Models of Hopfield-type quaternion neural networks and their energy functions

Recently models of neural networks that can directly deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. Furthermore models of neural networks that can deal with quaternion numbers, which is the extension of complex numbers, have also been proposed. However they are all multilayer quaternion neural networks. This paper proposes models of fully connected recurrent quaternion neural networks, Hopfield-type quaternion neural networks. Since quaternion numbers are non-commutative on multiplication, some different models can be considered. We investigate dynamics of these proposed models from the point of view of the existence of an energy function and derive their conditions for existence.     

Stability and synchronization analysis of inertial memristive neural networks with time delays

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.     

Are interlimb interactions disturbed in patients with Parkinson’s disease? A study under unloading conditions

During natural human locomotion, neural connections are activated that are typical of regulation of the quadrupedal walking. The interaction between the neural networks generating rhythmic movements of the upper and lower limbs depends on tonic state of each of these networks regulated by motor signals from the brain. Distortion of these signals in patients with Parkinson’s disease (PD) may lead to disruption of the interlimb interactions. We examined the effect of movements of the limbs of one girdle on the parameters of the motor activity of another limb girdle at their joint cyclic movements under the conditions of arm and leg unloading in 17 patients with PD and 16 healthy subjects. We have shown that, in patients, the effect of voluntary and passive movements of arms, as well as the active movement of the distal parts of arms, on the voluntary movement of legs is weak, while in healthy subjects, the effect of arm movements on the parameters of voluntary stepping is significant. The effect of arm movements on the activation of the involuntary stepping by vibrational stimulation of-legs in patients was absent, while in healthy subjects, the motor activity of arms increased the possibility of involuntary rhythmic movements activation. Differences in the effect of leg movements on the rhythmic movements of arms were found in both patients and healthy subjects. The interlimb interaction appeared after drug administration. However, the effect of the drug was not sufficient for the recovery of normal state of the neural networks in patients. In PD patients, neural networks generating stepping rhythm have an increased tonic activity, which prevents the activation and appearance of involuntary rhythmic movements facilitating the effects of arms on legs.     

Influence of the environment on adult CNS plasticity and repair

During developmental critical periods, external stimuli are crucial for information processing, acquisition of new functions or functional recovery after CNS damage. These phenomena depend on the capability of neurons to modify their functional properties and/or their connections, generally defined as "plasticity". Although plasticity decreases after the closure of critical periods, the adult CNS retains significant capabilities for structural remodelling and functional adaptation. At the molecular level, structural modifications of neural circuits depend on the balance between intrinsic growth properties of the involved neurons and growth-regulatory cues of the extracellular milieu. Interestingly, experience acts on this balance, so as to create permissive conditions for neuritic remodelling. Here, we present an overview of recent findings concerning the effects of experience on cellular and molecular processes responsible for producing structural plasticity of neural networks or functional recovery after an insult to the adult CNS (e.g. traumatic injury, ischemia or neurodegenerative disease). Understanding experience-dependent mechanisms is crucial for the development of tailored rehabilitative strategies, which can be exploited alone or in combination with specific therapeutic interventions to improve neural repair after damage.     

Fast time delay neural networks

This paper presents a new approach to speed up the operation of time delay neural networks. The entire data are collected together in a long vector and then tested as a one input pattern. The proposed fast time delay neural networks (FTDNNs) use cross correlation in the frequency domain between the tested data and the input weights of neural networks. It is proved mathematically and practically that the number of computation steps required for the presented time delay neural networks is less than that needed by conventional time delay neural networks (CTDNNs). Simulation results using MATLAB confirm the theoretical computations.     

人工神经网络模型及其在农业和生态学研究中的应用

对于一些复杂的农业生态系统,人们对其生态过程了解较少,且这些系统的不确定性和模糊性较大,用传统的方法难以模拟这些系统的行为,神经网络模型因为能较精确地模拟这些系统的行为,而引起生态学者们的广泛兴趣。该文着重介绍了误差逆传神经网络模型的结构、算法及其在农业和生态学中的应用研究。误差逆传神经网络模型一般采用三层神经网络模型结构,三层的神经网络模型能模拟任意复杂程度的连续函数,而且因为它的结构小而不容易产生与训练数据的过度吻合。误差逆传神经网络模型算法的主要特征是:利用当前的输入误差对权值进行调整。在生态学和农业研究中,误差逆传神经网络模型通常作为非线性函数模拟器用于预测作物产量、生物生产量、生物与环境之间的关系等。已有的研究表明:误差逆传神经网络模型的模拟精度要远远高于多元线性方程,类似于非线性方程,而在样本量足够的情况下,有一定的外推能力。但是误差逆传神经网络模型需要大量的样本量来保证所求取参数的可靠性,但这在实际研究中很难做到,因而限制了误差逆传神经网络模型的应用。近年来人们提出了强制训练停止、复合模型等多种技术来提高误差逆传神经网络模型的外推能力,也提出了Garson算法、敏感性分析以及随机化检验等技术对误差逆传神经网络模型的机理进行解释。误差逆传神经网络模型的真正优势在于模拟人们了解较少或不确定性和模糊性较大系统的行为,这些是传统模型所无法实现的,因而是对传统机理模型的重要补充。     

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks – neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non‐detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.     

Effects of nerve injury and segmental regeneration on the cellular correlates of neural morphallaxis

Functional recovery of neural networks after injury requires a series of signaling events similar to the embryonic processes that governed initial network construction. Neural morphallaxis, a form of nervous system regeneration, involves reorganization of adult neural connectivity patterns. Neural morphallaxis in the worm, Lumbriculus variegatus, occurs during asexual reproduction and segmental regeneration, as body fragments acquire new positional identities along the anterior-posterior axis. Ectopic head (EH) formation, induced by ventral nerve cord lesion, generated morphallactic plasticity including the reorganization of interneuronal sensory fields and the induction of a molecular marker of neural morphallaxis. Morphallactic changes occurred only in segments posterior to an EH. Neither EH formation, nor neural morphallaxis was observed after dorsal body lesions, indicating a role for nerve cord injury in morphallaxis induction. Furthermore, a hierarchical system of neurobehavioral control was observed, where anterior heads were dominant and an EH controlled body movements only in the absence of the anterior head. Both suppression of segmental regeneration and blockade of asexual fission, after treatment with boric acid, disrupted the maintenance of neural morphallaxis, but did not block its induction. Therefore, segmental regeneration (i.e., epimorphosis) may not be required for the induction of morphallactic remodeling of neural networks. However, on-going epimorphosis appears necessary for the long-term consolidation of cellular and molecular mechanisms underlying the morphallaxis of neural circuitry.     

The Rich Get Richer: Brain Injury Elicits Hyperconnectivity in Core Subnetworks

There remains much unknown about how large-scale neural networks accommodate neurological disruption, such as moderate and severe traumatic brain injury (TBI). A primary goal in this study was to examine the alterations in network topology occurring during the first year of recovery following TBI. To do so we examined 21 individuals with moderate and severe TBI at 3 and 6 months after resolution of posttraumatic amnesia and 15 age- and education-matched healthy adults using functional MRI and graph theoretical analyses. There were two central hypotheses in this study: 1) physical disruption results in increased functional connectivity, or hyperconnectivity, and 2) hyperconnectivity occurs in regions typically observed to be the most highly connected cortical hubs, or the “rich club”. The current findings generally support the hyperconnectivity hypothesis showing that during the first year of recovery after TBI, neural networks show increased connectivity, and this change is disproportionately represented in brain regions belonging to the brain''s core subnetworks. The selective increases in connectivity observed here are consistent with the preferential attachment model underlying scale-free network development. This study is the largest of its kind and provides the unique opportunity to examine how neural systems adapt to significant neurological disruption during the first year after injury.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

多比例时滞细胞神经网络的指数周期性与稳定性

研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e~t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论.     

Prediction of caspase cleavage sites using Bayesian bio-basis function neural networks

MOTIVATION: Apoptosis has drawn the attention of researchers because of its importance in treating some diseases through finding a proper way to block or slow down the apoptosis process. Having understood that caspase cleavage is the key to apoptosis, we find novel methods or algorithms are essential for studying the specificity of caspase cleavage activity and this helps the effective drug design. As bio-basis function neural networks have proven to outperform some conventional neural learning algorithms, there is a motivation, in this study, to investigate the application of bio-basis function neural networks for the prediction of caspase cleavage sites. RESULTS: Thirteen protein sequences with experimentally determined caspase cleavage sites were downloaded from NCBI. Bayesian bio-basis function neural networks are investigated and the comparisons with single-layer perceptrons, multilayer perceptrons, the original bio-basis function neural networks and support vector machines are given. The impact of the sliding window size used to generate sub-sequences for modelling on prediction accuracy is studied. The results show that the Bayesian bio-basis function neural network with two Gaussian distributions for model parameters (weights) performed the best and the highest prediction accuracy is 97.15 +/- 1.13%. AVAILABILITY: The package of Bayesian bio-basis function neural network can be obtained by request to the author.     

Signal flow graphs and neural networks

The application of signal flow graphs to the learning process of neural networks is presented. By introducing the so-called adjoint graph, new insight into the mechanism of learning phenomena of the weights in neural networks has been obtained. The derived updating formulas are valid for both feedforward and recurrent neural networks and are especially useful from the hardware implementation point of view of the self-learning networks. The presented numerical experiments confirmed the usefulness of the presented approach. Received: 24 February 1993/Accepted in revised form: 28 July 1993     

Feedforward neural network models for handling class overlap and class imbalance

This paper proposes a framework for training feedforward neural network models capable of handling class overlap and imbalance by minimizing an error function that compensates for such imperfections of the training set. A special case of the proposed error function can be used for training variance-controlled neural networks (VCNNs), which are developed to handle class overlap by minimizing an error function involving the class-specific variance (CSV) computed at their outputs. Another special case of the proposed error function can be used for training class-balancing neural networks (CBNNs), which are developed to handle class imbalance by relying on class-specific correction (CSC). VCNNs and CBNNs are compared with conventional feedforward neural networks (FFNNs), quantum neural networks (QNNs), and resampling techniques. The properties of VCNNs and CBNNs are illustrated by experiments on artificial data. Various experiments involving real-world data reveal the advantages offered by VCNNs and CBNNs in the presence of class overlap and class imbalance.     

Is mood chemistry?

The chemical hypothesis of depression suggests that mood disorders are caused by a chemical imbalance in the brain, which can be corrected by antidepressant drugs. However, recent evidence indicates that problems in information processing within neural networks, rather than changes in chemical balance, might underlie depression, and that antidepressant drugs induce plastic changes in neuronal connectivity, which gradually lead to improvements in neuronal information processing and recovery of mood.     

On the Relationships between Generative Encodings,Regularity, and Learning Abilities when Evolving Plastic Artificial Neural Networks

A major goal of bio-inspired artificial intelligence is to design artificial neural networks with abilities that resemble those of animal nervous systems. It is commonly believed that two keys for evolving nature-like artificial neural networks are (1) the developmental process that links genes to nervous systems, which enables the evolution of large, regular neural networks, and (2) synaptic plasticity, which allows neural networks to change during their lifetime. So far, these two topics have been mainly studied separately. The present paper shows that they are actually deeply connected. Using a simple operant conditioning task and a classic evolutionary algorithm, we compare three ways to encode plastic neural networks: a direct encoding, a developmental encoding inspired by computational neuroscience models, and a developmental encoding inspired by morphogen gradients (similar to HyperNEAT). Our results suggest that using a developmental encoding could improve the learning abilities of evolved, plastic neural networks. Complementary experiments reveal that this result is likely the consequence of the bias of developmental encodings towards regular structures: (1) in our experimental setup, encodings that tend to produce more regular networks yield networks with better general learning abilities; (2) whatever the encoding is, networks that are the more regular are statistically those that have the best learning abilities.     

Sustained oscillations generated by mutually inhibiting neurons with adaptation

Autonomic oscillatory activities exist in almost every living thing and most of them are produced by rhythmic activities of the corresponding neural systems (locomotion, respiration, heart beat, etc.). This paper mathematically discusses sustained oscillations generated by mutual inhibition of the neurons which are represented by a continuous-variable model with a kind of fatigue or adaptation effect. If the neural network has no stable stationary state for constant input stimuli, it will generate and sustain some oscillation for any initial state and for any disturbance. Some sufficient conditions for that are given to three types of neural networks: lateral inhibition networks of linearly arrayed neurons, symmetric inhibition networks and cyclic inhibition networks. The result suggests that the adaptation of the neurons plays a very important role for the appearance of the oscillations. Some computer simulations of rhythic activities are also presented for cyclic inhibition networks consisting of a few neurons.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov–Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.