ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.

BOUNDEDNESS AND EXPONENTIAL STABILITY FOR NONAUTONOMOUS FCNNs WITH REACTION-DIFFUSION TERMS AND TINE-VARYING DELAYS

In this paper, a class of nonautonomous fuzzy cellular neural networks (FCNNs) with reaction-diffusion terms and time-varying delays are investigated. By applying the inequality analysis technique, introducing ingeniously many real parameters and constructing new auxiliary functions, a series of new and useful criteria on the boundedness and globally exponential stability of solutions are established. The results obtained in this paper extend and improve the corresponding results given in previous works. Finally, two examples are given to verify the effectiveness of the obtained results.

HYBRID APPROACH FOR BRAIN TUMOR SEGMENTATION IN MAGNETIC RESONANCE IMAGES USING CELLULAR NEURAL NETWORKS AND OPTIMIZATION TECHNIQUES

Tumor segmentation from brain magnetic resonance image data is an important but time consuming task performed manually by medical experts. Automating this process is challenging due to the high diversity in appearance of tumor tissue among different patients and in many cases, similarity between tumor and normal tissue. This paper deals with an efficient segmentation algorithm for extracting brain tumors in magnetic resonance images using Cellular Neural Networks (CNN). Learning CNN templates values are formulated as an optimization problem. The template coefficients (weights) of an CNN which will give a desired performance, can be derived by learning genetic algorithm and simulated annealing optimization techniques. The objective of this work is to compare the performance of genetic algorithm (GA) and simulated annealing (SA) for finding the optimum template values in the CNN which is used for segmenting the tumor region in the abnormal MR images. The method is applied on real data of MRI images of thirty patients with four different types of tumors. The results are compared with radiologist labeled ground truth. Quantitative analysis between ground truth and segmented tumor is presented in terms of segmentation efficiency. From the analysis and performance measures like segmentation accuracy, it is inferred that the brain tumor segmentation is best done using CNN with genetic algorithm template optimization than CNN with simulated annealing template optimization. An average accuracy rate of above 95% was obtained using this segmentation algorithm.

Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction

Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.

Short-term plasticity and long-term potentiation mimicked in single inorganic synapses

Memory is believed to occur in the human brain as a result of two types of synaptic plasticity: short-term plasticity (STP) and long-term potentiation (LTP; refs 1-4). In neuromorphic engineering, emulation of known neural behaviour has proven to be difficult to implement in software because of the highly complex interconnected nature of thought processes. Here we report the discovery of a Ag(2)S inorganic synapse, which emulates the synaptic functions of both STP and LTP characteristics through the use of input pulse repetition time. The structure known as an atomic switch, operating at critical voltages, stores information as STP with a spontaneous decay of conductance level in response to intermittent input stimuli, whereas frequent stimulation results in a transition to LTP. The Ag(2)S inorganic synapse has interesting characteristics with analogies to an individual biological synapse, and achieves dynamic memorization in a single device without the need of external preprogramming. A psychological model related to the process of memorizing and forgetting is also demonstrated using the inorganic synapses. Our Ag(2)S element indicates a breakthrough in mimicking synaptic behaviour essential for the further creation of artificial neural systems that emulate characteristics of human memory.

On the global stability of time delayed CNNs

The objective of this paper is the concise presentation of the most important and recent lemmas and theorems associated with the global asymptotic and exponential stability of the equilibrium point of time delayed cellular neural networks. For each theorem a short proof is given, so that the reader can understand its features and its relationships to other theorems. In the last section, the presented theorems are grouped according to their characteristics and the way they relate to one another, and some of them are demonstrated, in order to draw conclusions about their use.

Delay-induced primary rhythmic behavior in a two-layer neural network

In this paper, we construct a two-layer feedback neural network to theoretically investigate the influence of symmetry and time delays on patterned rhythmic behaviors. Firstly, linear stability of the model is investigated by analyzing the associated transcendental characteristic equation. Next, by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups, we not only investigate the effect of synaptic delays of signal transmission on the pattern formation, but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio-temporal patterns. Thirdly, based on the normal form approach and the center manifold theory, we derive the formula to determine the bifurcation direction and stability of Hopf bifurcating periodic solutions. Finally, some numerical examples and the corresponding numerical simulations are used to illustrate the effectiveness of the obtained results.

Multiperiodicity of periodically oscillated discrete-time neural networks with transient excitatory self-connections and sigmoidal nonlinearities

The existing approaches to the multistability and multiperiodicity of neural networks rely on the strictly excitatory self-interactions of neurons or require constant interconnection weights. For periodically oscillated discrete-time neural networks (DTNNs), it is difficult to discuss multistable dynamics when the connection weights are periodically oscillated around zero. By using transient excitatory self-interactions of neurons and sigmoidal nonlinearities, we develop an approach to investigate multiperiodicity and attractivity of periodically oscillated DTNNs with time-varying and distributed delays. It shows that, under some new criteria, there exist multiplicity results of periodic solutions which are locally or globally exponentially stable. Computer numerical simulations are performed to illustrate the new theories.

An adaptive wavelet neural network for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks (AWNN) is introduced for spatio-temporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework.

Image processing with cellular nonlinear networks implemented on field-programmable gate arrays for real-time applications in nuclear fusion

In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN-unlike software CNN implementations.

Functional optical imaging at the microscopic level

Functional microscopic imaging of in vivo tissues aims at characterizing parameters at the level of the unitary cellular components under normal conditions, in the presence of blood flow, to understand and monitor phenomena that lead to maintaining homeostatic balance. Of principal interest are the setting of shear stress on the endothelium; formation of the plasma layer, where the balance between nitric oxide production and scavenging is established; and formation of the oxygen gradients that determine the distribution of oxygen from blood into the tissue. Optical techniques that enable the analysis of functional microvascular processes are the measurement of blood vessel dimensions by image shearing, the photometric analysis of the extent of the plasma layer, the dual-slit methodology for measuring blood flow velocity, and the direct measurement of oxygen concentration in blood and tissue. Each of these technologies includes the development of paired, related mathematical approaches that enable characterizing the transport properties of the blood tissue system. While the technology has been successful in analyzing the living tissue in experimental conditions, deployment to clinical settings remains an elusive goal, due to the difficulty of obtaining optical access to the depth of the tissue.

The evolution of reaction-diffusion controllers for minimally cognitive agents

This article describes work carried out to investigate whether a classic reaction-diffusion (RD) system could be used to control a minimally cognitive animat. The RD system chosen was that first described by Gray and Scott, and the minimally cognitive behaviors were those used by Beer et al. involving the fixation and discrimination of diamond and circle shapes by a whiskered animat. A further task was added, which required the RD controllers to maintain and use a chemical memory. The parameters of these controllers were evolved using an evolutionary, or genetic, algorithm.

A new method for stability analysis of recurrent neural networks with interval time-varying delay

This brief deals with the problem of stability analysis for a class of recurrent neural networks (RNNs) with a time-varying delay in a range. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. Since the obtained criterion realizes the decoupling of the Lyapunov function matrix and the coefficient matrix of the neural networks, it can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations

Universal perceptron (UP), a generalization of Rosenblatt's perceptron, is considered in this paper, which is capable of implementing all Boolean functions (BFs). In the classification of BFs, there are: 1) linearly separable Boolean function (LSBF) class, 2) parity Boolean function (PBF) class, and 3) non-LSBF and non-PBF class. To implement these functions, UP takes different kinds of simple topological structures in which each contains at most one hidden layer along with the smallest possible number of hidden neurons. Inspired by the concept of DNA sequences in biological systems, a novel learning algorithm named DNA-like learning is developed, which is able to quickly train a network with any prescribed BF. The focus is on performing LSBF and PBF by a single-layer perceptron (SLP) with the new algorithm. Two criteria for LSBF and PBF are proposed, respectively, and a new measure for a BF, named nonlinearly separable degree (NLSD), is introduced. In the sense of this measure, the PBF is the most complex one. The new algorithm has many advantages including, in particular, fast running speed, good robustness, and no need of considering the convergence property. For example, the number of iterations and computations in implementing the basic 2-bit logic operations such as AND, OR, and XOR by using the new algorithm is far smaller than the ones needed by using other existing algorithms such as error-correction (EC) and backpropagation (BP) algorithms. Moreover, the synaptic weights and threshold values derived from UP can be directly used in designing of the template of cellular neural networks (CNNs), which has been considered as a new spatial-temporal sensory computing paradigm.

Investigating the properties of self-organization and synchronization in electronic systems

Nonlinear cooperative behavior appears naturally in many systems, such as cardiac cell oscillations; cellular calcium oscillations; oscillatory chemical reactions, and fireflies. Such systems have been studied in detail due to their inherent properties of robustness, adaptability, scalability, and emergence. In this paper, such nonlinear cooperative behaviors are considered within the domain of electronic system design. We investigate these desirable properties in a system composed of electronic oscillators. The paper presents a series of circuit simulation results showing that self-organizing principles, which can be emulated in an electronic circuit, enable the systems to show a phase transition to synchronization, in a manner similar to those of natural systems. Circuit simulation results presented here show that the circuits are robust to the unreliable performance of the electronic oscillators and tolerant to their run-time faults. These are important findings for future engineering applications in which the system's elements are likely to be unreliable and faulty, such as in molecular- and nanoelectronic systems.

Convergence in networks with counterclockwise neural dynamics

The notion of counterclockwise (ccw) input-output (I-O) dynamics, introduced by Angeli (2006) to deal with questions of multistability in interconnected dynamical systems, is applied and further developed in order to analyze convergence and stability of neural networks. By pursuing a modular approach, we interpret a cellular nonlinear network (CNN) as a positive feedback of a parallel block of single-input-single-output (SISO) dynamical systems, the neurons, and a static multiple-input-multiple-output (MIMO) system that couples them (typically the so-called interconnection matrix). The analysis extends previously known results by enlarging the class of allowed neural dynamics to higher order neurons.

Bio-inspired grasp control in a robotic hand with massive sensorial input

The capability of grasping and lifting an object in a suitable, stable and controlled way is an outstanding feature for a robot, and thus far, one of the major problems to be solved in robotics. No robotic tools able to perform an advanced control of the grasp as, for instance, the human hand does, have been demonstrated to date. Due to its capital importance in science and in many applications, namely from biomedics to manufacturing, the issue has been matter of deep scientific investigations in both the field of neurophysiology and robotics. While the former is contributing with a profound understanding of the dynamics of real-time control of the slippage and grasp force in the human hand, the latter tries more and more to reproduce, or take inspiration by, the nature's approach, by means of hardware and software technology. On this regard, one of the major constraints robotics has to overcome is the real-time processing of a large amounts of data generated by the tactile sensors while grasping, which poses serious problems to the available computational power. In this paper a bio-inspired approach to tactile data processing has been followed in order to design and test a hardware-software robotic architecture that works on the parallel processing of a large amount of tactile sensing signals. The working principle of the architecture bases on the cellular nonlinear/neural network (CNN) paradigm, while using both hand shape and spatial-temporal features obtained from an array of microfabricated force sensors, in order to control the sensory-motor coordination of the robotic system. Prototypical grasping tasks were selected to measure the system performances applied to a computer-interfaced robotic hand. Successful grasps of several objects, completely unknown to the robot, e.g. soft and deformable objects like plastic bottles, soft balls, and Japanese tofu, have been demonstrated.

New stability criteria for uncertain neural networks with interval time-varying delays

This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.