As conventional computers based on von Neumann architecture approach their physical and performance limits, unconventional computing paradigms such as Cellular Neural Networks (CellNNs) have emerged as promising platforms for real-time, massively parallel analog computation. However, conventional analog CellNNs suffer from scalability and power constraints due to large cell hardware overhead. This work investigates the integration of memristor-based crossbar arrays into CellNN architectures to address these limitations by exploiting their analog tunability, high density, and low power operation. A 1-Transistor-1-Memristor (1T1R) crossbar is proposed for implementing the coupling weights defining the CellNN gene. Device nonlinearity, asymmetry and stochastic variability are incorporated using the physics-based JART VCM memristor model, enabling accurate mapping of target weights onto memristor conductances through numerical optimization and differential-pair encoding. Simulations of edge detection tasks confirm high functional accuracy and robustness, while Monte Carlo analysis reveals variability’s impact, underscoring the need for variability-aware design of reliable memristor-CNN hardware.

Memristive devices are promising enablers for computing-in-memory architectures, offering reduced latency and energy consumption compared to conventional designs. Among these, the memristive device-based Cellular Nonlinear Network (M-CNN) provides a compact framework for universal computing, including image processing and neuromorphic computing. In this work, we investigate the use of IGZO-based devices exhibiting gradual switching as core elements of M-CNN cells. A simulation approach based on measured I-V-characteristics is developed to evaluate device–circuit interactions. We first analyze the limitations of the conventional M-CNN cell core, where asymmetric I-V-characteristics restrict voltage levels and accelerate device degradation. To address these issues, we propose a symmetrized cell that mitigates asymmetry, intrinsically limits cell voltage, and supports differential readout. The results demonstrate that gradual switching enables reliable distinction of input current levels while ensuring stable operation and reduced power consumption, thus paving the way for robust IGZO-based M-CNN implementations.

Abstract Generative Adversarial Networks (GANs) are increasingly used in biometric systems. However, existing signature studies predominantly focus on strengthening discriminators or producing data for augmentation, leaving the quality and spoofing capability of generated forgeries insufficiently examined. To address this research gap, we propose Block-Induced Signature GAN (BISGAN )—a generator- focused architecture integrating inception-style blocks and attention mechanisms to preserve influential biometric features during forgery generation. We further introduce a train-shift learning strategy, grounded in adversarial robustness theory and the Resource-Based View (RBV), which enhances the generator’s ability to mimic authentic signature traits. Experiments on benchmark datasets demonstrate that BISGAN achieves 88%–100% spoofing success, exceeding prior GAN-based approaches by at least 12%. To support objective assessment, we develop a Generated Quality Metric (GQM) that evaluates forgery realism using latent feature distribution distances. The results confirm the importance of generator-centric adversarial modeling for advancing the robustness and security evaluation of signature verification systems.

In this work, we introduce a high speed and area efficient Cellular Nonlinear Network (CNN) cell, featuring two circuit variants that utilize threshold switches. The threshold switch (TS) model employed represents a current-controlled nanoscale negative differential resistance (NDR) device which exhibits an S-shaped DC I-V curve as a fingerprint. The proposed cell can be considered as the dual of the standard isolated CNN cell where the bistable cell characteristics, originating from the N-shaped voltage-controlled resistor, is implemented through the S-shaped current-controlled TSs. Similarly, the dynamics induced by the parallel capacitor accompanying the nonlinear resistor in the standard cell version are implemented through the internal inductive dynamics of the TSs, resulting in area and speed efficiency. The proposed CNN cell employs a DC voltage source, two bias resistors and 2 TSs, and essentially, features a differential-mode operation which helps to endow it with a symmetric DC I-V characteristic, as is the case for the standard CNN cell. The differential-mode approach further introduces design flexibility as the cell DC I-V characteristic can be adjusted by tuning circuit parameters. We demonstrate the functionality of the proposed cell by implementing image processing tasks ranging from edge detection and thresholding to logic AND and OR operations.

The symmetry-breaking phenomenon, appearing, under suitable conditions, when identical reaction cells, quiet on their own, are let interact via diffusion processes, is dubbedTuring Instability. Its local form exposes the local destabilization, which allows two multistable cells lose stability at one of its locallyasymptotically-stableoperating points. While the globalTuring Instabilityand its mechanisms have been recently explained in (Ascoli et al., 2022), its local form and an experimental demonstration of these complex effects on a physical memristive medium have not been reported yet. This paper investigates a local form ofTuring Instabilityin a two-cell array, when one of the possiblelocally asymptotically-stableandlocally-activestatic solutions loses stability, when let interact with an identical reaction cell via diffusion processes, resulting in the emergence of two different static solutions after transients fade away. In order to study its mechanisms, this paper first introduces a current-controlled Chua Corsage Memristor (CCM), and demonstrates the operating point destabilization in a single current-controlled CCM-based cell. Adding a dissipative resistor and a capacitor to the current-controlled CCM, preliminarily poised on anedge of chaosoperating point, gives birth to two unstable circuits, inducing a local quiescent bi-stability and a local oscillation, respectively. The mechanisms behind a local form ofTuring Instability, appearing in a current-controlled CCM-based two-cell array, have been elucidated, and the bifurcation, spawning symmetry-breaking effects, locally, across the cellular network, has been identified. Both numerical and experimental results confirm the correctness of the theoretical analysis.

The electrical engineering community, interested to develop bio-inspired circuits, approaching the efficiency of the neural networks, is searching passionately for accurate yet simple electronic neurons, or neuristors for short. In recent years, the advent of volatile memristor devices, typically referred to as threshold switches, which admit a negative differential resistance under suitable polarization, similarly as the sodium and potassium ion channels across neuronal axon membranes, has opened up new exciting opportunities in neuromorphic circuit design, enabling innovative analogue electronic cells, capable to reproduce closely the intricate dynamical behaviors of biological neurons without requiring a disproportionate use of resources. The study, presented in this manuscript, achieves an important milestone in this area of research, demonstrating, through a circuit design approach based upon concepts and techniques from Dynamical System Theory, how to leverage the rich dynamics of a threshold switch, capable to boost a periodic sine-wave current signal of infinitesimal amplitude, while acting as a source of local energy, when poised on a suitable bias point, lying along the negative differential resistance branch of the respective S-shaped DC current-voltage characteristic, to induce, one after the other, the three fundamental bifurcations, governing the evolution of an electrical voltage spike from birth to extinction via the All-to-None effect across a biological axon membrane under a reverse sweep in the net synaptic current, according to the fourth-order Hodgkin-Huxley neuron model, in a second-order three-element circuit of unprecedented simplicity, as the current, generated by a DC source, appearing in parallel to a linear capacitor as well as to the volatile locally-active memristor, is subject to a monotonic increase.

This manuscript sheds light into the fundamental importance of the Principles of Local Activity and Edge of Chaos for the future design of innovative circuits, which, employing biomimetic memristive devices, are ideally suited for the development of energy-efficient artificially-intelligent technical systems. The focus of the work is the design of a Second-Order Reactance-Less Oscillator, across which oscillations may develop if and only if at least one of its two different volatile thermally-activated memristor physical realizations is biased along a negative differential resistance branch of the respective DC locus, which turns it into a source of local energy. Very importantly, the proposed cell is first found to lock in the oscillatory mode out of a local Hopf Supercritical Bifurcation when its design parameters are chosen from the Edge of Chaos region, providing clear evidence for the high degree of excitability it acquires as a result.

Neuromorphic circuits using emerging memory technologies have recently gained popularity since they facilitate dense integration with reduced design complexity. In this work, we introduce a simplified modeling approach for the analysis of threshold switch (TS) based neuron circuits where, under given constraints, we represent the TS device as a nonlinear resistor in series with a parasitic inductor. As a result, we define the current of the TS as its state variable. In order to demonstrate the feasibility of the proposed approach, we analyze the conventional Leaky Integrate and Fire (LIF) neuron circuit along with two of its modified variants. We validate the accuracy of the provided analysis and key predictions through numerical simulation results. As a significant contribution, we demonstrate the effectiveness of the proposed method in modifying the nullclines of the TS based LIF neuron and qualitatively align them with the nullclines of a 2ndorder biologically plausible neuron model.

As demand grows for efficient edge computing systems, innovative architectures are crucial for achieving low-power, high-density data processing in resource-constrained environments. Compressed sensing (CS) and Analog In-Memory Computing (AIMC) offer promising pathways to meet these needs by enabling localized, efficient feature extraction and inference. This paper introduces an energy-efficient on-chip system that integrates CS with AIMC based on Phase-Change Memory (PCM) devices to enable robust feature extraction and inference. The proposed architecture employs CS for dimensionality reduction at the sensor level, generating low-dimensional feature vectors directly fed into a single-layer artificial neural network (ANN) implemented on PCM crossbars. To address inherent hardware non-idealities, we utilize hardware-aware (HWA) training combined with an attention-based regularization mechanism, improving both inference stability and drift resilience over extended periods. Performance evaluation on a face recognition task demonstrates that attention-enhanced HWA training effectively mitigates overfitting and maintains model accuracy under PCM drift conditions, highlighting the system's suitability for edge computing applications requiring low power consumption and long-term reliability.

We present a two-cell Tantalum oxide-based Memristor Cellular Neural Network (M-CellNN) capable of performing multiple logic operations (AND, OR, XOR) by changing only the initial states of its memristors. This flexible design leverages the dynamic state-change properties of memristors to adjust logic functions. Our results show that this approach significantly broadens the range of achievable logic tasks within a compact architecture, underscoring the potential of memristive elements for versatile and robust circuit designs. Additionally, we examine the impact of non-idealities in coupling weights and initial conditions on the outputs of the network.

Realized memristors exhibit a unique phenomenon called the fading memory effect, where the memristor response to an AC signal is determined by its characteristics (waveform, amplitude, frequency, and DC offset) rather than the memristor initial conditions. Recently, a method for programming Hewlett Packard’s TaOxmemristor to a target state was proposed, involving configuring the DC offset of a high-frequency square-wave AC voltage input. This served as a basic application example that exploits fading memory in non-volatile memristors, but didn’t consider non-ideal effects. Here, we assess the method applicability in a HfOx-based VCM resistive switch from Forschungszentrum Julich incorporating a variability-aware physics-based model.

We have successfully fabricated one of the earliest array-scale prototypes of a Memristive Cellular Nonlinear Network (M-CNN) with interconnected cells. In this live demonstration, we will showcase the operation of this 4x4 M-CNN array performing an edge detection task according to our previous work [1]. A user-defined input will be applied to the network, and the computing results will be visualized alongside the simulated operation of a standard CNN for comparison.

As demand grows for efficient, localized processing in edge and in-sensor computing, novel architectural approaches are essential to meet low-power, high-density requirements. Memristor Cellular Nonlinear Networks (M-CNNs) offer a promising path forward, leveraging the unique properties of memristors for adaptable and scalable computation. This paper presents a study of novel M-CNN cell configurations designed to enhance computational versatility and address operational challenges in M-CNN-based systems. By leveraging memristor technology within CNN cells, we propose three distinct configurations: (1) incorporating parallel and series resistive elements for refined control over cell dynamics, (2) introducing a fixed bias voltage to expand computational capabilities, and (3) integrating the Full-Range CNN (FR-CNN) model into M-CNNs for the first time. The proposed topologies are evaluated through dynamic route maps (DRM) and vector field analysis to systematically assess stability and performance across varying design parameters.

Chua corsage memristor (CCM) is characterized by its local activity and can be used to construct neuron circuits. Edge of chaos is a subset of the locally active domain, which is responsible for the emergence of complexity and neuromorphic behaviors. When two identical resting “dead” CCM neurons poised on the edge of chaos are coupled through a linear passive resistor, these two neurons can be activated and a couple of oscillations appear. This phenomenon is referred to as the Smale paradox, which has not been observed from hardware circuits. The present paper addresses this issue by proposing the stability criterion of the two-port coupled system using the small-signal analysis method and then derives an emergence condition of the Smale paradox based on two coupled “dead” CCM neurons in terms of the parameter value ranges. Simulation results demonstrate the correctness of the theoretical analysis. Interestingly, anti-phase synchronization is observed after two identical neurons are coupled with a linear resistor, which is different from the traditional in-phase synchronization between resistively coupled oscillators. The resistively coupled memristive neurons are implemented by hardware based on the poor man’s circuit. The experimental results confirm the reproduction of the Smale paradox and reveal the effect of the coupling resistance on the dynamics of the system.

Inspired by recent research reported in [1], this paper investigates the bio-inspired bifurcation patterns of a simple memristive neuron on edge of chaos. The adopted memristive neuron, comprising a DC current source, a current-controlled locally active memristor, and a capacitor, successfully reproduces the bifurcation cascade patterns observed in the Hodgkin-Huxley (H-H) neuron model, including fold limit cycle bifurcation (FLCB), subcritical Hopf bifurcation (SUB-HB), and supercritical Hopf bifurcation (SUP-HB). Through attraction basin analysis and pulse-based initial state regulation, we verify the coexistence phenomenon of stable and unstable limit cycles induced by FLCB, as well as the bistable behaviors triggered by SUB-HB. Furthermore, taking resistively coupled memristive neurons as an example, we explore the influence of the dynamics of individual neurons on the bifurcation patterns of coupled networks, where two neurons have identical parameters but different initial states. The results demonstrate that the three bifurcation modes also emerge in memristive coupled networks, and their evolutionary patterns are closely related to the dynamic behaviors of individual neurons. Finally, hardware experiments successfully reproduce the bifurcation cascade phenomenon thereby validating the correctness of theoretical analysis and simulation results.

The Edge of Chaos Principle lies at the origin of emergent phenomena in physical systems. Recurring to powerful concepts from the theory, establishing its rules, it is possible to identify regions of the parameter space of a system, endowing the latter with a high degree of excitability, which can then manifest itself vividly, as complexity emerges across the respective physical medium upon apparently-harmless changes to the environmental conditions. In this manuscript, the first of a two-paper contribution, the Edge of Chaos Principle is invoked to explain the mechanisms, underlying the development of recently-reported yet-unexplained oscillations across a biological cell, consisting of a voltage-driven sodium ion channel, including leakage effects. Our in-depth investigation of the Local Activity and Edge of Chaos of the biological cell, based upon the rigorous mathematical description, first proposed by Hodgkin and Huxley in 1952, identifies the subcritical Hopf, which emerges across its physical medium as it enters one of its two Edge of Chaos domains, giving birth to the aforementioned oscillations, whose unstable nature is thus revealed. The existence of an unstable limit-cycle attractor in the state space of the Hodgkin-Huxley neuron model is crucially important for the All-to-None dynamical phenomenon, which distinctively characterises the evolution of the membrane capacitance voltage under DC synaptic current sweep. Thus the discovery of the capability of the sodium ion channel to generate unstable oscillations on its own, highlights the fundamental role of this biological memristor in the mechanisms behind emergence and extinction of an Action Potential across a neuronal axon. As the cell, studied in this manuscript, is unable to sustain stable oscillations, the second companion paper shall demonstrate how the insertion of a membrane capacitance across the sodium ion channel, reduced to a first-order system by neglecting the dynamics of the fast activation gate variable, is necessary and sufficient to endow the original biological cell with the capability to undergo also a supercritical Hopf bifurcation, besides the subcritical one, which allows the observation of the entire life cycle of a neuronal spike under DC synaptic current sweep, including, especially, the All-to-None phenomenon spawned out of a fold or saddle-node limit cycle bifurcation.

This paper investigates the essential role of local activity theorem in pancreatic$\beta $-cells in the process of insulin secretion. It is shown that the ion channels in$\beta $-cells distributed over the pancreas are in fact generic memristors from the perspective of electrical circuit theory. Through our comprehensive analyses and extensive simulations from the Chay-Keizer Pancreatic$\beta $-model, Phantom Bursting Model (PBM)-I and PBM-II, this paper rigorously provides an ambient proof that the secretion and release of the insulin in the form of bursting or action potential are possible only when it satisfies the condition of local activity theorem. The local activity principle is analyzed by the small signal admittance function, pole zero diagram, and edge of chaos theorem. It is shown that the external stimulus or cell parameters chosen within the subset of the locally domain regime where the negative real part of the admittance function and the positive real part of the zeros (equivalent to the Eigen values) lead to the generation of complicated electrical signals in pancreatic$\beta $-cells. The examples presented in this paper demonstrate the local activity theorem is a novel and efficient tool for testing whether the secretion of insulin by pancreatic$\beta $-cells are possible or not. It follows from our in-depth analysis that the local activity is essential for the synthesis, secretion, and release of insulin by pancreatic$\beta $-cells. This principle serves as a critical condition, highlighting the intrinsic role of cellular dynamics in insulin regulation and emphasizing its significance in understanding pancreatic function and metabolic health.

In this paper, the design of an isolated Memristor Cellular Nonlinear Network (CNN) cell with discrete electronic elements is presented. The proposed versatile circuit allows for adjustable cell dynamical characteristics, controlled by design parameters, while the discrete element approach enables simple on-board implementation without the need for large-scale integration, which is necessary for testing hardware with individual fabricated memristors. A voltage-mode approach, that makes use of the diversity of operational amplifiers, is preferred here over a current-mode one that necessitates a large number of individual transistors. The dynamical properties of the system are initially investigated through the calculation of equilibrium points and further illustrated applying the concept of State Dynamic Routes (SDRs) for the cell assuming that the memristor dynamics are much slower than the capacitor voltage dynamics. Moreover, the effect of design parameters on the cell dynamics is being investigated, showing how the scaling of the operating voltage, as well as a plethora of CNN variants -i.e., the Chua-Yang and Full Range models-, can be implemented within the same design. Finally, the nonlinear conductance properties of real memristor devices are incorporated into the study, demonstrating interesting bifurcation phenomena between the cell monostability and bistability for specific parameter values.

Biological synapses behave as dynamically-rich nonlinear elements, participating in complicated computing tasks through their adaptation due to external stimuli. Such adaptivity constitutes an intrinsic property of non-volatile memristor devices, which are also able to maintain their internal state, under zero input, enabling novel bio-inspired learning operations. In this work, a synaptic element based on a memristive bridge, containing two resistors and two memristors, is studied, aiming to investigate complex memristor-based topologies that may result in rich synaptic dynamics. The proposed memristive bridge allows the realization of both positive and negative synaptic weights, while an asymmetric tuning of a weight, stemming from memristor's features and bridge topology, is demonstrated. In particular, by properly selecting the memristor's position and polarity within the bridge, different tuning behaviors have been observed, showcasing versatile learning properties of the topology. Along with the synaptic weight tuning, the read overall process of the synaptic weight, necessary for inference operations, is also investigated. We explore the dynamics of the bridge via numerical simulations.

In this paper, we present a new compact model of threshold switching devices which is suitable for efficient circuit-level simulations. First, a macro model, based on a compact transistor based circuit, was implemented in LTSPICE. Then, a descriptive model was extracted and implemented in MATLAB, which is based on the macro model. This macro model was extended to develop a physical model that describes the processes that occur during the threshold switching. The physical model derived comprises a delay structure with few electrical components adjacent to the second junction. The delay model incorporates an internal state variable, which is crucial to transform the descriptive model into a compact model and to parameterize it in terms of electrical parameters that represent the component’s behavior. Finally, we applied our model by fitting measured$i-v$data of an OTS device manufactured by Western Digital Research.

This paper presents an analytical investigation of the transient and steady-state response of non-volatile memristors to high frequency periodic inputs, using as a case study a$\textrm {TaO}_{\textrm {x}}$-based nano-scale memristor model derived at HP Labs. For the first time, we provide a mathematical proof for the fading memory phenomenon in memristors stimulated by periodic inputs in the high frequency limit. Specifically, we demonstrate that the steady-state response of a non-volatile memristor, exhibiting asymmetric switching kinetics with respect to the polarity of the input, depends only on the amplitude of the testing signal and not on the device initial conditions. Based on the results of our analyses, we provide an alternative method for tuning the memristor state by using high-frequency AC inputs, and introduce a new system-theoretic visualization tool, namely the input-referred High-Frequency Dynamic Route Map (HF-DRM), that allows the reproduction of the memristor time-response to any high-frequency periodic input from each admissible initial condition. The purely theoretical results introduced in this paper could inspire new approaches for modulating the memory states of practical non-volatile memristors.

In this paper, a method is presented to estimate and correct pulse and breathing motion artifacts of infrared (IR) brain images while preserving all-important image information. First, a complex steerable pyramid is carried out to decompose the image sequence and separate the amplitude from their phase. Second, a finite impulse response (FIR) filter is employed to separate the selected frequency bands at each scale and orientation followed by reconstructing the image sequence with corresponding amplitudes. Third, the optical flow method is applied to estimate pulse and breathing motion artifacts only. Fourth, bicubic interpolation is performed to compensate the estimated motion artifacts of the original thermal image sequence. To evaluate the motion correction performance and accuracy, four metrics are applied, as well as the analysis of a single pixel frequency spectrum before and after pulse and breathing motion artifacts correction. Results provide evidence that the proposed method can compensate pulse and breathing motion artifacts while preserving image structures, spatial resolution, and maintaining temperature values.

This paper proposes the derivation of a physics-based model of an analog memristive device realized as a bi-layer Al2O3/NB2O5stack. Memristive crossbar arrays implementing matrix-vector multiplications are a central building block of novel computing-in-memory architectures for artificial neural network and neuromorphic computing applications. The presented memristor shows analog, multi-level switching at high resistances without electroforming and is suitable for crossbar operations with low energy consumption. By including a graphical analysis method of the I-V curves obtained in a quasi-static approach, the dynamic behavior is analyzed with regard to ohmic and Poole-Frenkel behavior. Finally, a compact model, represented by an algebraic differential equation, is proposed and verified by fitting calculated solutions to experimental data.

Cellular Nonlinear Networks (CNN) as a powerful paradigm is highly suitable for signal processing of multiple tasks, since they can execute cascaded processing operations in a one-layer array via real-time template updating. Their VLSI implementation by using the conventional CMOS-based integration technology, however, remains a big challenge. The memristive CNN (M-CNN) offers several merits over conventional CNN, such as compactness, nonvolatility, versatility. This paper presents a direct comparison of computing performance between the M-CNN and the conventional CNN for the implementation of a LOGAND operation template using circuit simulation. Our findings show that the M-CNN implementation offers rapid attainment of equilibrium state compared to the CNN implementation. In addition, the result is stored in a non-volatile manner in the M-CNN whereas the CNN only offers a volatile storage.

No isolated system may ever support complexity. Emergent phenomena may however appear in an open system, if, as established by the Edge of Chaos theory, some of its constitutive elements feature the capability to amplify infinitesimal fluctuations in energy, provided an external source supplies them with a sufficient amount of DC power, which is known to be a signature for locally-active behaviour. In particular, complex behaviours, including static and dynamic pattern formation, may emerge in arrays of identical diffusively-coupled cells, if and only if the basic unit is poised on a particular sub-domain of the Local Activity regime, referred to as Edge of Chaos, within which a quiet state hides in fact a high degree of excitability. Here we show, for the first time, that these counterintuitive phenomena may emerge in a basic memristor cellular neural network, consisting of two identical diffusively-coupled second-order cells. The proposed bio-inspired array represents the simplest ever-reported open system, which reproduces the shocking phenomenon, reported by Smale in 1974, when, while studying a model from cellular biology, he observed two identical reaction cells, “mathematically dead” on their own, pulsating together upon diffusive coupling. Impressively, the bio-inspired two-cell reaction-diffusion network contains only nine circuit elements, specifically two DC voltage sources, three linear resistors, two linear capacitors, and two functional niobium oxide (NbO) memristors from NaMLab. Applying the theory of Local Activity to an accurate model of the memristor oscillator, a comprehensive picture for its local and global dynamics may be drawn, providing a systematic method to tune the design parameters of the two-cell array to enable diffusion-driven instabilities therein.

Diffusion-driven instabilities with pattern formation may occur in a network of identical, regularly-spaced, and resistively-coupled cells if and only if the uncoupled cell is poised on a locally-active and stable operating point in the Edge of Chaos domain. This manuscript presents the simplest ever-reported two-cell neural network, combining together only 7 two-terminal components, namely 2 batteries, 3 resistors, and 2 volatile NbOx memristive threshold switches from NaMLab, and subject to diffusion-driven instabilities with the concurrent emergence of Turing patterns. Very remarkably, this is the first time an homogeneous cellular medium, with no other dynamic element than 2 locally-active memristors, hence the attribute all-memristor coined to address it in this paper, is found to support complex phenomena. The destabilization of the homogeneous solution occurs in this second-order two-cell array if and only if the uncoupled cell circuit parameters are chosen from the Edge of Chaos domain. A deep circuit- and system-theoretic investigation, including linearization analysis and phase portrait investigation, provides a comprehensive picture for the local and global dynamics of the bio-inspired network, revealing how a theory-assisted approach may guide circuit design with inherently non-linear memristive devices.

We present a compact, continuous, and numerically stable version of a tantalum oxide (TaOx) memristor model which can be employed for robust and reliable simulations of large scale memristor based circuits. The original model contains a piecewise differentiable function in the memductance expression and discontinuous step functions in the state equation. Additionally, the original model does not set a proper upper bound for the state variable and may admit blowing up solutions due to an exponential power term, preventing the use of it for numerically reliable simulations. Considering these drawbacks, we modify the original model so as to i) simplify the memductance function while removing its piecewise differentiable nonlinearity, ii) include a proper window function for the ON state dynamics, which is missing in the original model, iii) modify and bound the exponential power term to prevent an uncontrollable blow-up of the solutions, and iv) apply a process called unification, allowing us to remove the step functions inherent in the model, which is a novelty in state-limited memristor models. We validate the accuracy of the proposed model via DC and transient simulations, dynamic route map analysis and a Spice implementation of an anti-series configuration, showing the applicability of the model.

Repeated epileptic seizures impair around 65 million people worldwide and a successful prediction of seizures could significantly h elp p atients suffering from refractory epilepsy. For two dogs with yearlong intracranial electroencephalography (iEEG) recordings, we studied the influence of time series nonstationarity on the performance of seizure prediction using in-house developed machine learning algorithms. We observed a long-term evolution on the scale of weeks or months in iEEG time series that may be represented as switching between certain meta-states. To better predict impending seizures, retraining of prediction algorithms is therefore necessary and the retraining schedule should be adjusted to the change in meta-states. There is evidence that the nature of seizure-free interictal clips also changes with the transition between meta-states, which has been shown relevant for seizure prediction.

This paper presents the analytical investigation of complex pattern formation in a Memristor Cellular Nonlinear Network (M-CNN) by applying the theory of local activity. The proposed M-CNN has the conventional two dimensional (2D) planar structure, where all the memristive cells are identical and resistively coupled to each other. The single cell is composed of a suitable combination of a DC voltage source, a bias resistor, a locally active NbOx memristor, and a capacitor. The locally active memristor has a simplified generic form, enhancing the simulation speed, and a functional AC equivalent circuit, facilitating further inspections. The stability analysis of the single cell is followed by the extraction of the parameters of the local activity, edge-of-chaos, and sharp-edge-of-chaos domains. Simulation results demonstrate that pattern formation can emerge in a dissipatively coupled M-CNN with locally active memristors.

In this paper we shall study a class of memristor CNN with hysteresis. We shall investigate the dynamics of this model via local activity theory and we shall determine the edge of chaos region in which complex phenomena can be exhibited. Applications of the memristor CNN with hysteresis model in pattern formation will be presented. Nonuniform spatial patterns generation will be derived which is due the memristor polarity, stimulations and initial conditions.

In this paper, we present a compact memristor model for bipolar neuromorphic ReRAM devices. The proposed model focuses on the high level description of the device, and it reproduces some of the most important characteristics (i.e. conductance, energy dissipation) without needing a detailed electrical simulation. Its functionality is shown by using it to model the behavior of three different ReRAM devices that were fabricated and measured at the CNR-IMM, MDM Laboratory. The parameters extraction procedure is also discussed. The obtained results clearly show that the model proposed in this paper is able to capture the influence of the programming pulse parameters (i.e. pulse duration and height) changes. This is accomplished by the introduction of a parameter, which is related to the specific device technology.

We present and experimentally validate two minimal compact memristive models for spiking neuronal signal generation using commercially available low-cost components. The first neuron model is called the Memristive Integrate-and-Fire (MIF) model, for neuronal signaling with two voltage levels: the spike-peak, and the rest-potential. The second model MIF2 is also presented, which promotes local adaptation by accounting for a third refractory voltage level during hyperpolarization. We show both compact models are minimal in terms of the number of circuit elements and integration area. Using the MIF and MIF2 models, we postulate the design of a memristive solid-state brain with an estimation of its surface area and power consumption. Analytical projections show that a memristive solid-state brain could be realized within (i) the surface area of the median human brain, 2,400cm2, (ii) the same volume of the median human brain, and (iii) a total power budget of approximately 20 W using a 3.5 nm technology. Distinct from the past decade of memristive neuron literature, our benchmarks are attained using generic commercially available memristors that are reproducible using off-the-shelf components. We expect this work can promote more experimental demonstrations of memristive circuits that do not rely on prohibitively expensive fabrication processes.

This paper presents a circuit-theoretic analysis of a NbO2-Mott memristor fabricated at Hewlett-Packard Labs. It investigates mechanisms behind the origin of complexity based on local activity, which characterizes the behavior of this outstanding nanodevice. We propose an accurate, particularly simplified version of a recently introduced physical model suitable for large-scale circuit simulations. Following the concept of local activity, we then conduct a small-signal circuit-theoretic derivation of the impedance and associated small-signal equivalent circuit elements to analyze device stability and frequency response. Finally, our analysis reveals locally active operating regions, as well as regions where the device dynamics are positioned on the edge of chaos. The latter regions are crucial for designing bio-inspired computing systems.

The main focus of this paper is the presentation of reliable methods for the determination of the optimum coloring of a graph, commonly known in the literature as vertex coloring problem. It has been shown that networks of capacitively coupled oscillators can be used to solve vertex coloring problems. In this paper we address the negative impact of an unbalanced number of couplings for the oscillators on the performance of the network and compensate for this non-uniform coupling structure by an adjustment in the network itself. The negative effect of the memristor device-to-device variability of the NbOxmemristor on the array functionality will be investigated and reduced via an adaptation of the memristor operating point. The main improvement in network performance is achieved by setting up a control procedure allowing the network to bypass the local solutions and converge to the global one. Two strategies inspired by global optimization algorithms will be proposed to allow the network to overcome sub-optimal solutions, and find the solution corresponding to the absolute minimum of a performance measure function of the vertex coloring problem.

The introduction of memcomputing memristors into the design of Cellular Nonlinear Networks (CNNs) allows to reduce the integrated circuit area typically allocated to each processing element in hardware realizations. Furthermore, the highly nonlinear dynamics of memristors enriches the multivariate signal processing capabilities of these cellular memprocessing structures. This is demonstrated in this paper, where the standard and generalized Dynamic Route Map analysis tools are employed to elucidate the mechanisms by which a Memristor CNN with bistable-like and analog dynamic nonvolatile memristors executes fundamental image processing operations, respectively.

Most of the previous investigations are dealing with the derivation of memristor models in voltage-current V-I domain. Recently, the flux-charge Ø - Q approach has been introduced by F. Corinto et al. [1] showing the capability to simulate the behaviour of a memristive device for a wide range of input signals. A simple memristor model for neuromorphic ReRAM devices derived in the flux-charge domain will be proposed in this paper. Thereby, special attention has been paid to the switching kinetics of a ReRAM memristive device excited by pulses of different height and width. The obtained theoretical results, which have been compared to measurements, exhibit a high accuracy in all treated cases, thus supporting the development of memory and logic applications using ReRAM elements.

In this paper, we propose a new model for practical, nano-scale, NbO2-based Mott memristors, which is based on a thorough analysis performed on a recently presented physics-based model for these devices. Our investigations revealed that the 3D Poole-Frenkel conduction mechanism adopted in the aforementioned model, can be well-approximated by a transport equation in which: a) memristor current is expressed as a linear function of memristor voltage and b) the device memductance is solely dependent on the device temperature which represents the memristor state. The resulting simplified mathematical form of the original differential algebraic equation set is not only more suitable for simulating large-scale, nano-scale NbO2-based memristor circuits, but is also ideal for circuit-theoretic investigations which may allow an in depth understanding of the peculiar nonlinear behaviors of these devices.

In this paper we propose a new mem-computing image processing architecture, called Memristor Cellular Nonlinear Network, which leverages the unique capability of nonvolatile memristors to compute and store data in the same physical nano-scale locations. Adopting a bistable-like memristor in place for the linear resistor in the standard realization of a cell of the nonlinear dynamic array, the resulting network is capable to process information by exploiting the time evolution of the voltages across the memristors as well as to store/retrieve results into/ from the memristances. This attractive feature, absent in a standard Cellular Nonlinear Network, may pave the way towards the future development of a new generation of visual processors with unprecedented spatial resolution.

In this paper analytical results are derived for nanoscale memristor CNN (NM-CNN) in which neurons operate in a regime called edge of chaos. The system describing the model consists of highly nonlinear differential equations. We propose new algorithm based on the generalized local activity scheme for the determination of the edge of chaos regime in nanoscale memristor CNN model under consideration. MATLAB implementation of algorithms based on a numerical integration of the NM-CNN state equations allowing a reliable and accurate determination of the edge of chaos parameter regime is proposed. Application of the obtained results for pattern formation is presented.

To reduce the risk for patients during neurosurgical procedures, an intraoperative imaging system is required for the identification and localisation of functional areas and brain tumours. Thermography is based on the measurement of long-wave infrared radiation and constitutes a promising non-invasive and marker-free technique for intraoperative functional imaging. In this paper, different methods for the fusion of thermographic and white-light images are discussed and appropriate architectures for digital hardware implementations are proposed. We demonstrate the real-time capability of the derived architectures implemented on a Xilinx Zynq FPGA.

In this two-part paper we present an innovative bio-inspired approach to control the lift of a limb of a humanoid robot called Myon from the stable rest state to the unstable upright position. The proposed paradigm outperforms the state-of-the art approach in terms of time- and energy-efficiency, while maintaining a good degree of adaptability to changes to the nominal operating conditions. This Part I paper introduces the theory behind the novel three-phase control strategy, while the companion Part II manuscript derives its circuit implementation, and analyses its performance to validate the theoretic findings. The critical steps in the proposed strategy are the determination of an estimate for the time duration of the first phase, the storage of the result of this computation over the time interval between two consecutive applications of the control action, and the adaptation of this calculation to changes to the nominal operating conditions. All these three tasks may be successfully accomplished by leveraging the computing, memory, and learning capabilities of a single non-volatile memristor.

The standard Go-Against-the-Force strategy to lift a limb of a humanoid robot from the stable rest state to the upright position and to maintain it there afterwards is slow and consumes a significant amount of energy due to the iterative cycle of sensing and driving operations its application consists of. In order to enhance the performance of the control action, the Part I paper introduced the theory behind an innovative three-phase strategy, called Kick-Fly-Catch paradigm, which is expected to lead to a faster limb motion under a lower energy cost as compared to the original approach. The combined ability of a non-volatile memristor to process data according to Ohm's law, store computation results at power off, and adapt its dynamic behaviour on the basis of its state equation is at the origin for the performance benefits of the proposed strategy over the standard approach. This Part II paper designs a circuit implementation for the overall dynamic system under the new control strategy, and validates the theoretic predictions of the Part I manuscript.

Developing highly accurate and predictive models of redox-based memristive devices is highly important to enable future memory and logic design. As the switching mechanism is not known in all details yet, accurate device modeling is quite challenging. Here, we introduce six evaluation criteria for modeling filamentary switching devices based on the valence change mechanism, which is a subclass of redox-based memristive devices. The criteria include the plausibility of the simulated I-V and I-t characteristics, the nonlinearity of the switching kinetics, the feasibility of predicting complementary resistive switching correctly, the possibility of programming different resistance states, the state-dependence of the resistive switching, and the occurrence of a fading memory behavior. Four different models that have been proposed in literature are analyzed with respect to these criteria. These models are Kvatinsky's VTEAM model, the Stanford RRAM model, Strachan's TaOx memristor model and a nonlinear physics-based model proposed by our group.

In this contribution an image classification by uncoupled Cellular Nonlinear Networks (CNN) is proposed and evaluated on typical datasets, like CIFAR-10 and MNIST. The algorithm is based on the application of backpropagation for the training of synaptic coupling weights and is capable of binary classification by means of a threshold-based classifier. The design is inspired by recent deep neural network architectures, but can be implemented on a CNN Universal Machine, enabling complex image recognition on low-power embedded devices.

This paper proposes a novel BiFeO3memristor-based electronic circuit for the encryption of sensitive medical data. The hardware cryptographic system is tested through the use of neural signals from a patient experiencing a number of focal epileptic seizures. The Cellular Nonlinear Network theoretical framework provides a basis for sophisticated neural signal processing techniques capable to anticipate the emergence of an epileptic seizure in many cases. The application of these techniques to original data successfully reveals changes before the onset of each epileptic seizure. This information may not be extracted from the encoded data, validating the proper functioning of the memristor-based encryption.

Recently a circuit-theoretical work showed that a purely mathematical memristor model may exhibit two distinct stable DC characteristics, as well as two distinct stable pinched hysteresis loops emerging under the same AC periodic excitation by simply changing the memristor initial state. This work presents the first ever real memristor which exhibits such a peculiar bistable behaviour, thus giving a strong practical evidence for the latest theoretical developments in memristor circuit theory.

Emulations of cellular nonlinear networks on digital reconfigurable hardware are renowned for an efficient computation of massive data, exceeding the accuracy and flexibility of full-custom designs. In this contribution, a digital implementation with polynomial coupling weight functions is proposed for the first time, establishing novel fields of application, e.g., in the medical signal processing and in the solution of partial differential equations. We present an architecture that is capable of processing large-scale networks with a high degree of parallelism, implemented on state-of-the-art field-programmable gate arrays.

A class of memristor circuits is obtained by cascading a static nonlinear two-port with a dynamical one-port. The terminals of the input port of the static nonlinearity represent the access nodes for each memristor in the class. The class may be splitted into two sub-classes, namely the current- and voltagecontrolled memristors. Two further sets of memristors may be identied within each of such sub-classes, particularly the current- and voltage state memristors. The simplest memristor circuits from the proposed class employ solely passive two-terminal elements from circuit theory. This represents an absolute novelty in the panorama of memristor emulators. The passive elements from the class are volatile memories. However, non-volatile memory behaviour may arise in case the dynamical one-port contains active elements. The versatile nature of the circuit topologies of the proposed memristors allows the emergence of a wide variety of complex dynamical behaviours, which may enable the accomplishment of novel signal processing tasks or lead to improvements in the performance of conventional circuits.

In this paper1a stability analysis sheds light into aspects of memristor circuit design, revealing a circuit theoretic technique for the stabilization of the NDR portion of the device DC characteristic. This type of studies supports the work of designers exploring memristor potential in electronics. Concepts from nonlinear dynamics theory allow us to gain a deep understanding of the dynamics of our locally-active memristor. The analysis provides hints on how to design an oscillator where limit-cycle behavior emerges from the locally-active threshold switching of the memristor, as theoretically proved here.

The seizure prediction problem has been addressed by many researchers from very different fields for more than three decades. The vision of an implantable seizure prediction device may become reality now: the first clinical study of such a device has been realized very recently and other realizations are not far behind. Cellular Nonlinear Networks (CNN) were firstly introduced by Chua and Yang in 1988 and later extended to an inherently parallel processing framework called the CNN Universal Machine (CNN-UM). This framework combines high computational power with low power consumption and miniaturized design - making it a very promising basis for the realization of a seizure warning device. In this contribution, we compare the seizure prediction performance of an eigenvalue based PCA-preprocessing followed by a nonlinear CNN signal prediction to the performance of a linear signal prediction approach followed by a level-crossing behavior analysis.

Besides being at the core of novel ultra-high density low-power non-volatile memories and innovative pattern recognition systems based upon oscillatory associative and dynamic memories, the nano-scale memristor also has the potential to reproduce the behavior of a biological synapse more efficiently and accurately than any conventional electronic emulator. As in a living being the weight of a synapse is adapted by the ionic flow through it, so the conductance of a memristor is adjusted by the flux across it. This article is organized according to the regulations of the ISCAS2014 special session on the state-of-the-art in memristor-based nonlinear circuits and architectures. In this work we focus on arrays of oscillatory cells locally coupled through memristors. Our investigations shows how the nonlinear dynamics of the memristor plays a key role in the mechanisms underlying the synchronization properties of the networks. This work provides new insights into the nonlinear behavior of the still largely unexplored memristor element, which promises to revolutionize integrated circuit design in the incoming years.

Coupling, as a third relation is introduced to memristive systems, beyond series and parallel. Rich unconventional dynamics are demonstrated in three coupled systems, including multi-leaf and multi-pinched hysteresis loops, resonance-induced chaos and spontaneous symmetry breaking (SSB).

This paper proposes a simple PSpice implementation of the boundary condition model for memristor nano-structures. The boundary condition model is equivalent to the linear drift model except for the introduction of adaptable boundary conditions, which impose an activation threshold of the state dynamics at the boundaries, i.e. once the state gets clipped at one of the boundaries, it may not be released from it unless the input reverses its sign and gets larger than a certain activation threshold in magnitude. Thanks to the adaptability of the boundary behavior, the boundary condition model is able to describe a variety of physical nano-scale systems, where mem-ristor dynamics arise from distinct physical mechanisms. The proposed PSpice emulator may be used for the investigation of potential applications of memristive systems in integrated circuit design, especially for the development of non-volatile memories and neuromorphic platforms. The accuracy of the PSpice circuit model is validated through comparison with experimental results relative to the Hewlett-Packard memristor.

In this paper, we propose a novel approach to describe and analyze circuits which consist of any linear circuit connected to an arbitrary number of memristors. Due to the memristors the whole circuit is a nonlinear system. We use a Volterra series approach to derive solutions of voltages and currents in memristive circuits. Thereby, the memristors are presented by polynomial functions which cover a broad class of devices. It will be shown that the different order Volterra kernels depend on the one hand on the structure and parameters of the linear part of the circuit - represented by the admittance or impedance matrix - and on the other hand on the coefficients in the polynomial memristor representation. We consider this approach to be an important step in the development of memristive network theory.

Summary form only given. The memristor is a new nano-electronic device very promising for emerging technologies. Although 40 years ago Leon Chua has postulated this circuit element, only the invention of the crossbar latch by the HP group of Stanley Williams provided the first nanoelectronic realization of such a device in 2008. Thus it has been shown that the ideal circuit elements (R,C,L) were not sufficient to model basic real-world circuits. Memristors being essentially resistors with memory are able to perform logic operations as well as storage of information. Recently, it has been announced that “Williams expects to see memristors used in computer memory chips within the next few years. HP Labs already has a production-ready architecture for such a chip” (http://www.hpl.hp.com/news/2010/apr-jun/memristor.html). Memristors are outstanding candidates for future analog, digital, and mixed signal circuits.

In this paper, a novel visual multi-feature detecting algorithm for the real time monitoring and control of laser beam welding (LBW) processes is discussed. It was implemented in the Eye-RIS vision system (VS) which includes a focal plane processor programmable by typical Cellular Neural Network (CNN) operators. The algorithm is based on the extraction of “spatters” - explosions of rear melt pool - to provide on-line quality information about the process and on the detection of the full penetration hole (FPH) for the laser power control to maintain a constant penetration depth into the workpiece. A single image evaluating step is performed in about 90 µs.

The memristor as a basic circuit element has drawn wide attention in the international research community of electrical engineers, physicists, and biologists. Memristors - being prominent for the realization of non-volatile VLSI resistive random access memories (RRAM) and for their applicability as synapses in neuromorphic systems provide even further surprising properties in electric circuits, which opens up new horizons to future applications. This article is in accordance with the special session of ISCAS2012 having the same title. We present a tutorial overview of the state-of-the-art of theory and applications of single memristor devices as well as memristive circuits.

Real time monitoring of laser welding has a more and more importance in several manufacturing processes ranging from automobile production to precision mechanics. Despite the huge improvement in welding technology, sophisticated image based closed loop control systems have not been integrated in commercially available equipments yet. Due to the high dynamics of laser beam welding (LBW) processes, robust closed loop control systems require fast real time image processing with frame rates in the multi kilo Hertz range. In the last few years, some new high speed Cellular Neural Network (CNN) based algorithms for the full penetration hole detection in keyhole welding processes have been introduced. In particular, they can be distinguished in two categories: Orientation dependent and orientation independent algorithms. The former can be used only for the welding of straight lines, while the latter has been implemented for the control of curved weld seams. Both algorithms have been used to build up a real time closed loop control system for LBW processes. An algorithm comparison by the description of some experimental results is addressed in this paper.

In this paper the results obtained by the use of new CNN based visual algorithms for the control of welding processes are described. The growing number of laser welding applications from automobile production to micro mechanics requires fast systems to create closed loop control for error prevention and correction. Nowadays the image processing frame rates of conventional architectures are not sufficient to control high speed laser welding processes due to the fast fluctuation of the full penetration hole. This paper focuses the attention on new strategies obtained by the use of the Eye-RIS system v1.2 which includes a pixel parallel cellular neural network (CNN) based architecture called Q-Eye. In particular, new algorithms for the full penetration hole detection with frame rates up to 24 kHz will be presented. Finally, the results obtained performing real time control of welding processes by the use of these algorithms will be discussed.

In this paper new CNN based visual algorithms for the control of welding processes are proposed. The high dynamics of laser welding in several manufacturing processes ranging from automobile production to precision mechanics requires the introduction of new fast real time controls. In the last few years, analogic circuits like cellular neural networks (CNN) have obtained a primary place in the development of efficient electronic devices because of their real-time signal processing properties. Furthermore, several pixel parallel CNN based architectures are now included within devices like the family of EyeRis systems [1]. In particular, the algorithms proposed in the following have been implemented on the EyeRis system v1.2 with the aim to be run at frame rates up to 20 kHz.

Adaptive signal processing on cellular nonlinear networks (CNN) based electronic devices is an exciting challenge, which needs a fast and robust parameter adaptation. In this contribution implementations and the analysis of optimisation algorithms will be proposed and discussed using the EyeRIStrade hardware system with an embedded ACE16kv2 focal plane processor having 128 times 128 cells. The parameter training performance were analysed in detail.

Cellular Nonlinear Networks (CNN) are characterized by local couplings of comparatively simple dynamical systems. In spite their compact structure, CNN exhibit complex phenomena like nonlinear wave propagation or chaotic behavior. The well studied Reaction-Diffusion Systems are widely used to describe phenomena like pattern formation and other processes in the fields of biology, chemistry and physics. By spatial discretization Reaction-Diffusion Partial Differential equations can be mapped to the cellular structures of Reaction-Diffusion Cellular Nonlinear Networks (RD-CNN). In this contribution simple RD-CNN models are determined in numerical optimization procedures in order to approximate short segments of EEG signals. Thereby effects of higher order nonlinear cell couplings are studied. Parameter changes of the RD-CNN models may be used for precursor detection of impending seizures in epilepsy.

We have shown in different studies (Gollas et al., 2004; Niederhofer and Tetzlaff, 2005; Weib and Tetzlaff, 2002) that the analysis of EEG-signals in epilepsy (Engels, 1989) using algorithms based on cellular nonlinear networks (CNN) (Leon and Chua, 1998) can contribute to the unsolved seizure prediction problem. For an automated prediction of impending epileptic seizures a precursor detection has to be performed which is based on an extraction of signal features in an pre-processing step. In different approaches (Fischer and Tetzlaff; Niederhofer et al., 2003, 2002; Kunz et al., 2000) to the feature extraction problem, weakly nonlinear discrete-time (DT) CNN with polynomial weight functions have been used especially for the signal prediction. In this paper the signal prediction by DT-CNN will be treated for increasing order of the polynomial weight functions. The aim of our work is to find out whether an increasing nonlinear degree will lead to more accurate results. Thereby the effects of taking EEG data as network boundary conditions will be studied

About 0.5% of the world population is suffering from a focal epilepsy (J. Engel et al., 2003), which is a widely spread disease. The goal of the investigations discussed in this paper is an early detection of precursors of an impending epileptic seizure by the analysis of brain electrical activity of multi-electrode EEG recordings. Therefore, methods of nonlinear signal processing were used in CNN simulations. This investigation is based on long-term recordings of approximately one week length, where analysis algorithms proposed in previous investigations (C. Niederhoefer et al., 2003) have been generalised toward new feature extraction methods which are presented in this paper.

Image coding still is an important research field in image processing. Although storage capacitates increase permanently, image file sizes are of high interest in the area of image transmission, e.g. in the Internet the number of bytes transmitted is directly correlated to the costs and the time consumption for the transmission. Furthermore, because of the extremely high amount of data, in video processing efficient compression methods are always point of interest. In this contribution a new approach of image coding is presented, which uses the relatively new paradigm of cellular neural networks (CN). CNN are massively parallel computing arrays which are perfectly suited for high speed image processing. Furthermore, their robustness is another outstanding feature of CNN hardware implementations, so that they predominate many other neural network implementations.

In this paper we show that the Cellular Nonlinear Network Universal Machine (CNN-UM) is an excellent tool for analyzing time series of multidimensional binary signals. The developed algorithm is dedicated to process electrophysiological multi-neuron recordings: our aim is to find specific multidimensional activity patterns, which may reflect higher order functional cell-assemblies. The analysis consists of two parts: first, the occurrences of different patterns are counted, then the statistical significance of each occurrence frequency is calculated separately.

In this paper, we present a novel approach to the prediction of epileptic seizures using boolean CNN with linear weight functions. Three different binary pattern occurrence behaviours will be discussed and analysed for several invasive recordings of brain electrical activity. Furthermore analogic binary pattern detection algorithms will be introduced for a possible prediction of epileptic seizures.

Cellular neural networks (CNN) are excellently suited for image processing. A big challenge thereby is the determination of CNN templates for special image processing tasks. In many cases, appropriate templates can only be found by a parameter optimization. Unfortunately, especially in the context of image processing, such an optimization is frequently a difficult task due to a lot of local minima in the error measure. We present a new method of optimization that detects a global minimum of an error measure even if the function contains many local minima. To prove this assertion, we constructed a number of multidimensional test functions, which have not only a global minimum but also many local minima. We present a comparison between the introduced iterative annealing method and other analytical and statistical optimization methods. Furthermore, by using the new optimization method we realized a feature point extractor with CNN.

We present a new approach for the analysis of the spatio-temporal dynamics of brain electrical activity in epilepsy with cellular neural networks (CNN). We have shown in recent investigations [1999] that the dimension D/sub 2/*(k, m) of brain electrical activity can be approximated by a function of CNN cell outputs. These results obtained with CNN, having non- steady-states, were sensitive to parameter deviations occurring in CNN hardware realizations. In this contribution we present an enhanced approximation method, which is based on a steady state determination showing an increased robustness and higher accuracy.

A learning procedure for the dynamics of cellular neural networks (CNN) with nonlinear cell interactions is presented. It is applied in order to find the parameters of CNN that model the dynamics of certain nonlinear systems, which are characterized by partial differential equations (PDEs). Values of a solution of the considered PDEs for a particular initial condition are taken as the training pattern at only a small number of points in time. Our results demonstrate that CNN obtained with our method approximate the dynamical behaviour of various nonlinear systems accurately. Results for two nonlinear PDEs, the /spl Phi//sup 4/-equation and the sine-Gordon equation, are discussed in detail.