing

Experiments were carried out to investigate the possibility of training cellular automata (CA) to perform several image processing tasks. Even if only binary images are considered, the space of all possible rule sets is still very large, and so the training process is the main bottleneck of such an approach. In this paper, the sequential floating forward search method for feature selection was used to select good rule sets for a range of tasks, namely noise filtering (also applied to grayscale images using threshold decomposition), thinning, and convex hulls. Various objective functions for driving the search were considered. Several modifications to the standard CA formulation were made (the B-rule and two-cycle CAs), which were found, in some cases, to improve performance.

Associative memory design for 256 gray-level images using a multilayer neural network

A design procedure is presented for neural associative memories storing gray-scale images. It is an evolution of a previous work based on the decomposition of the image with 2L gray levels into L binary patterns, stored in L uncoupled neural networks. In this letter, an L-layer neural network is proposed with both intralayer and interlayer connections. The connections between different layers introduce interactions among all the neurons, increasing the recall performance with respect to the uncoupled case. In particular, the proposed network can store images with the commonly used number of 256 gray levels instead of 16, as in the previous approach.

A cellular nonlinear network: real-time technology for the analysis of microfluidic phenomena in blood vessels

A new approach to the observation and analysis of dynamic structural and functional parameters in the microcirculation is described. The new non-invasive optical system is based on cellular nonlinear networks (CNNs), highly integrated analogue processor arrays whose processing elements, the cells, interact directly within a finite local neighbourhood. CNNs, thanks to their parallel processing feature and spatially distributed structure, are widely used to solve high-speed image processing and recognition problems and in the description and modelling of biological dynamics through the solution of time continuous partial differential equations (PDEs). They are therefore considered extremely suitable for spatial-temporal dynamic characterization of fluidic phenomena at micrometric to nanometric scales, such as blood flow in microvessels and its interaction with the cells of the vessel wall. A CNN universal machine (CNN-UM) structure was used to implement, via simulation and hardware (ACE16k), the algorithms to determine the functional capillarity density (FCD) and red blood cell velocity (RBCV) in capillaries obtained by intravital microscopy during in vivo experiments on hamsters. The system exploits the moving particles to distinguish the functional capillaries from the stationary background. This information is used to reconstruct a map and to calculate the velocity of the moving objects.

Image processing for a tactile/vision substitution system using digital CNN

In view of the parallel processing and easy implementation properties of CNN, we propose to use digital CNN as the image processor of a tactile/vision substitution system (TVSS). The digital CNN processor is used to execute the wavelet down-sampling filtering and the half-toning operations, aiming to extract important features from the images. A template combination method is used to embed the two image processing functions into a single CNN processor. The digital CNN processor is implemented on an intellectual property (IP) and is implemented on a XILINX VIRTEX II 2000 FPGA board. Experiments are designated to test the capability of the CNN processor in the recognition of characters and human subjects in different environments. The experiments demonstrates impressive results, which proves the proposed digital CNN processor a powerful component in the design of efficient tactile/vision substitution systems for the visually impaired people.

A new approach to exponential stability analysis of neural networks with time-varying delays

This paper considers the problem of exponential stability analysis of neural networks with time-varying delays. The activation functions are assumed to be globally Lipschitz continuous. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally exponentially stable. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the reduced conservativeness of the proposed results.

New conditions for global exponential stability of cellular neural networks with delays

In this paper, we study further a class of cellular neural networks model with delays. By employing the inequality api(m)(k=1)1 b(q(k))(k) <or= 1/r sigma(m)(k=1) q(k)b(r)(k) + 1/r a(r) (a >or=0, b(k) >or=0, q(k) > 0 with sigma(m)(k=1) q(k) = r-1, and r > 1), constructing a new Lyapunov functional, and applying the Homeomorphism theory, we derive some new conditions ensuring the existence, uniqueness of the equilibrium point and its global exponential stability for cellular neural networks. These conditions are independent of delays and possess infinitely adjustable real parameters, which are of highly important significance in the designs and applications of networks. In addition, we extend or improve the previously known results.

Improved Global Robust Asymptotic Stability Criteria for Delayed Cellular Neural Networks

This paper considers the problem of global robust stability analysis of delayed cellular neural networks (DCNNs) with norm-bounded parameter uncertainties. In terms of a linear matrix inequality, a new sufficient condition ensuring a nominal DCNN to have a unique equilibrium point which is globally asymptotically stable is proposed. This condition is shown to be a generalization and improvement over some previous criteria. Based on the stability result, a robust stability condition is developed, which contains an existing robust stability result as a special case. An example is provided to demonstrate the reduced conservativeness of the proposed results.

Deriving Sufficient Conditions for Global Asymptotic Stability of Delayed Neural Networks via Nonsmooth Analysis—II

Following our recent approach of nonsmooth analysis, we report a new set of sufficient conditions and its implications for the global asymptotic stability of delayed cellular neural networks (DCNN). The new conditions not only unify a string of previous stability results, but also yield strict improvement over them by allowing the symmetric part of the feedback matrix positive definite, hence enlarging the application domain of DCNNs. Advantages of the new results over existing ones are illustrated with examples. We also compare our results with those related results obtained via LMI approach.

Estimating phase synchronization in dynamical systems using cellular nonlinear networks

We propose a method for estimating phase synchronization between time series using the parallel computing architecture of cellular nonlinear networks (CNN's). Applying this method to time series of coupled nonlinear model systems and to electroencephalographic time series from epilepsy patients, we show that an accurate approximation of the mean phase coherence R--a bivariate measure for phase synchronization--can be achieved with CNN's using polynomial-type templates.

Automated Detection of Small-Size Pulmonary Nodules Based on Helical CT Images

A computer-aided diagnosis (CAD) system to detect small-size (from 2 mm to around 10 mm) pulmonary nodules in helical CT scans is developed. This system uses different schemes to locate juxtapleural nodules and non-pleural nodules. For juxtapleural nodules, morphological closing, thresholding and labeling are performed to obtain volumetric nodule candidates; gray level and geometric features are extracted and analyzed using a linear discriminant analysis (LDA) classifier. To locate non-pleural nodules, a discrete-time cellular neural network (DTCNN) uses local shape features which successfully capture the differences between nodules and non-nodules, especially vessels. The DTCNN was trained using genetic algorithm (GA). Testing on 17 cases with 3979 slice images showed the effectiveness of the proposed system, yielding sensitivity of 85.6% with 9.5 FPs/case (0.04 FPs/image). Moreover, the CAD system detected many nodules missed by human visual reading. This showed that the proposed CAD system acted effectively as an assistant for human experts to detect small nodules and provided a "second opinion" to human observers.

Global robust stability for shunting inhibitory CNNs with delays

In this paper, the problem of global robust stability for shunting inhibitory cellular neural networks (SICNNs) is studied. A sufficient condition guaranteeing the network's global robust stability is established. The result can easily be used to verify globally robust stable networks. An example is given to illustrate that the conditions of our results are feasible.

Boundedness and stability for nonautonomous cellular neural networks with delay

In this paper, a class of nonautonomous cellular neural networks is studied. By constructing a suitable Liapunov functional, applying the boundedness theorem for general functional-differential equations and the Banach fixed point theorem, a series of new criteria are obtained on the boundedness, global exponential stability, and existence of periodic solutions.

Estimating the Lyapunov exponents of discrete systems

In the present paper, our aim is to determine both upper and lower bounds for all the Lyapunov exponents of a given finite-dimensional discrete map. To show the efficiency of the proposed estimation method, two examples are given, including the well-known Henon map and a coupled map lattice.

Absolutely exponential stability of a class of neural networks with unbounded delay

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of neural networks with partially Lipschitz continuous activation functions are investigated. The neural networks contain both variable and unbounded delays. Using the matrix property, a necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions and nonlinear integro-differential inequalities involving both variable delays and unbounded delay, using M-matrix theory, sufficient conditions for absolutely exponential stability are obtained.

Distributed sensor networks: a cellular nonlinear network perspective

Large-scale networks of integrated wireless sensors become increasingly tractable. Advances in hardware technology and engineering design have led to dramatic reductions in size, power consumption, and cost for digital circuitry, and wireless communications. Networking, self-organization, and distributed operation are crucial ingredients to harness the sensing, computing, and computational capabilities of the nodes into a complete system. This article shows that those networks can be considered as cellular nonlinear networks (CNNs), and that their analysis and design may greatly benefit from the rich theoretical results available for CNNs.

On stability of cellular neural networks with polynomial interactions

Cellular neural/nonlinear networks (CNNs) are analog dynamic processor arrays, that present local interconnections. CNN models with polynomial interactions among the cells (Polynomial type CNNs) have been recently introduced. They are useful for solving some complex computational problems and for real-time implementation of PDE-based algorithms. This manuscript provides some simple and rigorous sufficient conditions for stability of polynomial type CNNs. A particular emphasis is given to conditions that can be expressed in terms of template elements, since they can be exploited for design purposes.

On the mathematical integration of the nervous tissue based on the S-propagator formalism: II. Numerical simulations for molecular-dependent activity

In a previous article (G. A. Chauvet, 2002), presenting a theoretical approach for integrating physiological functions in nervous tissue, we showed that a specific hierarchical representation, incorporating the novel concepts of non-symmetry and non-locality, and an appropriate formalism (the S-propagator formalism) could provide a good description of a living system in general, and the nervous system in particular. We now show that, in the framework of this theory, in spite of the complexity inherent to nervous tissue and the great number of elementary mechanisms involved, the numerical resolution of the global non-local system allows us to envisage simulations that would otherwise be impossible to realize. Here, the study is limited to one physiological function, i.e., the spatiotemporal variation of membrane potential in neuronal tissue. We demonstrate that the role of the kinetic constants at the molecular level is in agreement with the observed activity of the neuronal network. The method also reveals the critical role of the maximum density of synapses along the dendritic tree in the behavior of the network. This illustrates the great advantage of the theoretical approach in studying separately any other complementary coupled function without having to modify the computational methods used here. The application of this method to the spatiotemporal variation of synaptic efficacy, which is the basis of the learning and memory function, will be treated in a forthcoming paper.

Dynamics of periodic delayed neural networks

This paper formulates and studies a model of periodic delayed neural networks. This model can well describe many practical architectures of delayed neural networks, which is generalization of some additive delayed neural networks such as delayed Hopfield neural networks and delayed cellular neural networks, under a time-varying environment, particularly when the network parameters and input stimuli are varied periodically with time. Without assuming the smoothness, monotonicity and boundedness of the activation functions, the two functional issues on neuronal dynamics of this periodic networks, i.e. the existence and global exponential stability of its periodic solutions, are investigated. Some explicit and conclusive results are established, which are natural extension and generalization of the corresponding results existing in the literature. Furthermore, some examples and simulations are presented to illustrate the practical nature of the new results.

CrossNets: High-Performance Neuromorphic Architectures for CMOL Circuits

The exponential, Moore's Law, progress of electronics may be continued beyond the 10-nm frontier if the currently dominant CMOS technology is replaced by hybrid CMOL circuits combining a silicon MOSFET stack and a few layers of parallel nanowires connected by self-assembled molecular electronic devices. Such hybrids promise unparalleled performance for advanced information processing, but require special architectures to compensate for specific features of the molecular devices, including low voltage gain and possible high fraction of faulty components. Neuromorphic networks with their defect tolerance seem the most natural way to address these problems. Such circuits may be trained to perform advanced information processing including (at least) effective pattern recognition and classification. We are developing a family of distributed crossbar network (CrossNet) architectures that permit the combination of high connectivity neuromorphic circuits with high component density. Preliminary estimates show that this approach may eventually allow us to place a cortex-scale circuit with about 10(10) neurons and about 10(14) synapses on an approximately 10 x 10 cm(2) silicon wafer. Such systems may provide an average cell-to-cell latency of about 20 nsec and, thus, perform information processing and system training (possibly including self-evolution after initial training) at a speed that is approximately six orders of magnitude higher than in its biological prototype and at acceptable power dissipation.

Global convergence of delayed neural network systems

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.