Dynamics and synchronization control of fractional conformable neuron system.

Dynamic analysis, electrical coupling and synchronization control of the conformable FitzHugh-Nagumo neuronal models have been presented in this work. Firstly, equations of the Adomian-Decomposition-Method and conformable neuron model have been introduced. The Adomian-Decomposition-Method has been employed for the numerical simulation analysis, since it converges fast and provides serial solutions. Fractional order and external current stimulus have been considered as bifurcation parameters and their effects on neuron model dynamics have been examined in detail. Then, the electrical coupling of the two conformable neuronal models without any controller has been revealed and the significance of the coupling strength parameter has been evaluated. To eliminate impact of the coupling strength parameter on synchronization status of neurons, Lyapunov control method has been employed for synchronization control. In the last step, the numerical simulation studies have been experimentally verified using the Texas Instrument Delfino digital signal processor board. Numerical simulation results together with experimental validation have showed that the types of dynamics of the related neuron model are not affected from the change of the fractional order of conformable derivative, but the frequency of the dynamic response of the neuronal model is changed from the alteration of the fractional order. The frequency of response of the neuron model increases with decreasing values of the fractional order. On the other hand, if there is no synchronization control method, the coupled neuron models exhibit response ranging from synchronous to asynchronous depending on the sign and value of the coupling parameter. Additionally, decreasing values of the fractional order may allow the coupled neurons to enter the synchronous state more quickly due to increasing frequency of response of the neuronal model. Finally, the coupled neuron models could exhibit synchronous behavior, that is determined by calculating the standard deviation results, regardless of the value of the coupling parameter by using the Lyapunov control method.

Purkinje cell models: past, present and future.

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields.

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model.

Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.

Multitask Adversarial Networks Based on Extensive Nonlinear Spiking Neuron Models.

Deep learning technology has been successfully used in Chest X-ray (CXR) images of COVID-19 patients. However, due to the characteristics of COVID-19 pneumonia and X-ray imaging, the deep learning methods still face many challenges, such as lower imaging quality, fewer training samples, complex radiological features and irregular shapes. To address these challenges, this study first introduces an extensive NSNP-like neuron model, and then proposes a multitask adversarial network architecture based on ENSNP-like neurons for chest X-ray images of COVID-19, called MAE-Net. The MAE-Net serves two tasks: (i) converting low-quality CXR images to high-quality images; (ii) classifying CXR images of COVID-19. The adversarial architecture of MAE-Net uses two generators and two discriminators, and two new loss functions have been introduced to guide the optimization of the network. The MAE-Net is tested on four benchmark COVID-19 CXR image datasets and compared them with eight deep learning models. The experimental results show that the proposed MAE-Net can enhance the conversion quality and the accuracy of image classification results.

A scalable spiking amygdala model that explains fear conditioning, extinction, renewal and generalization.

The amygdala (AMY) is widely implicated in fear learning and fear behaviour, but it remains unclear how the many biological components present within AMY interact to achieve these abilities. Building on previous work, we hypothesize that individual AMY nuclei represent different quantities and that fear conditioning arises from error-driven learning on the synapses between AMY nuclei. We present a computational model of AMY that (a) recreates the divisions and connections between AMY nuclei and their constituent pyramidal and inhibitory neurons; (b) accommodates scalable high-dimensional representations of external stimuli; (c) learns to associate complex stimuli with the presence (or absence) of an aversive stimulus; (d) preserves feature information when mapping inputs to salience estimates, such that these estimates generalize to similar stimuli; and (e) induces a diverse profile of neural responses within each nucleus. Our model predicts (1) defensive responses and neural activities in several experimental conditions, (2) the consequence of artificially ablating particular nuclei and (3) the tendency to generalize defensive responses to novel stimuli. We test these predictions by comparing model outputs to neural and behavioural data from animals and humans. Despite the relative simplicity of our model, we find significant overlap between simulated and empirical data, which supports our claim that the model captures many of the neural mechanisms that support fear conditioning. We conclude by comparing our model to other computational models and by characterizing the theoretical relationship between pattern separation and fear generalization in healthy versus anxious individuals.

Improving Classification Performance in Dendritic Neuron Models through Practical Initialization Strategies.

A dendritic neuron model (DNM) is a deep neural network model with a unique dendritic tree structure and activation function. Effective initialization of its model parameters is crucial for its learning performance. This work proposes a novel initialization method specifically designed to improve the performance of DNM in classifying high-dimensional data, notable for its simplicity, speed, and straightforward implementation. Extensive experiments on benchmark datasets show that the proposed method outperforms traditional and recent initialization methods, particularly in datasets consisting of high-dimensional data. In addition, valuable insights into the behavior of DNM during training and the impact of initialization on its learning performance are provided. This research contributes to the understanding of the initialization problem in deep learning and provides insights into the development of more effective initialization methods for other types of neural network models. The proposed initialization method can serve as a reference for future research on initialization techniques in deep learning.

Effect of the electromagnetic induction in the electrical activity of the Kazantsev model of inferior Olive Neuron model.

In this paper, based on the four variables Kazantsev et al. inferior olive neuron (ION) dynamic equations, a five variables neuron model is designed to describe the effect of electromagnetic induction in ION activities. Within the new ION model, the effect of magnetic flow on membrane potential is described by imposing additive memristive current in the master block of the Kasantsev et al. neuron model. The impact of magnetic flux on the stability of equilibrium point is studied. Hopf bifurcation and bifurcation diagram indicated that, as the electromagnetic field strength parameter changes, the value of the critical point also changes. Furthermore, as the electromagnetic induction is increasing, there is appearance of bursting dynamic in the slave subsystem and an increase in the spike amplitude of the master subsystem. In addition, the analog circuit of the master block confirms the observed results from numerical simulation.

On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks.

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is often much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and the exact value of each parameter is frequently less interesting than the distribution of the parameters. In this paper, we aim to estimate the distribution of the parameters in the mesoscopic neuronal network model from the macroscopic experimental data, for example, the BOLD (blood oxygen level dependent) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently and identically distributed from certain distributions with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the Leaky Integral-Fire (LIF) neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with high preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.

A Novel Biophysical Model for the Generation of Sharp Wave Ripples in CA1 Hippocampus.

Synchronous activities among neurons in the brain generate emergent network oscillations such as the hippocampal Sharp-wave ripples (SPWRs) that facilitate information processing during memory formation. However, how neurons and circuits are functionally organized to generate oscillations remains unresolved. Biophysical models of neuronal networks can shed light on how thousands of neurons interact in intricate circuits to generate such emergent SPWR network events. Here we developed a large-scale biophysically realistic neural network model of CA1 hippocampus with functionally organized circuit modules containing distinct types of neurons. Model simulations reproduced synaptic, cellular and network aspects of physiological SPWRs. The model provided insights into the role of neuronal types and their microcircuit motifs in generating SPWRs in the CA1 region. The model also suggests experimentally testable predictions including the role of specific neuron types in the genesis of hippocampal SPWRs.

Modeling apical and basal tree contribution to orientation selectivity in a mouse primary visual cortex layer 2/3 pyramidal cell.

Pyramidal neurons, a mainstay of cortical regions, receive a plethora of inputs from various areas onto their morphologically distinct apical and basal trees. Both trees differentially contribute to the somatic response, defining distinct anatomical and possibly functional sub-units. To elucidate the contribution of each tree to the encoding of visual stimuli at the somatic level, we modeled the response pattern of a mouse L2/3 V1 pyramidal neuron to orientation tuned synaptic input. Towards this goal, we used a morphologically detailed computational model of a single cell that replicates electrophysiological and two-photon imaging data. Our simulations predict a synergistic effect of apical and basal trees on somatic action potential generation: basal tree activity, in the form of either depolarization or dendritic spiking, is necessary for producing somatic activity, despite the fact that most somatic spikes are heavily driven by apical dendritic spikes. This model provides evidence for synergistic computations taking place in the basal and apical trees of the L2/3 V1 neuron along with mechanistic explanations for tree-specific contributions and emphasizes the potential role of predictive and attentional feedback input in these cells.

Coexisting Firing Patterns in an Improved Memristive Hindmarsh-Rose Neuron Model with Multi-Frequency Alternating Current Injection.

With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh-Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high-low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results.

Chimera state in a feed-forward neuronal network.

Feed-forward effect gives rise to synchronization in neuron firing in deep layers of multiple neuronal network. But complete synchronization means the loss of encoding ability. In order to avoid the contradiction, we ask whether partial synchronization (coexistence of disordered and synchronized neuron firing emerges, also called chimera state) as a compromise strategy can achieve in the feed-forward multiple-layer network. The answer is YES. In order to manifest our argument, we design a multi-layer neuronal network in which neurons in every layer are arranged in a ring topology and neuron firing propagates within (intra-) and across (inter-) the multiply layers. Emergence of chimera state and other patterns highly depends on initial condition of neuronal network and strength of feed-forward effect. Chimera state, cluster and synchronization intra- and inter- layers are displayed by sequence through layers when initial values are elaborately chosen to guarantee emergence of chimera state in the first layer. All type of patterns except chimera state propagates down toward deeper layers in different speeds varying with strength of feed-forward effect. If chimera state already exists in every layer, feed-forward effect with strong and moderate strength spoils chimera states in deep layers and they can only survive in first few layers. When the effect is small enough, chimera states will propagate down toward deeper layers. Indeed, chimera states could exist and transit to deeper layers in a regular multiple network under very strict conditions. The results help understanding better the neuron firing propagating and encoding scheme in a feed-forward neuron network.

The NEF-SPA Approach as a Framework for Developing a Neurobiologically Inspired Spiking Neural Network Model for Speech Production.

BACKGROUND: The computer-based simulation of the whole processing route for speech production and speech perception in a neurobiologically inspired way remains a challenge. Only a few neural based models of speech production exist, and these models either concentrate on the cognitive-linguistic component or the lower-level sensorimotor component of speech production and speech perception. Moreover, these existing models are second-generation neural network models using rate-based neuron approaches. The aim of this paper is to describe recent work developing a third-generation spiking-neuron neural network capable of modeling the whole process of speech production, including cognitive and sensorimotor components. METHODS: Our neural model of speech production was developed within the Neural Engineering Framework (NEF), incorporating the concept of Semantic Pointer Architecture (SPA), which allows the construction of large-scale neural models of the functioning brain based on only a few essential and neurobiologically well-grounded modeling or construction elements (i.e., single spiking neuron elements, neural connections, neuron ensembles, state buffers, associative memories, modules for binding and unbinding of states, modules for time scale generation (oscillators) and ramp signal generation (integrators), modules for input signal processing, modules for action selection, etc.). RESULTS: We demonstrated that this modeling approach is capable of constructing a fully functional model of speech production based on these modeling elements (i.e., biologically motivated spiking neuron micro-circuits or micro-networks). The model is capable of (i) modeling the whole processing chain of speech production and, in part, for speech perception based on leaky-integrate-and-fire spiking neurons and (ii) simulating (macroscopic) speaking behavior in a realistic way, by using neurobiologically plausible (microscopic) neural construction elements. CONCLUSIONS: The model presented here is a promising approach for describing speech processing in a bottom-up manner based on a set of micro-circuit neural network elements for generating a large-scale neural network. In addition, the model conforms to a top-down design, as it is available in a condensed form in box-and-arrow models based on functional imaging and electrophysiological data recruited from speech processing tasks.

A Bio-Inspired Chaos Sensor Model Based on the Perceptron Neural Network: Machine Learning Concept and Application for Computational Neuro-Science.

The study presents a bio-inspired chaos sensor model based on the perceptron neural network for the estimation of entropy of spike train in neurodynamic systems. After training, the sensor on perceptron, having 50 neurons in the hidden layer and 1 neuron at the output, approximates the fuzzy entropy of a short time series with high accuracy, with a determination coefficient of R2~0.9. The Hindmarsh-Rose spike model was used to generate time series of spike intervals, and datasets for training and testing the perceptron. The selection of the hyperparameters of the perceptron model and the estimation of the sensor accuracy were performed using the K-block cross-validation method. Even for a hidden layer with one neuron, the model approximates the fuzzy entropy with good results and the metric R2~0.5 ÷ 0.8. In a simplified model with one neuron and equal weights in the first layer, the principle of approximation is based on the linear transformation of the average value of the time series into the entropy value. An example of using the chaos sensor on spike train of action potential recordings from the L5 dorsal rootlet of rat is provided. The bio-inspired chaos sensor model based on an ensemble of neurons is able to dynamically track the chaotic behavior of a spike signal and transmit this information to other parts of the neurodynamic model for further processing. The study will be useful for specialists in the field of computational neuroscience, and also to create humanoid and animal robots, and bio-robots with limited resources.

Representation of single neuron dynamics using 1-D and 2-D Discrete dynamical systems.

Biological neurons are typically modeled using the Hodgkin-Huxley formalism, which requires significant computational power to simulate. However, since realistic neural network models require thousands of synaptically coupled neurons, a faster approach is needed. Discrete dynamical systems are promising alternatives to continuous models, as they can simulate neuron activity in far fewer steps. Many existing discrete models are based on Poincaré-map-like approaches, which trace periodic activity at a cross section of the cycle. However, this approach is limited to periodic solutions. Biological neurons have many key properties beyond periodicity, such as the minimum applied current required for a resting cell to generate an action potential. To address these properties, we propose a discrete dynamical system model of a biological neuron that incorporates the threshold dynamics of the Hodgkin-Huxley model, the logarithmic relationship between applied current and frequency, modifications to relaxation oscillators, and spike-frequency adaptation in response to modulatory hyperpolarizing currents. It is important to note that several critical parameters are transferred from the continuous model to our proposed discrete dynamical system. These parameters include the membrane capacitance, leak conductance, and maximum conductance values for sodium and potassium ion channels, which are essential for accurately simulating the behavior of biological neurons. By incorporating these parameters into our model, we can ensure that it closely approximates the continuous model's behavior, while also offering a more computationally efficient alternative for simulating neural networks.

Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation.

To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.

Adaptive closed-loop paradigm of electrophysiology for neuron models.

The traditional electrophysiological experiments based on an open-loop paradigm are relatively complicated and limited when facing an individual neuron with uncertain nonlinear factors. Emerging neural technologies enable tremendous growth in experimental data leading to the curse of high-dimensional data, which obstructs the mechanism exploration of spiking activities in the neurons. In this work, we propose an adaptive closed-loop electrophysiology simulation experimental paradigm based on a Radial Basis Function neural network and a highly nonlinear unscented Kalman filter. On account of the complex nonlinear dynamic characteristics of the real neurons, the proposed simulation experimental paradigm could fit the unknown neuron models with different channel parameters and different structures (i.e. single or multiple compartments), and further compute the injected stimulus in time according to the arbitrary desired spiking activities of the neurons. However, the hidden electrophysiological states of the neurons are difficult to be measured directly. Thus, an extra Unscented Kalman filter modular is incorporated in the closed-loop electrophysiology experimental paradigm. The numerical results and theoretical analyses demonstrate that the proposed adaptive closed-loop electrophysiology simulation experimental paradigm achieves desired spiking activities arbitrarily and the hidden dynamics of the neurons are visualized by the unscented Kalman filter modular. The proposed adaptive closed-loop simulation experimental paradigm can avoid the inefficiency of data at increasingly greater scales and enhance the scalability of electrophysiological experiments, thus speeding up the discovery cycle on neuroscience.

Prediction of PM2.5 time series by seasonal trend decomposition-based dendritic neuron model.

The rapid industrial development in the human society has brought about the air pollution, which seriously affects human health. PM2.5 concentration is one of the main factors causing the air pollution. To accurately predict PM2.5 microns, we propose a dendritic neuron model (DNM) trained by an improved state-of-matter heuristic algorithm (DSMS) based on STL-LOESS, namely DS-DNM. Firstly, DS-DNM adopts STL-LOESS for the data preprocessing to obtain three characteristic quantities from original data: seasonal, trend, and residual components. Then, DNM trained by DSMS predicts the residual values. Finally, three sets of feature quantities are summed to obtain the predicted values. In the performance test experiments, five real-world PM2.5 concentration data are used to test DS-DNM. On the other hand, four training algorithms and seven prediction models were selected for comparison to verify the rationality of the training algorithms and the accuracy of the prediction models, respectively. The experimental results show that DS-DNM has the more competitive performance in PM2.5 concentration prediction problem.

Synchronization and oscillation behaviors of excitatory and inhibitory populations with spike-timing-dependent plasticity.

The effect of synaptic plasticity on the synchronization mechanism of the cerebral cortex has been a hot research topic over the past two decades. There are a great deal of literatures on excitatory pyramidal neurons, but the mechanism of interaction between the inhibitory interneurons is still under exploration. In this study, we consider a complex network consisting of excitatory (E) pyramidal neurons and inhibitory (I) interneurons interacting with chemical synapses through spike-timing-dependent plasticity (STDP). To study the effects of eSTDP and iSTDP on synchronization and oscillation behaviors emerged in an excitatory-inhibitory balanced network, we analyzed three different cases, a small-world network of purely excitatory neurons with eSTDP, a small-world network of purely inhibitory neurons with iSTDP and a small-world network with excitatory-inhibitory balanced neurons. By varying the number of inhibitory interneurons, and that of connected edges in a small-world network, and the coupling strength, these networks exhibit different synchronization and oscillation behaviors. We found that the eSTDP facilitates synchronization effectively, while iSTDP has no significant impact on it. In addition, eSTDP and iSTDP restrict the balance of the excitatory-inhibitory balanced neuronal network together and play a fundamental role in maintaining network stability and synchronization. They also can be used to guide the treatment and further research of neurodegenerative diseases.