Fluctuations in nonlinear systems can enhance the synchronization with weak input signals. Chaotic resonance (CR) is one of such phenomena, caused by a system-intrinsic chaotic fluctuation. CR is observed in systems with chaos-chaos intermittency (CCI), where a chaotic orbit appears between separate regions. Based on the characteristics of CR, we previously proposed a novel method for controlling the chaotic state to an appropriate CR state by adopting a feedback signal from the system itself. This method is called the reduced-region-of-orbit (RRO) feedback method. The RRO feedback method was applied to discrete and continuous time chaotic systems, and its versatility was confirmed. Moreover, we have applied this method to frontal cortex neural system model, and the effectiveness for controlling the system behavior by inducing CR was confirmed. In this study, we examined the responsiveness of CCI to a weak periodic signal by extending the model to the brain circuit level composed of frontal cortex, basal ganglia and thalamus. As a result, we confirmed the effectiveness of the RRO feedback method for stabilizing the neural activity observed in the brain circuit model of cerebral cortex-basal ganglia.

Chaotic resonance, resembling stochastic resonance, is induced by internal fluctuations (i.e., chaos). This phenomenon has been observed in numerous systems. The most representative form of chaotic resonance is the synchronization with respect to weak applied signals under chaos-chaos intermittency, where a chaotic orbit moves among multiple attractors. Chaotic resonance exhibits higher sensitivity than stochastic resonance, but its engineering applications are limited by concerns such as the requirement to adjust the state of chaos by internal system parameters to induce chaotic resonance rather than the external noise strength. However, achieving this adjustment is challenging, especially in biological systems. Therefore, to handle this limitation, we proposed a novel double-Gaussian-filtered reduced region of orbit (RRO) method (called the DG-RRO method) for obtaining perturbed feedback signals lower than the conventional RRO method. This DG-RRO feedback signal is determined by the inverse sign of the map function and double-Gaussian filters around the local maximum/minimum values of the map. Because of its fine local specification, the DG-RRO feedback signal induces a chaotic resonance by one-third the feedback strength of the conventional signal. This method may pave the way for using chaotic resonance in engineering applications.

An echo state network (ESN) is a reservoir computing framework consisting of an input layer, a reservoir, and a readout layer. A reservoir is a recursive network comprising neuron models. In the reservoir, various models use analog neurons with a logistic output function. Time-series learning for ESNs requires a high memory capacity for storing the historical information of past inputs. However, analog neurons are incapable of storing time history by themselves. Therefore, historical information gained by introducing internal neural dynamics can enhance the memory capacity of ESNs. In this context, we hypothesized that the evaluation of the functions of internal-neural decay factors and optimal balances between the decay factors of chaotic neurons can provide useful results for improving the performance of ESNs comprising chaotic neural networks. Therefore, to validate this hypothesis, we investigated the performance of an ESN using a reservoir comprising a chaotic neural network (ChESN). The ChESN significantly outperformed a conventional ESN owing to its high memory capacity at a large temporal scale, even when the spectral radius of the reservoir synaptic weight was small. The proposed approach is expected to have wide applications in reservoir computing.

Recent studies on stochastic resonance have been considered in various fields for engineering applications. Chaotic dynamics derive a phenomenon called chaotic resonance, which is similar to stochastic resonance. The engineering applications of chaotic resonance are limited due to its controlling difficulty, although it exhibits a high sensitivity to signal responses. To address this limitation, we previously proposed a "reduced region of orbit" (RRO) feedback method which induces chaotic resonance using external feedback signals. This method was evaluated under noise-free conditions. However, in practical scenarios, background noise and measurement error are observed when estimating the RRO feedback strength. The influence of these factors on chaotic resonance must be evaluated for preliminary practical application of chaotic resonance. Therefore, in this study, we evaluated chaotic resonance induced by the RRO feedback method in chaotic neural systems under stochastic noise. We focus on chaotic resonance induced by RRO feedback signals in a discrete neural system comprising excitatory and inhibitory neurons, which are typical neural systems that entail chaotic resonance under additive noise and feedback signals, including measurement errors (called contaminant noise). Although both types of noise commonly degrade the degree of synchronization of chaotic resonance induced by the RRO feedback strength, their characteristics are considerably different. In actual neural systems, the influence of noise is inevitable; therefore, this study highlighted the importance of noise countermeasures during the application of chaotic resonance.

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

A convolutional neural network based on quaternion, a four-dimensional hypercomplex number system, is proposed and evaluated in this paper. Called Quaternionic Convolutional Neural Networks (QCNNs), these networks can accept and operate three-dimensional signals by neurons in the networks. The performances of the proposed networks are investigated through classification of CIFAR-10 color images, and it is shown that the proposed QCNN outperforms a conventional (real-valued) CNN.

We propose a neural network model based on quantum information processing with quaternionic representation and operations, called Quaternionic Qubit Neural Network. The state of a neuron is represented by a point on the Bloch sphere with incorporating quaternionic representation. The operations for this neuron also follow the operations in quaternions. The proposed neural networks are evaluated through numerical experiments for predicting chaotic time series produced by a Lorentz system. They have better performances in predicting long-term series, as compared to conventional (real-valued) neural networks.

In coupled chaotic systems, chaos synchronization is widely observed under the condition with specific coupled forms, such as complete, phase, and generalized synchronizations. Recently, several methods for controlling this chaos synchronization by a nonlinear feedback controller have been proposed. In this study, by focusing on coupled cubic maps, we developed a new method to control synchronization of chaos-chaos intermittency by a nonlinear feedback controller to adjust the range of existence of chaotic orbits. Through the evaluation of the dependence of system behaviors on the feedback strength and the coupled strength, we confirmed that the synchronization of chaos-chaos intermittency could be induced by this nonlinear feedback controller. Especially, the degree of synchronization becomes high at the edge between the parameter region of the feedback strength of chaos-chaos intermittency and the region of nonchaos-chaos intermittency.

A growing number of nonlinear EEG studies have elucidated the reduced fractality in Alzheimer's disease (AD). However, despite the importance of studying EEG dynamics within physiologically relevant frequency ranges, far fewer studies have explored temporal-dependent fractal properties in AD. This study was aimed at assessing the temporal-scale specific fractal properties in AD using Higuchi's fractal algorithm. As a result, we found both enhanced and reduced fractality in a temporal-scale relevant manner. Our findings suggest that investigating temporal specific fractal properties in EEG might serve as a useful approach for characterizing neural basis of AD.

Physical biometrics technologies are introduced to the login process on smart devices. However, many of them have several disadvantages: requirement of embedding special sensor, limited environment to use and copy of key information for authentication. In this research, we proposed a new biometrics technique which can capture user's inimitable behavioral features in his/her spontaneous flick reactions on a touch-screen display for unlocking the device when it wakes up. For practical use of the technique, we adopted one-class classification approaches and they achieved about 1-2% EERs for 2500 samples from 50 subjects.

In this paper, we propose a Hopfield Associative Memory with Complex-valued and Real-valued neurons (CRHAM). CRHAM is an associative memory which can perform storing and recalling multi-valued patterns. A part of neurons in the network are complex-valued neurons, and the rest of neurons are conventional (real-valued) neurons. Spurious patterns that degrade the retrieval performance can be reduced by the combination of those two types of neurons. The experimental results show that high robustness for noisy inputs is achieved by CRHAM as compared with conventional complex-valued associative memories, such as Complex-valued Hopfield Associative Memory (CHAM) and Complex-valued Bipartite Auto-Associative Memory (CBAAM).

Spiking neuron models, which can realize diverse kinds of neural coding by describing spiking activity of membrane potential, have been widely utilized. Among these models, several hybrid spiking neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. Izhikevich neuron model as this kind of model can reproduce many spiking patterns. It has also become clear that this model has various kinds of bifurcation and routes to chaos under the effect of the state dependent jump in the resetting process. In response to this situation, we have further gotten interested in the relation between chaotic behaviors and the state dependent jump. In this paper, we approach the subject from the comparison of spiking neuron models without the resetting process and with it. We first adopt a continuous two-dimensional spiking neuron model where the orbit at spiking state does not exhibit the divergent behavior and next insert the resetting process to it.

Synaptic plasticity is widely recognized to support adaptable information processing in the brain. Spike-timing-dependent plasticity, one subtype of plasticity, can lead to synchronous spike propagation with temporal spiking coding information. Recently, it was reported that in a noisy environment, like the actual brain, the spike-timing-dependent plasticity may be made efficient by the effect of stochastic resonance. In the stochastic resonance, the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal. However, previous studies have ignored the full variety of spiking patterns and many relevant factors in neural dynamics. Thus, in order to prove the physiological possibility for the enhancement of spike-timing-dependent plasticity by stochastic resonance, it is necessary to demonstrate that this stochastic resonance arises in realistic cortical neural systems. In this study, we evaluate this stochastic resonance phenomenon in the realistic cortical neural system described by the Izhikevich neuron model and compare the characteristics of typical spiking patterns of regular spiking, intrinsically bursting and chattering experimentally observed in the cortex.

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron's characteristics, but it was not as easy for SR.

This paper presents Quaternionic Bidirectional Auto-Associative Memory (QBAAM) that is an associative memory network storing patterns with multiple levels. A part of neurons in the network are quaternionic neurons, where their states are encoded by quaternion, which is a four-dimensional hypercomplex number system. These neurons can represent three kinds of discretized phases, i.e., three-dimensional multilevel values. The rest of neurons are conventional (real-valued) neurons. QBAAM is expected to have a rich representation ability by employing quaternionic neurons, as well as to have fewer spurious patterns in the network by a combination of real-valued and quaternionic neurons. The experimental results show that high robustness of noisy inputs is achieved by QBAAM, as compared with Quaternionic Hopfield Associative Memory where all neurons in the network are quaternionic neurons.

The performance of layered neural networks with quaternionic encoding variables are investigated in this paper. The form of local analyticity with Wirtinger representation is adopted for a backpropagation learning algorithm in this network. A quaternionic version of tanh function is used for the activation function in neuron states' updates. As tasks of the performance evaluation of the presented networks, two types of three dimensional data processing problem are used; the prediction of the Lorentz attractor and affine transformations in three dimensional space.

Choosing an appropriate activation function is a challenging problem in quaternionic neural networks, due to the analyticity in quaternionic domain. This paper presents a Hopfield-type neural network with an activation function with quaternionic equivalent of tanh function. This activation function is obtained by incorporating so-called “local analyticity” on quaternionic domain and the recent results on complex-valued activation functions. The stability of the network is shown by proving monotonic decrease of energy with the changes of neuron states.

Recently, numerous attempts have been made to understand the dynamic behavior of complex brain systems using neural network models. The fluctuations in blood-oxygen-level-dependent (BOLD) brain signals at less than 0.1 Hz have been observed by functional magnetic resonance imaging (fMRI) for subjects in a resting state. This phenomenon is referred to as a "default-mode brain network." In this study, we model the default-mode brain network by functionally connecting neural communities composed of spiking neurons in a complex network. Through computational simulations of the model, including transmission delays and complex connectivity, the network dynamics of the neural system and its behavior are discussed. The results show that the power spectrum of the modeled fluctuations in the neuron firing patterns is consistent with the default-mode brain network's BOLD signals when transmission delays, a characteristic property of the brain, have finite values in a given range.

Properties and performances of associative memories, based on Complex-valued Synergetic Computer (CVSC), are explored in this paper. All the parameters of CVSC are encoded by complex values. CVSC is extended from the conventional Synergetic Computer (RVSC) in which the parameters are real values. Performances of associative memories in CVSC are investigated through a problem of image retrievals where the input images are partially occluded or noise-affected. From the experimental results concerning the retrieval performances related to various sizes of images and different levels of defectiveness of input images, we found that CVSC outperforms RVSC.

Double contrast (DC) X-ray images are useful and cost-effective for the diagnosis of stomach tumors. However, it is difficult to automatically extract tumors from these images. This is due to the variations in the tumors appearing in the images as a result of the changes in stomach shapes and the distribution of barium meal in the stomach. In this paper, we propose an automated method for detecting tumors in DC X-ray images. Our method utilizes the distributions of contrast gradients in the images. The performance of our method is demonstrated by using actual DC X-ray images.

This paper explores two types of multistate Hopfield neural networks, based on commutative quaternions that are similar to Hamilton's quaternions but with commutative multiplication. In one type of the networks, the state of a neuron is represented by two kinds of phases and one real number. The other type of the networks adopts the decomposed form of commutative quaternion, i.e., the state of a neuron consists of a combination of two complex values. We have investigated the stabilities of these networks, i.e., the energies monotonically decreases with respect to the changes of the network states.

We propose a learning scheme for multistate complex-valued and quaternionic neural networks in order to store correlated patterns with respect to each other. This is an extension of the so-called local iterative scheme for real-valued Hopfield neural networks. We first show the stability of desired memory patterns for a multistate complex-valued network and also for the multistate quaternionic network.

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

We introduce a stimulus-response scheme that supports plastic variation of synapse weights in neural networks, and analyze how memory formation evolves under external stimulation. In so doing, chaotic networks and stochastic networks that have very different dynamics are compared. Experimental results suggest that chaotic activity remarkably outperforms stochastic activity in stimulus-response memorization. This seems to be indicative of effectiveness of the chaos in dynamic learning by stimulus-response scheme oriented to natural learning.

Associative memory by Hopfleld-type recurrent neural networks with quaternionic algebra, called quaternionic Hopfield neural network, is proposed in this paper. The variables in the network are represented by quaternions of four dimensional hypercomplex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the network are introduced. The properties of this network are analyzed concretely through examples of the network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the network, i.e., the pattern association from test pattern close to a stored pattern is possible in the quaternionic network, as in real-valued Hopfleld networks.

Neural networks have attracted much interest in the two decades for their potential to describe brain function realistically. Quantum computing is a likely candidate for improving the computational efficiency of neural networks, since it has been very successful in doing so for a selected set of computational problems. We have proposed Qubit neural network that is a multilayered neural network composed of Qubit inspired neurons with Quantum Back Propagation learning and confirmed the performance concerning basic benchmark problems such as 4-bit and 6-bit parity check problems. In this paper, we examine this Qubit neural network through more practical problems, for example, the Iris data classification and the night vision processing.

In nonstationary environments, it is difficult to apply traditional genetic algorithms (GAs) because they use strong selection pressure and lose the diversity of individuals rapidly. We propose a GA with neutral variation that can track environmental changes. The idea of this GA is inspired by Kimura's neutral theory (1983). The scheme of this GA allows neutral characters, which do not directly affect the fitness with respect to environments, thus increasing the diversity of individuals. In order to demonstrate the properties of this GA, we apply it to a permutation problem called the ladder-network, of which the imposed alignment on the output changes regularly. We show that the GA with neutral variation can adapt better to environmental changes than a traditional GA.

In recent years, some researchers have been exploring quantum computers in view of neural networks to realize a distributed and strongly connectionist system that achieves parallel and fast information processing. We (1998) have proposed and investigated a qubit neuron model based on quantum mechanics, and constructed the quantum backpropagation learning rule (QBP). In this paper, we show an improved QBP neural network model and discuss its performance on solving the 4 bit parity check problem and the function identification problem. Then, we conclude that our model is more effective than the conventional one in information processing efficiency.