Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

Electrical Stimulation Induced Current Distribution in Peripheral Nerves Varies Significantly with the Extent of Nerve Damage: A Computational Study Utilizing Convolutional Neural Network and Realistic Nerve Models

Electrical stimulation of the peripheral nervous system is a promising therapeutic option for several conditions; however, its effects on tissue and the safety of the stimulation remain poorly understood. In order to devise stimulation protocols that enhance therapeutic efficacy without the risk of causing tissue damage, we constructed computational models of peripheral nerve and stimulation cuffs based on extremely high-resolution cross-sectional images of the nerves using the most recent advances in computing power and machine learning techniques. We developed nerve models using nonstimulated (healthy) and over-stimulated (damaged) rat sciatic nerves to explore how nerve damage affects the induced current density distribution. Using our in-house computational, quasi-static, platform, and the Admittance Method (AM), we estimated the induced current distribution within the nerves and compared it for healthy and damaged nerves. We also estimated the extent of localized cell damage in both healthy and damaged nerve samples. When the nerve is damaged, as demonstrated principally by the decreased nerve fiber packing, the current penetrates deeper into the over-stimulated nerve than in the healthy sample. As safety limits for electrical stimulation of peripheral nerves still refer to the Shannon criterion to distinguish between safe and unsafe stimulation, the capability this work demonstrated is an important step toward the development of safety criteria that are specific to peripheral nerve and make use of the latest advances in computational bioelectromagnetics and machine learning, such as Python-based AM and CNN-based nerve image segmentation.

A realistic morpho-anatomical connection strategy for modelling full-scale point-neuron microcircuits

The modeling of extended microcircuits is emerging as an effective tool to simulate the neurophysiological correlates of brain activity and to investigate brain dysfunctions. However, for specific networks, a realistic modeling approach based on the combination of available physiological, morphological and anatomical data is still an open issue. One of the main problems in the generation of realistic networks lies in the strategy adopted to build network connectivity. Here we propose a method to implement a neuronal network at single cell resolution by using the geometrical probability volumes associated with pre- and postsynaptic neurites. This allows us to build a network with plausible connectivity properties without the explicit use of computationally intensive touch detection algorithms using full 3D neuron reconstructions. The method has been benchmarked for the mouse hippocampus CA1 area, and the results show that this approach is able to generate full-scale brain networks at single cell resolution that are in good agreement with experimental findings. This geometric reconstruction of axonal and dendritic occupancy, by effectively reflecting morphological and anatomical constraints, could be integrated into structured simulators generating entire circuits of different brain areas facilitating the simulation of different brain regions with realistic models.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Cerebellum involvement in dystonia: insights from a spiking neural network model during associative learning

Dystonia is a neurological movement disorder characterized by twisting and repetitive movements or abnormal fixed postures. This complex brain disease has usually been associated with damages to the Basal Ganglia. However, recent studies point out the potential role of the cerebellum. Indeed, motor learning is impaired in dystonic patients, e.g. during eyeblink classical conditioning, a typical cerebellum-driven associative learning protocol, and rodents with local cerebellar damages exhibit dystonic movements. Alterations in the olivocerebellar circuit connectivity have been identified as a potential neural substrate of dystonia. Here, we investigated this hypothesis through simulations of eyeblink conditioning driven by a realistic spiking model of the cerebellum. The pathological model was generated by decreasing the signal transmission from the Inferior Olive to cerebellar cortex, as observed in animal experiments. The model was able to reproduce a reduced acquisition of eyeblink motor responses, with also an unproper timing. Indeed, this pathway is fundamental to drive cerebellar cortical plasticity, which is the basis of cerebellum-driven motor learning. Exploring different levels of damage, the model predicted the possible amount of underlying impairment associated with the misbehavior observed in patients. Simulations of other debated lesions reported in mouse models of dystonia will be run to investigate the cerebellar involvement in different types of dystonia. Indeed, the eyeblink conditioning phenotype could be used to discriminate between them, identifying specific deficits in the generation of motor responses. Future studies will also include simulations of pharmacological or deep brain stimulation treatments targeting the cerebellum, to predict their impact in improving symptoms.

Localization of long-term synaptic plasticity defects in cerebellar circuits using optokinetic reflex learning profile

Objective.Functional maps of the central nervous system attribute the coordination and control of many body movements directly or indirectly to the cerebellum. Despite this general picture, there is little information on the function of cerebellar neural components at the circuit level. The presence of multiple synaptic junctions and the synergistic action of different types of plasticity make it virtually difficult to determine the distinct contribution of cerebellar neural processes to behavioral manifestations. In this study, investigating the effect of long-term synaptic changes on cerebellar motor learning, we intend to provide quantitative criteria for localizing defects in the major forms of synaptic plasticity in the cerebellum.Approach.To this end, we develop a firing rate model of the cerebellar circuits to simulate learning of optokinetic reflex (OKR), one of the most well-known cerebellar-dependent motor tasks. In the following, by comparing the simulated OKR learning profile for normal and pathosynaptic conditions, we extract the learning features affected by long-term plasticity disorders. Next, conducting simulation with different massed (continuous with no rest) and spaced (interleaved with rest periods) learning paradigms, we estimate the detrimental impact of plasticity defects at corticonuclear synapses on short- and long-term motor memory.Main results.Our computational approach predicts a correlation between location and grade of the defect with some learning factors such as the rate of formation and retention of motor memory, baseline performance, and even cerebellar motor reserve capacity. Further, spacing analysis reveal the dependence of learning paradigm efficiency on the spatiotemporal characteristic of defect in the network. Indeed, defects in cortical memory formation and nuclear memory consolidation mainly harm massed and spaced learning, respectively. This result is used to design a differential assay for identifying the faulty phases of cerebellar learning.Significance.The proposed computational framework can help develop neural-screening systems and prepare meso-scale functional maps of the cerebellar circuits.

Cerebellum Involvement in Dystonia During Associative Motor Learning: Insights From a Data-Driven Spiking Network Model

Dystonia is a movement disorder characterized by sustained or intermittent muscle contractions causing abnormal, often repetitive movements, postures, or both. Although dystonia is traditionally associated with basal ganglia dysfunction, recent evidence has been pointing to a role of the cerebellum, a brain area involved in motor control and learning. Cerebellar abnormalities have been correlated with dystonia but their potential causative role remains elusive. Here, we simulated the cerebellar input-output relationship with high-resolution computational modeling. We used a data-driven cerebellar Spiking Neural Network and simulated a cerebellum-driven associative learning task, Eye-Blink Classical Conditioning (EBCC), which is characteristically altered in relation to cerebellar lesions in several pathologies. In control simulations, input stimuli entrained characteristic network dynamics and induced synaptic plasticity along task repetitions, causing a progressive spike suppression in Purkinje cells with consequent facilitation of deep cerebellar nuclei cells. These neuronal processes caused a progressive acquisition of eyelid Conditioned Responses (CRs). Then, we modified structural or functional local neural features in the network reproducing alterations reported in dystonic mice. Either reduced olivocerebellar input or aberrant Purkinje cell burst-firing resulted in abnormal learning curves imitating the dysfunctional EBCC motor responses (in terms of CR amount and timing) of dystonic mice. These behavioral deficits might be due to altered temporal processing of sensorimotor information and uncoordinated control of muscle contractions. Conversely, an imbalance of excitatory and inhibitory synaptic densities on Purkinje cells did not reflect into significant EBCC deficit. The present work suggests that only certain types of alterations, including reduced olivocerebellar input and aberrant PC burst-firing, are compatible with the EBCC changes observed in dystonia, indicating that some cerebellar lesions can have a causative role in the pathogenesis of symptoms.

Cortico-Cerebellar Hyper-Connections and Reduced Purkinje Cells Behind Abnormal Eyeblink Conditioning in a Computational Model of Autism Spectrum Disorder

Empirical evidence suggests that children with autism spectrum disorder (ASD) show abnormal behavior during delay eyeblink conditioning. They show a higher conditioned response learning rate and earlier peak latency of the conditioned response signal. The neuronal mechanisms underlying this autistic behavioral phenotype are still unclear. Here, we use a physiologically constrained spiking neuron model of the cerebellar-cortical system to investigate which features are critical to explaining atypical learning in ASD. Significantly, the computer simulations run with the model suggest that the higher conditioned responses learning rate mainly depends on the reduced number of Purkinje cells. In contrast, the earlier peak latency mainly depends on the hyper-connections of the cerebellum with sensory and motor cortex. Notably, the model has been validated by reproducing the behavioral data collected from studies with real children. Overall, this article is a starting point to understanding the link between the behavioral and neurobiological basis in ASD learning. At the end of the paper, we discuss how this knowledge could be critical for devising new treatments.

ROA: A Rapid Learning Scheme for In-Situ Memristor Networks

Memristors show great promise in neuromorphic computing owing to their high-density integration, fast computing and low-energy consumption. However, the non-ideal update of synaptic weight in memristor devices, including nonlinearity, asymmetry and device variation, still poses challenges to the in-situ learning of memristors, thereby limiting their broad applications. Although the existing offline learning schemes can avoid this problem by transferring the weight optimization process into cloud, it is difficult to adapt to unseen tasks and uncertain environments. Here, we propose a bi-level meta-learning scheme that can alleviate the non-ideal update problem, and achieve fast adaptation and high accuracy, named Rapid One-step Adaption (ROA). By introducing a special regularization constraint and a dynamic learning rate strategy for in-situ learning, the ROA method effectively combines offline pre-training and online rapid one-step adaption. Furthermore, we implemented it on memristor-based neural networks to solve few-shot learning tasks, proving its superiority over the pure offline and online schemes under noisy conditions. This method can solve in-situ learning in non-ideal memristor networks, providing potential applications of on-chip neuromorphic learning and edge computing.

Hysteresis Modeling in Iron-Dominated Magnets Based on a Multi-Layered Narx Neural Network Approach

A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.

Parallel Binary Image Cryptosystem Via Spiking Neural Networks Variants

Due to the inefficiency of multiple binary images encryption, a parallel binary image encryption framework based on the typical variants of spiking neural networks, spiking neural P (SNP) systems is proposed in this paper. More specifically, the two basic units in the proposed image cryptosystem, the permutation unit and the diffusion unit, are designed through SNP systems with multiple channels and polarizations (SNP-MCP systems), and SNP systems with astrocyte-like control (SNP-ALC systems), respectively. Different from the serial computing of the traditional image permutation/diffusion unit, SNP-MCP-based permutation/SNP-ALC-based diffusion unit can realize parallel computing through the parallel use of rules inside the neurons. Theoretical analysis results confirm the high efficiency of the binary image proposed cryptosystem. Security analysis experiments demonstrate the security of the proposed cryptosystem.

Design and Implementation of a Spiking Neural Network with Integrate-and-Fire Neuron Model for Pattern Recognition

In contrast to the previous artificial neural networks (ANNs), spiking neural networks (SNNs) work based on temporal coding approaches. In the proposed SNN, the number of neurons, neuron models, encoding method, and learning algorithm design are described in a correct and pellucid fashion. It is also discussed that optimizing the SNN parameters based on physiology, and maximizing the information they pass leads to a more robust network. In this paper, inspired by the "center-surround" structure of the receptive fields in the retina, and the amount of overlap that they have, a robust SNN is implemented. It is based on the Integrate-and-Fire (IF) neuron model and uses the time-to-first-spike coding to train the network by a newly proposed method. The Iris and MNIST datasets were employed to evaluate the performance of the proposed network whose accuracy, with 60 input neurons, was 96.33% on the Iris dataset. The network was trained in only 45 iterations indicating its reasonable convergence rate. For the MNIST dataset, when the gray level of each pixel was considered as input to the network, 600 input neurons were required, and the accuracy of the network was 90.5%. Next, 14 structural features were used as input. Therefore, the number of input neurons decreased to 210, and accuracy increased up to 95%, meaning that an SNN with fewer input neurons and good skill was implemented. Also, the ABIDE1 dataset is applied to the proposed SNN. Of the 184 data, 79 are used for healthy people and 105 for people with autism. One of the characteristics that can differentiate between these two classes is the entropy of the existing data. Therefore, Shannon entropy is used for feature extraction. Applying these values to the proposed SNN, an accuracy of 84.42% was achieved by only 120 iterations, which is a good result compared to the recent results.

On the Modeling of the Three Types of Non-spiking Neurons of the Caenorhabditis elegans

The nematode Caenorhabditis elegans (C. elegans) is a well-known model organism in neuroscience. The relative simplicity of its nervous system, made up of few hundred neurons, shares some essential features with more sophisticated nervous systems, including the human one. If we are able to fully characterize the nervous system of this organism, we will be one step closer to understanding the mechanisms underlying the behavior of living things. Following a recently conducted electrophysiological survey on different C. elegans neurons, this paper aims at modeling the three non-spiking RIM, AIY and AFD neurons (arbitrarily named with three upper case letters by convention). To date, they represent the three possible forms of non-spiking neuronal responses of the C. elegans. To achieve this objective, we propose a conductance-based neuron model adapted to the electrophysiological features of each neuron. These features are based on current biological research and a series of in-silico experiments which use differential evolution to fit the model to experimental data. From the obtained results, we formulate a series of biological hypotheses regarding currents involved in the neuron dynamics. These models reproduce experimental data with a high degree of accuracy while being biologically consistent with state-of-the-art research.

Quaternion Spiking and Quaternion Quantum Neural Networks: Theory and Applications

Biological evidence shows that there are neural networks specialized for recognition of signals and patterns acting as associative memories. The spiking neural networks are another kind which receive input from a broad range of other brain areas to produce output that selects particular cognitive or motor actions to perform. An important contribution of this work is to consider the geometric processing in the modeling of feed-forward neural networks. Since quaternions are well suited to represent 3D rotations, it is then well justified to extend real-valued neural networks to quaternion-valued neural networks for task of perception and control of robot manipulators. This work presents the quaternion spiking neural networks which are able to control robots, where the examples confirm that these artificial neurons have the capacity to adapt on-line the robot to reach the desired position. Also, we present the quaternionic quantum neural networks for pattern recognition using just one quaternion neuron. In the experimental analysis, we show the excellent performance of both quaternion neural networks.

A Complete Arithmetic Calculator Constructed from Spiking Neural P Systems and its Application to Information Fusion

Several variants of spiking neural P systems (SNPS) have been presented in the literature to perform arithmetic operations. However, each of these variants was designed only for one specific arithmetic operation. In this paper, a complete arithmetic calculator implemented by SNPS is proposed. An application of the proposed calculator to information fusion is also proposed. The information fusion is implemented by integrating the following three elements: (1) an addition and subtraction SNPS already reported in the literature; (2) a modified multiplication and division SNPS; (3) a novel storage SNPS, i.e. a method based on SNPS is introduced to calculate basic probability assignment of an event. This is the first attempt to apply arithmetic operation SNPS to fuse multiple information. The effectiveness of the presented general arithmetic SNPS calculator is verified by means of several examples.

A Basal Ganglia Computational Model to Explain the Paradoxical Sensorial Improvement in the Presence of Huntington's Disease

The basal ganglia (BG) represent a critical center of the nervous system for sensorial discrimination. Although it is known that Huntington's disease (HD) affects this brain area, it still remains unclear how HD patients achieve paradoxical improvement in sensorial discrimination tasks. This paper presents a computational model of the BG including the main nuclei and the typical firing properties of their neurons. The BG model has been embedded within an auditory signal detection task. We have emulated the effect that the altered levels of dopamine and the degree of HD affectation have in information processing at different layers of the BG, and how these aspects shape transient and steady states differently throughout the selection task. By extracting the independent components of the BG activity at different populations, it is evidenced that early and medium stages of HD affectation may enhance transient activity in the striatum and the substantia nigra pars reticulata. These results represent a possible explanation for the paradoxical improvement that HD patients present in discrimination task performance. Thus, this paper provides a novel understanding on how the fast dynamics of the BG network at different layers interact and enable transient states to emerge throughout the successive neuron populations.

Spiking Neural P Systems with Delay on Synapses

Based on the feature and communication of neurons in animal neural systems, spiking neural P systems (SN P systems) were proposed as a kind of powerful computing model. Considering the length of axons and the information transmission speed on synapses, SN P systems with delay on synapses (SNP-DS systems) are proposed in this work. Unlike the traditional SN P systems, where all the postsynaptic neurons receive spikes at the same instant from their presynaptic neuron, the postsynaptic neurons in SNP-DS systems would receive spikes at different instants, depending on the delay time on the synapses connecting them. It is proved that the SNP-DS systems are universal as number generators. Two small universal SNP-DS systems, with standard or extended rules, are constructed to compute functions, using 56 and 36 neurons, respectively. Moreover, a simulator has been provided, in order to check the correctness of these two SNP-DS systems, thus providing an experimental validation of the universality of the systems designed.

How the Cerebellum and Prefrontal Cortex Cooperate During Trace Eyeblinking Conditioning

Several data have demonstrated that during the widely used experimental paradigm for studying associative learning, trace eye blinking conditioning (TEBC), there is a strong interaction between cerebellum and medial prefrontal cortex (mPFC). Despite this evidence, the neural mechanisms underlying this interaction are still not clear. Here, we propose a neurophysiologically plausible computational model to address this issue. The model is constrained on the basis of two critical anatomo-physiological features: (i) the cerebello-cortical organization through two circuits, respectively, targeting M1 and mPFC; (ii) the different timing in the plasticity mechanisms of these parallel circuits produced by the granule cells time sensitivity according to which different subpopulations are active at different moments during conditioned stimuli. The computer simulations run with the model suggest that these features are critical to understand how the cooperation between cerebellum and mPFC supports motor areas during TEBC. In particular, a greater trace interval produces greater plasticity changes at the slow path synapses involving mPFC with respect to plasticity changes at the fast path involving M1. As a consequence, the greater is the trace interval, the stronger is the mPFC involvement. The model has been validated by reproducing data collected through recent real mice experiments.

Temporal Backpropagation for Spiking Neural Networks with One Spike per Neuron

We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with any number of layers. This approach reaches state-of-the-art performance with supervised multi-fully connected layer SNNs: test accuracy of 97.4% for the MNIST dataset, and 99.2% for the Caltech Face/Motorbike dataset. Yet, the neuron model that we use, nonleaky integrate-and-fire, is much simpler than the one used in all previous works. The source codes of the proposed S4NN are publicly available at https://github.com/SRKH/S4NN .

Nonlinear Spiking Neural P Systems

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron’s firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively.

A Cerebellum-Inspired Learning Approach for Adaptive and Anticipatory Control

The cerebellum, which is responsible for motor control and learning, has been suggested to act as a Smith predictor for compensation of time-delays by means of internal forward models. However, insights about how forward model predictions are integrated in the Smith predictor have not yet been unveiled. To fill this gap, a novel bio-inspired modular control architecture that merges a recurrent cerebellar-like loop for adaptive control and a Smith predictor controller is proposed. The goal is to provide accurate anticipatory corrections to the generation of the motor commands in spite of sensory delays and to validate the robustness of the proposed control method to input and physical dynamic changes. The outcome of the proposed architecture with other two control schemes that do not include the Smith control strategy or the cerebellar-like corrections are compared. The results obtained on four sets of experiments confirm that the cerebellum-like circuit provides more effective corrections when only the Smith strategy is adopted and that minor tuning in the parameters, fast adaptation and reproducible configuration are enabled.

Descriptor Selection Improvements for Quantitative Structure-Activity Relationships

Molecular descriptor selection is an essential procedure to improve a predictive quantitative structure–activity relationship (QSAR) model. However, within the QSAR model, there are a number of redundant, noisy and irrelevant descriptors. In this study, we propose a novel descriptor selection framework using self-paced learning (SPL) via sparse logistic regression (LR) with Logsum penalty (SPL-Logsum), which can simultaneously adaptively identify the simple and complex samples and avoid over-fitting. SPL is inspired by the learning process of humans or animals gradually learned from simple and complex samples to train models, and the Logsum penalized LR helps to select a small subset of significant molecular descriptors for improving the QSAR models. Experimental results on some simulations and three public QSAR datasets show that our proposed SPL-Logsum framework outperforms other existing sparse methods regarding the area under the curve, sensitivity, specificity, accuracy, and [Formula: see text]-values.

Reachability Analysis of Neural Masses and Seizure Control Based on Combination Convolutional Neural Network

Epileptic seizures arise from synchronous firing of multiple spatially separated neural masses; therefore, many synchrony measures are used for seizure detection and characterization. However, synchrony measures reflect only the overall interaction strength among populations of neurons but cannot reveal the coupling strengths among individual populations, which is more important for seizure control. The concepts of reachability and reachable cluster were proposed to denote the coupling strengths of a set of neural masses. Here, we describe a seizure control method based on coupling strengths using combination convolutional neural network (CCNN) modeling. The neurophysiologically based neural mass model (NMM), which can bridge signal processing and neurophysiology, was used to simulate the proposed controller. Although the adjacency matrix and reachability matrix could not be identified perfectly, the vast majority of adjacency values were identified, reaching 95.64% using the CCNN with an optimal threshold. For cases of discrete and continuous coupling strengths, the proposed controller maintained the average reachable cluster strengths at about 0.1, indicating effective seizure control.

Response Dynamics in an Olivocerebellar Spiking Neural Network With Non-linear Neuron Properties

Sensorimotor signals are integrated and processed by the cerebellar circuit to predict accurate control of actions. In order to investigate how single neuron dynamics and geometrical modular connectivity affect cerebellar processing, we have built an olivocerebellar Spiking Neural Network (SNN) based on a novel simplification algorithm for single point models (Extended Generalized Leaky Integrate and Fire, EGLIF) capturing essential non-linear neuronal dynamics (e.g., pacemaking, bursting, adaptation, oscillation and resonance). EGLIF models specifically tuned for each neuron type were embedded into an olivocerebellar scaffold reproducing realistic spatial organization and physiological convergence and divergence ratios of connections. In order to emulate the circuit involved in an eye blink response to two associated stimuli, we modeled two adjacent olivocerebellar microcomplexes with a common mossy fiber input but different climbing fiber inputs (either on or off). EGLIF-SNN model simulations revealed the emergence of fundamental response properties in Purkinje cells (burst-pause) and deep nuclei cells (pause-burst) similar to those reported in vivo. The expression of these properties depended on the specific activation of climbing fibers in the microcomplexes and did not emerge with scaffold models using simplified point neurons. This result supports the importance of embedding SNNs with realistic neuronal dynamics and appropriate connectivity and anticipates the scale-up of EGLIF-SNN and the embedding of plasticity rules required to investigate cerebellar functioning at multiple scales.

Neurons with Multiplicative Interactions of Nonlinear Synapses

Neurons are the fundamental units of the brain and nervous system. Developing a good modeling of human neurons is very important not only to neurobiology but also to computer science and many other fields. The McCulloch and Pitts neuron model is the most widely used neuron model, but has long been criticized as being oversimplified in view of properties of real neuron and the computations they perform. On the other hand, it has become widely accepted that dendrites play a key role in the overall computation performed by a neuron. However, the modeling of the dendritic computations and the assignment of the right synapses to the right dendrite remain open problems in the field. Here, we propose a novel dendritic neural model (DNM) that mimics the essence of known nonlinear interaction among inputs to the dendrites. In the model, each input is connected to branches through a distance-dependent nonlinear synapse, and each branch performs a simple multiplication on the inputs. The soma then sums the weighted products from all branches and produces the neuron’s output signal. We show that the rich nonlinear dendritic response and the powerful nonlinear neural computational capability, as well as many known neurobiological phenomena of neurons and dendrites, may be understood and explained by the DNM. Furthermore, we show that the model is capable of learning and developing an internal structure, such as the location of synapses in the dendritic branch and the type of synapses, that is appropriate for a particular task — for example, the linearly nonseparable problem, a real-world benchmark problem — Glass classification and the directional selectivity problem.

An Attention-Based Spiking Neural Network for Unsupervised Spike-Sorting

Bio-inspired computing using artificial spiking neural networks promises performances outperforming currently available computational approaches. Yet, the number of applications of such networks remains limited due to the absence of generic training procedures for complex pattern recognition, which require the design of dedicated architectures for each situation. We developed a spike-timing-dependent plasticity (STDP) spiking neural network (SSN) to address spike-sorting, a central pattern recognition problem in neuroscience. This network is designed to process an extracellular neural signal in an online and unsupervised fashion. The signal stream is continuously fed to the network and processed through several layers to output spike trains matching the truth after a short learning period requiring only few data. The network features an attention mechanism to handle the scarcity of action potential occurrences in the signal, and a threshold adaptation mechanism to handle patterns with different sizes. This method outperforms two existing spike-sorting algorithms at low signal-to-noise ratio (SNR) and can be adapted to process several channels simultaneously in the case of tetrode recordings. Such attention-based STDP network applied to spike-sorting opens perspectives to embed neuromorphic processing of neural data in future brain implants.

Compact Hardware Synthesis of Stochastic Spiking Neural Networks

Spiking neural networks (SNN) are able to emulate real neural behavior with high confidence due to their bio-inspired nature. Many designs have been proposed for the implementation of SNN in hardware, although the realization of high-density and biologically-inspired SNN is currently a complex challenge of high scientific and technical interest. In this work, we propose a compact digital design for the implementation of high-volume SNN that considers the intrinsic stochastic processes present in biological neurons and enables high-density hardware implementation. The proposed stochastic SNN model (SSNN) is compared with previous SSNN models, achieving a higher processing speed. We also show how the proposed model can be scaled to high-volume neural networks trained by using back propagation and applied to a pattern classification task. The proposed model achieves better results compared with other recently-published SNN models configured with unsupervised STDP learning.

The Concept of Transmission Coefficient Among Different Cerebellar Layers: A Computational Tool for Analyzing Motor Learning

High-fidelity regulation of information transmission among cerebellar layers is mainly provided by synaptic plasticity. Therefore, determining the regulatory foundations of synaptic plasticity in the cerebellum and translating them to behavioral output are of great importance. To date, many experimental studies have been carried out in order to clarify the effect of synaptic defects, while targeting a specific signaling pathway in the cerebellar function. However, the contradictory results of these studies at the behavioral level further add to the ambiguity of the problem. Information transmission through firing rate changes in populations of interconnected neurons is one of the most widely accepted principles of neural coding. In this study, while considering the efficacy of synaptic interactions among the cerebellar layers, we propose a firing rate model to realize the concept of transmission coefficient. Thereafter, using a computational approach, we test the effect of different values of transmission coefficient on the gain adaptation of a cerebellar-dependent motor learning task. In conformity with the behavioral data, the proposed model can accurately predict that disruption in different forms of synaptic plasticity does not have the same effect on motor learning. Specifically, impairment in training mechanisms, like in the train-induced LTD in parallel fiber-Purkinje cell synapses, has a significant negative impact on all aspects of learning, including memory formation, transfer, and consolidation, although it does not disrupt basic motor performance. In this regard, the overinduction of parallel fiber-molecular layer interneuron LTP could not prevent motor learning impairment, despite its vital role in preserving the robustness of basic motor performance. In contrast, impairment in plasticity induced by interneurons and background activity of climbing fibers is partly compensable through overinduction of train-induced parallel fiber-Purkinje cell LTD. Additionally, blockade of climbing fiber signaling to the cerebellar cortex, referred to as olivary system lesion, shows the most destructive effect on both motor learning and basic motor performance. Overall, the obtained results from the proposed computational framework are used to provide a map from procedural motor memory formation in the cerebellum. Certainly, the generalization of this concept to other multi-layered networks of the brain requires more physiological and computational researches.

Fluctuation Scaling of Neuronal Firing and Bursting in Spontaneously Active Brain Circuits

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency - regularly firing neurons (RNs) - from 1 to 8Hz while 8% fired in burst with two dominant frequencies - bursting neurons (BNs) - corresponding to the inter-burst (2-6Hz) and intra-burst intervals (20-160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

How Far can Neural Correlations Reduce Uncertainty? Comparison of Information Transmission Rates for Markov and Bernoulli Processes

The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the firing rates of individual spikes (rate code) or by the precise timing of every spike (temporal code)? Here we compare the loss of information due to correlations for these two possible neural codes. The essence of Shannon's definition of information is to combine information with uncertainty: the higher the uncertainty of a given event, the more information is conveyed by that event. Correlations can reduce uncertainty or the amount of information, but by how much? In this paper we address this question by a direct comparison of the information per symbol conveyed by the words coming from a binary Markov source (temporal code) with the information per symbol coming from the corresponding Bernoulli source (uncorrelated, rate code). In a previous paper we found that a crucial role in the relation between information transmission rates (ITRs) and firing rates is played by a parameter s, which is the sum of transition probabilities from the no-spike state to the spike state and vice versa. We found that in this case too a crucial role is played by the same parameter s. We calculated the maximal and minimal bounds of the quotient of ITRs for these sources. Next, making use of the entropy grouping axiom, we determined the loss of information in a Markov source compared with the information in the corresponding Bernoulli source for a given word length. Our results show that in the case of correlated signals the loss of information is relatively small, and thus temporal codes, which are more energetically efficient, can replace rate codes effectively. These results were confirmed by experiments.

Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

Atypical temporal-scale-specific fractal changes in Alzheimer's disease EEG and their relevance to cognitive decline

Recent advances in nonlinear analytic methods for electroencephalography have clarified the reduced complexity of spatiotemporal dynamics in brain activity observed in Alzheimer’s disease (AD). However, there are far fewer studies exploring temporal scale dependent fractal properties in AD, despite the importance of studying the dynamics of brain activity within physiologically relevant frequency ranges. Higuchi’s fractal dimension is a widely used index for evaluating fractality in brain activity, but temporal-scale-specific characteristics are lost due to its requirement of averaging over the entire range of temporal scales. In this study, we adapted Higuchi’s fractal algorithm into a method for investigating temporal-scale-specific fractal properties. We then compared the values of the temporal-scale-specific fractal dimension between healthy control (HC) and AD patient groups. Our data indicate that relative to the HC group, the AD group demonstrated reduced fractality at both slow and fast temporal scales. Moreover, we confirmed that the fractality at fast temporal scales correlates with cognitive decline. These properties might serve as a basis for a useful approach to characterizing temporal neural dynamics in AD or other neurodegenerative disorders.

Dynamic Redistribution of Plasticity in a Cerebellar Spiking Neural Network Reproducing an Associative Learning Task Perturbed by TMS

During natural learning, synaptic plasticity is thought to evolve dynamically and redistribute within and among subcircuits. This process should emerge in plastic neural networks evolving under behavioral feedback and should involve changes distributed across multiple synaptic sites. In eyeblink classical conditioning (EBCC), the cerebellum learns to predict the precise timing between two stimuli, hence EBCC represents an elementary yet meaningful paradigm to investigate the cerebellar network functioning. We have simulated EBCC mechanisms by reconstructing a realistic cerebellar microcircuit model and embedding multiple plasticity rules imitating those revealed experimentally. The model was tuned to fit experimental EBCC human data, estimating the underlying learning time-constants. Learning started rapidly with plastic changes in the cerebellar cortex followed by slower changes in the deep cerebellar nuclei. This process was characterized by differential development of long-term potentiation and depression at individual synapses, with a progressive accumulation of plasticity distributed over the whole network. The experimental data included two EBCC sessions interleaved by a trans-cranial magnetic stimulation (TMS). The experimental and the model response data were not significantly different in each learning phase, and the model goodness-of-fit was [Formula: see text] for all the experimental conditions. The models fitted on TMS data revealed a slowed down re-acquisition (sessions-2) compared to the control condition ([Formula: see text]). The plasticity parameters characterizing each model significantly differ among conditions, and thus mechanistically explain these response changes. Importantly, the model was able to capture the alteration in EBCC consolidation caused by TMS and showed that TMS affected plasticity at cortical synapses thereby altering the fast learning phase. This, secondarily, also affected plasticity in deep cerebellar nuclei altering learning dynamics in the entire sensory-motor loop. This observation reveals dynamic redistribution of changes over the entire network and suggests how TMS affects local circuit computation and memory processing in the cerebellum.

Spiking Neural P Systems with Communication on Request

Spiking Neural [Formula: see text] Systems are Neural System models characterized by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural [Formula: see text] systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these [Formula: see text] systems, a specified number of spikes are consumed and a specified number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron.

[Formula: see text]In the present work, a novel communication strategy among neurons of Spiking Neural [Formula: see text] Systems is proposed. In the resulting models, called Spiking Neural [Formula: see text] Systems with Communication on Request, the spikes are requested from neighboring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural [Formula: see text] systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron).

[Formula: see text]The Spiking Neural [Formula: see text] Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems.