Nonlinear dynamic modeling of spike train transformations for hippocampal-cortical prostheses

ReplaceNet: real-time replacement of a biological neural circuit with a hardware-assisted spiking neural network

Recent developments in artificial neural networks and their learning algorithms have enabled new research directions in computer vision, language modeling, and neuroscience. Among various neural network algorithms, spiking neural networks (SNNs) are well-suited for understanding the behavior of biological neural circuits. In this work, we propose to guide the training of a sparse SNN in order to replace a sub-region of a cultured hippocampal network with limited hardware resources. To verify our approach with a realistic experimental setup, we record spikes of cultured hippocampal neurons with a microelectrode array (in vitro). The main focus of this work is to dynamically cut unimportant synapses during SNN training on the fly so that the model can be realized on resource-constrained hardware, e.g., implantable devices. To do so, we adopt a simple STDP learning rule to easily select important synapses that impact the quality of spike timing learning. By combining the STDP rule with online supervised learning, we can precisely predict the spike pattern of the cultured network in real-time. The reduction in the model complexity, i.e., the reduced number of connections, significantly reduces the required hardware resources, which is crucial in developing an implantable chip for the treatment of neurological disorders. In addition to the new learning algorithm, we prototype a sparse SNN hardware on a small FPGA with pipelined execution and parallel computing to verify the possibility of real-time replacement. As a result, we can replace a sub-region of the biological neural circuit within 22 μs using 2.5 × fewer hardware resources, i.e., by allowing 80% sparsity in the SNN model, compared to the fully-connected SNN model. With energy-efficient algorithms and hardware, this work presents an essential step toward real-time neuroprosthetic computation.

A Library of Polymer-based Microelectrode Array Designs for Recording from the Brain of Different Animal Models

Large-scale network recording technology is critical in linking neural activity to behavior. Stable, long-term recordings collected from behaving animals are the foundation for understanding neural dynamics and the plasticity of neural circuits. Penetrating microelectrode arrays (MEAs) can obtain high-resolution neural activity from different brain regions. However, ensuring the longevity of implantable devices and the consistency of neural signals over time remains one big challenge. A potential solution is to use flexible, polymer-based MEAs to minimize the foreign body response and prolong the lifetime of neural interfacing devices. Rodents and nonhuman primates (NHP) are commonly used animal models in neuroscience and neuroengineering studies. Specially designed MEAs that capture morphological features of different animal brains and various brain structures are powerful tools to simultaneously obtain neural activities from multiple brain regions. In this work, we develop a set of prototype designs of polymer MEAs that cover cortical, sub-cortical, and multiple brain regions of rodents and NHP.

Nonlinear dynamical modeling of neural activity using volterra series with GA-enhanced particle swarm optimization algorithm

In order to improve the modeling performance of Volterra sequence for nonlinear neural activity, in this paper, a new optimization algorithm is proposed to identify Volterra sequence parameters. Algorithm combines the advantages of particle swarm optimization (PSO) and genetic algorithm (GA) improve the performance of the identification of nonlinear model parameters from rapidity and accuracy. In the modeling experiments of neural signal data generated by the neural computing model and clinical neural data set in this paper, the proposed algorithm shows its excellent potential in nonlinear neural activity modeling. Compared with PSO and GA, the algorithm can achieve less identification error, and better balance the convergence speed and identification error. Further, we explore the influence of algorithm parameters on identification efficiency, which provides possible guiding significance for parameter setting in practical application of the algorithm.

A Double-Layer Multi-Resolution Classification Model for Decoding Spatiotemporal Patterns of Spikes With Small Sample Size

We build a double-layer, multiple temporal-resolution classification model for decoding single-trial spatiotemporal patterns of spikes. The model takes spiking activities as input signals and binary behavioral or cognitive variables as output signals and represents the input-output mapping with a double-layer ensemble classifier. In the first layer, to solve the underdetermined problem caused by the small sample size and the very high dimensionality of input signals, B-spline functional expansion and L1-regularized logistic classifiers are used to reduce dimensionality and yield sparse model estimations. A wide range of temporal resolutions of neural features is included by using a large number of classifiers with different numbers of B-spline knots. Each classifier serves as a base learner to classify spatiotemporal patterns into the probability of the output label with a single temporal resolution. A bootstrap aggregating strategy is used to reduce the estimation variances of these classifiers. In the second layer, another L1-regularized logistic classifier takes outputs of first-layer classifiers as inputs to generate the final output predictions. This classifier serves as a meta-learner that fuses multiple temporal resolutions to classify spatiotemporal patterns of spikes into binary output labels. We test this decoding model with both synthetic and experimental data recorded from rats and human subjects performing memory-dependent behavioral tasks. Results show that this method can effectively avoid overfitting and yield accurate prediction of output labels with small sample size. The double-layer, multi-resolution classifier consistently outperforms the best single-layer, single-resolution classifier by extracting and utilizing multi-resolution spatiotemporal features of spike patterns in the classification.

Observing cell assemblies from spike train recordings based on the biological basis of synaptic connectivity

Cell assemblies are difficult to observe because they consist of many neurons. We aimed to observe cell assemblies based on biological statistics, such as synaptic connectivity. We developed an estimation method to estimate the activity and synaptic connectivity of cell assemblies from spike trains using mathematical models of individual neurons and cell assemblies. Synaptic transmissions were averaged to generate postsynaptic currents with the same timing and waveform but different amplitudes, as the number of presynaptic neurons was large. We estimated the average synaptic transmission and synaptic connectivity from active cell assemblies based on the stochastic prediction of membrane potentials and verified the estimation ability of the average synaptic transmission and synaptic connectivity using the proposed method on simulated neural activity. Different cell assembly activities evoked by electrical stimuli were correctly sorted into various clusters in experiments using rat cortical neurons cultured on microelectrode arrays. We observed multiple cell assemblies from the spontaneous activity of rat cortical networks on microelectrode arrays, based on the synaptic connectivity patterns estimated by the proposed method. The proposed method was superior to the conventional method for detecting the activity of multiple cell assemblies. Using the proposed method, it is possible to observe multiple cell assemblies based on the biological basis of synaptic connectivity. In summary, we report a novel method to observe cell assemblies from spike train recordings based on the biological basis of synaptic connectivity, rather than merely relying on a statistical method.

Efficient Point-Process Modeling of Spiking Neurons for Neuroprosthesis

Neuroprosthesis refers to implantable medical devices which can replace injured biological functions in the brain. One of the core problems in neuroprosthesis study is to construct a neural signal transformation model from one cortical area to another. Since the brain encodes and transmits information in spike trains, spiking neural network (SNN) can be an ideal choice for neuroprosthesis modeling. This paper proposes a spiking neuron point-process model (SNPM), which receives spike times as input, and is capable of modeling nonlinear interactions between cortical areas. The proposed SNPM can be implemented on neuromorphic chips for low-energy computing, thus has potential for clinical applications. Experiments show that SNPM can accurately reconstruct functional relationships from PMd (dorsal premotor cortex) to M1 (primary motor cortex) areas.

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.

A sparse multiscale nonlinear autoregressive model for seizure prediction

Objectives.Accurate seizure prediction is highly desirable for medical interventions such as responsive electrical stimulation. We aim to develop a classification model that can predict seizures by identifying preictal states, i.e. the precursor of a seizure, based on multi-channel intracranial electroencephalography (iEEG) signals.Approach.A two-level sparse multiscale classification model was developed to classify interictal and preictal states from iEEG data. In the first level, short time-scale linear dynamical features were extracted as autoregressive (AR) model coefficients; arbitrary (usually long) time-scale linear and nonlinear dynamical features were extracted as Laguerre-Volterra AR model coefficients; root-mean-square error of model prediction was used as a feature representing model unpredictability. In the second level, all features were fed into a sparse classifier to discriminate the iEEG data between interictal and preictal states.Main results. The two-level model can accurately classify seizure states using iEEG data recorded from ten canine and human subjects. Adding arbitrary (usually long) time-scale and nonlinear features significantly improves model performance compared with the conventional AR modeling approach. There is a high degree of variability in the types of features contributing to seizure prediction across different subjects.Significance. This study suggests that seizure generation may involve distinct linear/nonlinear dynamical processes caused by different underlying neurobiological mechanisms. It is necessary to build patient-specific classification models with a wide range of dynamical features.

Stimulation and Recording of the Hippocampus Using the Same Pt-Ir Coated Microelectrodes

Same-electrode stimulation and recording with high spatial resolution, signal quality, and power efficiency is highly desirable in neuroscience and neural engineering. High spatial resolution and signal-to-noise ratio is necessary for obtaining unitary activities and delivering focal stimulations. Power efficiency is critical for battery-operated implantable neural interfaces. This study demonstrates the capability of recording single units as well as evoked potentials in response to a wide range of electrochemically safe stimulation pulses through high-resolution microelectrodes coated with co-deposition of Pt-Ir. It also compares signal-to-noise ratio, single unit activity, and power efficiencies between Pt-Ir coated and uncoated microelectrodes. To enable stimulation and recording with the same microelectrodes, microelectrode arrays were treated with electrodeposited platinum-iridium coating (EPIC) and tested in the CA1 cell body layer of rat hippocampi. The electrodes' ability to (1) inject a large range of electrochemically reversable stimulation pulses to the tissue, and (2) record evoked potentials and single unit activities were quantitively assessed over an acute time period. Compared to uncoated electrodes, EPIC electrodes recorded signals with higher signal-to-noise ratios (coated: 9.77 ± 1.95 dB; uncoated: 1.95 ± 0.40 dB) and generated lower voltages (coated: 100 mV; uncoated: 650 mV) for a given stimulus (5 μA). The improved performance corresponded to lower energy consumptions and electrochemically safe stimulation above 5 μA (>0.38 mC/cm2), which enabled elicitation of field excitatory post synaptic potentials and population spikes. Spontaneous single unit activities were also modulated by varying stimulation intensities and monitored through the same electrodes. This work represents an example of stimulation and recording single unit activities from the same microelectrode, which provides a powerful tool for monitoring and manipulating neural circuits at the single neuron level.

Validation of a Convolutional Neural Network Model for Spike Transformation Using a Generalized Linear Model

Identification of causal relationships of neural activity is one of the most important problems in neuroscience and neural engineering. We show that a novel deep learning approach using a convolutional neural network to model output neural spike activity from input neural spike activity is able to achieve high correlation between the predicted probability of spiking in the output neuron and the true probability of spiking in the output neuron for data generated with a generalized linear model. The convolutional neural network is also able to recover the true model variables (kernels) used to generate the probability of spiking in the output neuron. Based on the convolutional neural network model's validation via a generalized linear model, future work will include validation with non-linear models that use higher-order kernels.

Binless Kernel Machine: Modeling Spike Train Transformation for Cognitive Neural Prostheses

Modeling spike train transformation among brain regions helps in designing a cognitive neural prosthesis that restores lost cognitive functions. Various methods analyze the nonlinear dynamic spike train transformation between two cortical areas with low computational eficiency. The application of a real-time neural prosthesis requires computational eficiency, performance stability, and better interpretation of the neural firing patterns that modulate target spike generation. We propose the binless kernel machine in the point-process framework to describe nonlinear dynamic spike train transformations. Our approach embeds the binless kernel to eficiently capture the feedforward dynamics of spike trains and maps the input spike timings into reproducing kernel Hilbert space (RKHS). An inhomogeneous Bernoulli process is designed to combine with a kernel logistic regression that operates on the binless kernel to generate an output spike train as a point process. Weights of the proposed model are estimated by maximizing the log likelihood of output spike trains in RKHS, which allows a global-optimal solution. To reduce computational complexity, we design a streaming-based clustering algorithm to extract typical and important spike train features. The cluster centers and their weights enable the visualization of the important input spike train patterns that motivate or inhibit output neuron firing. We test the proposed model on both synthetic data and real spike train data recorded from the dorsal premotor cortex and the primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaling Kolmogorov-Smirnov tests. Our model outperforms the existing methods with higher stability regardless of weight initialization and demonstrates higher eficiency in analyzing neural patterns from spike timing with less historical input (50%). Meanwhile, the typical spike train patterns selected according to weights are validated to encode output spike from the spike train of single-input neuron and the interaction of two input neurons.

Accelerating Estimation of a Multi-Input Multi-Output Model of the Hippocampus with a Parallel Computing Strategy

To build hippocampal memory prosthesis for restoring memory functions, we previously developed and implemented a multi-input multi-output (MIMO) nonlinear dynamic model of the hippocampus. This model can successfully predict hippocampal output spike activities based on input spike activities, and thus be used to drive microstimulation to bypass the damaged hippocampal region. Building such a MIMO model involves estimations of a large number of model coefficients, which typically takes hundreds of hours using a single personal computer. In practice, however, due to the requirement of medical care and clinical trials, the modeling processes must be completed within 72 hours after the recording, so that models can be used to drive stimulations. To solve this problem, we utilized a parallelization strategy to divide the whole MIMO model computation involving iterative estimation and optimization into independent computing tasks that can be performed simultaneously in multiple computer nodes. Such a strategy was implemented on the high-performance computing cluster at the University of Southern California. It reduced the model estimation time to tens of hours and thus allowed us to complete the modeling process within the required time frame to further test model-driven electrical stimulation for the hippocampal memory prosthesis.

Nonlinear dynamics based machine learning: Utilizing dynamics-based flexibility of nonlinear circuits to implement different functions

The core element of machine learning is a flexible, universal function approximator that can be trained and fit into the data. One of the main challenges in modern machine learning is to understand the role of nonlinearity and complexity in these universal function approximators. In this research, we focus on nonlinear complex systems, and show their capability in representation and learning of different functions. Complex nonlinear dynamics and chaos naturally yield an almost infinite diversity of dynamical behaviors and functions. Physical, biological and engineered systems can utilize this diversity to implement adaptive, robust behaviors and operations. A nonlinear dynamical system can be considered as an embodiment of a collection of different possible behaviors or functions, from which different behaviors or functions can be chosen as a response to different conditions or problems. This process of selection can be manual in the sense that one can manually pick and choose the right function through directly setting parameters. Alternatively, we can automate the process and allow the system itself learn how to do it. This creates an approach to machine learning, wherein the nonlinear dynamics represents and embodies different possible functions, and it learns through training how to pick the right function from this function space. We report on how we utilized nonlinear dynamics and chaos to design and fabricate nonlinear dynamics based, morphable hardware in silicon as a physical embodiment for different possible functions. We demonstrate how this flexible, morphable hardware learns through learning and searching algorithms such as genetic algorithm to implement different desired functions. In this approach, we combine two powerful natural and biological phenomenon, Darwinian evolution and nonlinear dynamics and chaos, as a dynamics-oriented approach to designing intelligent, adaptive systems with applications. Nonlinear dynamics embodies different functions at the hardware level, while an evolutionary method is utilized in order to find the parameters to implement the right function.

A K-Medoids based Point-Process Modeling on Neural Spike Transformation using Binless Kernel

A neural prosthesis is designed to compensate for cognitive functional losses by modeling the information transmission among cortical areas. Existing methods generally build a generalized linear model to approximate the nonlinear transformation among two areas, and use the temporal information of the neural spike with low efficiency. It is essential to efficiently model the nonlinearity embedded in spike generation and transmission for the real-time. This paper proposes a nonlinear point-process model to describe spike-in and spike-out transformation using the theory of reproducing kernel Hilbert space (RKHS) and the binless kernel on spike trains. The binless kernel efficiently maps exact spike timing information to the RKHS to describe nonlinear transformations with global minimum regardless of the weight initialization. A streaming K-medoids algorithm is introduced to select typical and important features in this nonlinear binless kernel for further modeling. We test our model on the nonlinearly generated synthetic neural spike trains, and compare with the existing spike transformation methods, such as Volterra model and staged point-process model. The results show that our model has higher goodness-of-fit evaluated by Kolmogorov-Smirnov test and less variance on the prediction results, which indicates the potential better modeling approach for neural prosthesis application.

A Multi-Channel Asynchronous Neurostimulator With Artifact Suppression for Neural Code-Based Stimulations

A novel neurostimulator for generating neural code-based, precise, asynchronous electrical stimulation pulses is designed, fabricated, and characterized. Through multiplexing, this system can deliver constant current biphasic pulses, with arbitrary temporal patterns, and pulse parameters to 32 electrodes using one pulse generator. The design also features a stimulus artifact suppression (SAS) technique that can be integrated with commercial amplifiers. Using an array of CMOS switches, electrodes are disconnected from recording amplifiers during stimulation, while the input of the recording system is shorted to ground through another CMOS switch to suppress ringing in the recording system. The timing of the switches used to block and suppress the stimulus artifact are crucial and are determined by the electrochemical properties of the electrode. This system allows stimulation and recording from the same electrodes to monitor local field potentials with short latencies from the region of stimulation for achieving feedback control of neural stimulation. In this way, timing between each pulse is controlled by inputs from an external source and stimulus magnitude is controlled by feed-back from neural response from the stimulated tissue. The system was implemented with low-power and compact packaged microchips to constitute an effective, cost-efficient, and miniaturized neurostimulator. The device has been first evaluated in phantom preparations and then tested in hippocampi of behaving rats. Benchtop results demonstrate the capability of the stimulator to generate arbitrary spatio-temporal pattern of stimulation pulses dictated by random number generators (RNGs) to control magnitude and timing between each individual biphasic pulse. In vivo results show that evoked potentials elicited by the neurostimulator can be recorded ∼2 ms after the termination of stimulus pulses from the same electrodes where stimulation pulses are delivered, whereas commercial amplifiers without such an artifact suppression typically result in tens to hundreds of milliseconds recovery period. This neurostimulator design is desirable in a variety of neural interface applications, particularly hippocampal memory prosthesis aiming to restore cognitive functions by reinstating neural code transmissions in the brain.

Multi-Input, Multi-Output Neuronal Mode Network Approach to Modeling the Encoding Dynamics and Functional Connectivity of Neural Systems

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

Policy Approximation in Policy Iteration Approximate Dynamic Programming for Discrete-Time Nonlinear Systems

Policy iteration approximate dynamic programming (DP) is an important algorithm for solving optimal decision and control problems. In this paper, we focus on the problem associated with policy approximation in policy iteration approximate DP for discrete-time nonlinear systems using infinite-horizon undiscounted value functions. Taking policy approximation error into account, we demonstrate asymptotic stability of the control policy under our problem setting, show boundedness of the value function during each policy iteration step, and introduce a new sufficient condition for the value function to converge to a bounded neighborhood of the optimal value function. Aiming for practical implementation of an approximate policy, we consider using Volterra series, which has been extensively covered in controls literature for its good theoretical properties and for its success in practical applications. We illustrate the effectiveness of the main ideas developed in this paper using several examples including a practical problem of excitation control of a hydrogenerator.

ASIC Implementation of a Nonlinear Dynamical Model for Hippocampal Prosthesis

A hippocampal prosthesis is a very large scale integration (VLSI) biochip that needs to be implanted in the biological brain to solve a cognitive dysfunction. In this letter, we propose a novel low-complexity, small-area, and low-power programmable hippocampal neural network application-specific integrated circuit (ASIC) for a hippocampal prosthesis. It is based on the nonlinear dynamical model of the hippocampus: namely multi-input, multi-output (MIMO)-generalized Laguerre-Volterra model (GLVM). It can realize the real-time prediction of hippocampal neural activity. New hardware architecture, a storage space configuration scheme, low-power convolution, and gaussian random number generator modules are proposed. The ASIC is fabricated in 40 nm technology with a core area of 0.122 mm[Formula: see text] and test power of 84.4 [Formula: see text]W. Compared with the design based on the traditional architecture, experimental results show that the core area of the chip is reduced by 84.94% and the core power is reduced by 24.30%.

Multiple Approaches to the Investigation of Cell Assembly in Memory Research-Present and Future

In this review article we focus on research methodologies for detecting the actual activity of cell assemblies, which are populations of functionally connected neurons that encode information in the brain. We introduce and discuss traditional and novel experimental methods and those currently in development and briefly discuss their advantages and disadvantages for the detection of cell-assembly activity. First, we introduce the electrophysiological method, i.e., multineuronal recording, and review former and recent examples of studies showing models of dynamic coding by cell assemblies in behaving rodents and monkeys. We also discuss how the firing correlation of two neurons reflects the firing synchrony among the numerous surrounding neurons that constitute cell assemblies. Second, we review the recent outstanding studies that used the novel method of optogenetics to show causal relationships between cell-assembly activity and behavioral change. Third, we review the most recently developed method of live-cell imaging, which facilitates the simultaneous observation of firings of a large number of neurons in behaving rodents. Currently, all these available methods have both advantages and disadvantages, and no single measurement method can directly and precisely detect the actual activity of cell assemblies. The best strategy is to combine the available methods and utilize each of their advantages with the technique of operant conditioning of multiple-task behaviors in animals and, if necessary, with brain-machine interface technology to verify the accuracy of neural information detected as cell-assembly activity.

Designing Patient-Specific Optimal Neurostimulation Patterns for Seizure Suppression

Neurostimulation is a promising therapy for abating epileptic seizures. However, it is extremely difficult to identify optimal stimulation patterns experimentally. In this study, human recordings are used to develop a functional 24 neuron network statistical model of hippocampal connectivity and dynamics. Spontaneous seizure-like activity is induced in silico in this reconstructed neuronal network. The network is then used as a testbed to design and validate a wide range of neurostimulation patterns. Commonly used periodic trains were not able to permanently abate seizures at any frequency. A simulated annealing global optimization algorithm was then used to identify an optimal stimulation pattern, which successfully abated 92% of seizures. Finally, in a fully responsive, or closed-loop, neurostimulation paradigm, the optimal stimulation successfully prevented the network from entering the seizure state. We propose that the framework presented here for algorithmically identifying patient-specific neurostimulation patterns can greatly increase the efficacy of neurostimulation devices for seizures.

Evolving Applications, Technological Challenges and Future Opportunities in Neuromodulation: Proceedings of the Fifth Annual Deep Brain Stimulation Think Tank

The annual Deep Brain Stimulation (DBS) Think Tank provides a focal opportunity for a multidisciplinary ensemble of experts in the field of neuromodulation to discuss advancements and forthcoming opportunities and challenges in the field. The proceedings of the fifth Think Tank summarize progress in neuromodulation neurotechnology and techniques for the treatment of a range of neuropsychiatric conditions including Parkinson's disease, dystonia, essential tremor, Tourette syndrome, obsessive compulsive disorder, epilepsy and cognitive, and motor disorders. Each section of this overview of the meeting provides insight to the critical elements of discussion, current challenges, and identified future directions of scientific and technological development and application. The report addresses key issues in developing, and emphasizes major innovations that have occurred during the past year. Specifically, this year's meeting focused on technical developments in DBS, design considerations for DBS electrodes, improved sensors, neuronal signal processing, advancements in development and uses of responsive DBS (closed-loop systems), updates on National Institutes of Health and DARPA DBS programs of the BRAIN initiative, and neuroethical and policy issues arising in and from DBS research and applications in practice.

Glutaminase C overexpression in the brain induces learning deficits, synaptic dysfunctions, and neuroinflammation in mice

Glutaminolysis, a metabolic process that converts glutamine to glutamate, is particularly important for the central nervous system since glutamate is the major transmitter of excitatory synapses. Glutaminase is the mitochondrial enzyme that catalyzes the first step of glutaminolysis. Two genes encode at least four isoforms of glutaminase in humans. Gls1 gene encodes isoforms kidney-type glutaminase (KGA) and glutaminase C (GAC) through alternative splicing, whereas Gls2 gene encodes liver-type glutaminase isoforms. KGA and GAC have been associated with several neurological diseases. However, it remains unclear whether changes in their expressions can directly cause brain abnormalities. Using a transgenic approach, we generated mice that overexpressed GAC in the brain. The resulting transgenic mice had severe impairments in spatial and fear learning compared with littermate controls. The learning deficits were consistent with diminished hippocampal long-term potentiation in the hippocampal slices of the GAC transgenic mice. Furthermore, we found increases in astrocyte and microglia markers, inflammatory factors, and a decrease in synapse marker synaptophysin, suggesting neuroinflammation and synaptic changes in the GAC transgenic mouse brains. In conclusion, these findings provide the first evidence that GAC overexpression in the brain has deleterious effects on learning and synaptic integrity in vivo.

Multi-resolution multi-trial sparse classification model for decoding visual memories from hippocampal spikes in human

To understand how memories are encoded in the hippocampus, we build memory decoding models to classify visual memories based on hippocampal activities in human. Model inputs are spatio-temporal patterns of spikes recorded in the hippocampal CA3 and CA1 regions of epilepsy patients performing a delayed match-to-sample (DMS) task. Model outputs are binary labels indicating categories and features of sample images. To solve the super high-dimensional estimation problem with short data length, we develop a multi-trial, sparse model estimation method utilizing B-spline basis functions with a large range of temporal resolutions and a regularized logistic classifier. Results show that this model can effectively avoid overfitting and provide significant amount of prediction to memory categories and features using very limited number of data points. Stable estimation of sparse classification function matrices for each label can be obtained with this multi-resolution, multi-trial procedure. These classification models can be used not only to predict memory contents, but also to design optimal spatio-temporal patterns for eliciting specific memories in the hippocampus, and thus have important implications to the development of hippocampal memory prostheses.

Mechanism-Based and Input-Output Modeling of the Key Neuronal Connections and Signal Transformations in the CA3-CA1 Regions of the Hippocampus

This letter examines the results of input-output (nonparametric) modeling based on the analysis of data generated by a mechanism-based (parametric) model of CA3-CA1 neuronal connections in the hippocampus. The motivation is to obtain biological insight into the interpretation of such input-output (Volterra-equivalent) models estimated from synthetic data. The insights obtained may be subsequently used to interpretat input-output models extracted from actual experimental data. Specifically, we found that a simplified parametric model may serve as a useful tool to study the signal transformations in the hippocampal CA3-CA1 regions. Input-output modeling of model-based synthetic data show that GABAergic interneurons are responsible for regulating neuronal excitation, controlling the precision of spike timing, and maintaining network oscillations, in a manner consistent with previous studies. The input-output model obtained from real data exhibits intriguing similarities with its synthetic-data counterpart, demonstrating the importance of a dynamic resonance in the system/model response around 2 Hz to 3 Hz. Using the input-output model from real data as a guide, we may be able to amend the parametric model by incorporating more mechanisms in order to yield better-matching input-output model. The approach we present can also be applied to the study of other neural systems and pathways.

Structure Function Revisited: A Simple Tool for Complex Analysis of Neuronal Activity

Neural systems are characterized by their complex dynamics, reflected on signals produced by neurons and neuronal ensembles. This complexity exhibits specific features in health, disease and in different states of consciousness, and can be considered a hallmark of certain neurologic and neuropsychiatric conditions. To measure complexity from neurophysiologic signals, a number of different nonlinear tools of analysis are available. However, not all of these tools are easy to implement, or able to handle clinical data, often obtained in less than ideal conditions in comparison to laboratory or simulated data. Recently, the temporal structure function emerged as a powerful tool for the analysis of complex properties of neuronal activity. The temporal structure function is efficient computationally and it can be robustly estimated from short signals. However, the application of this tool to neuronal data is relatively new, making the interpretation of results difficult. In this methods paper we describe a step by step algorithm for the calculation and characterization of the structure function. We apply this algorithm to oscillatory, random and complex toy signals, and test the effect of added noise. We show that: (1) the mean slope of the structure function is zero in the case of random signals; (2) oscillations are reflected on the shape of the structure function, but they don't modify the mean slope if complex correlations are absent; (3) nonlinear systems produce structure functions with nonzero slope up to a critical point, where the function turns into a plateau. Two characteristic numbers can be extracted to quantify the behavior of the structure function in the case of nonlinear systems: (1). the point where the plateau starts (the inflection point, where the slope change occurs), and (2). the height of the plateau. While the inflection point is related to the scale where correlations weaken, the height of the plateau is related to the noise present in the signal. To exemplify our method we calculate structure functions of neuronal recordings from the basal ganglia of parkinsonian and healthy rats, and draw guidelines for their interpretation in light of the results obtained from our toy signals.

Cannabinoids disrupt memory encoding by functionally isolating hippocampal CA1 from CA3

Much of the research on cannabinoids (CBs) has focused on their effects at the molecular and synaptic level. However, the effects of CBs on the dynamics of neural circuits remains poorly understood. This study aims to disentangle the effects of CBs on the functional dynamics of the hippocampal Schaffer collateral synapse by using data-driven nonparametric modeling. Multi-unit activity was recorded from rats doing an working memory task in control sessions and under the influence of exogenously administered tetrahydrocannabinol (THC), the primary CB found in marijuana. It was found that THC left firing rate unaltered and only slightly reduced theta oscillations. Multivariate autoregressive models, estimated from spontaneous spiking activity, were then used to describe the dynamical transformation from CA3 to CA1. They revealed that THC served to functionally isolate CA1 from CA3 by reducing feedforward excitation and theta information flow. The functional isolation was compensated by increased feedback excitation within CA1, thus leading to unaltered firing rates. Finally, both of these effects were shown to be correlated with memory impairments in the working memory task. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs.

Research into cannabinoids (CBs) over the last several decades has found that they induce a large variety of oftentimes opposing effects on various neuronal receptors and processes. Due to this plethora of effects, disentangling how CBs influence neuronal circuits has proven challenging. This paper contributes to our understanding of the circuit level effects of CBs by using data driven modeling to examine how THC affects the input-output relationship in the Schaffer collateral synapse in the hippocampus. It was found that THC functionally isolated CA1 from CA3 by reducing feedforward excitation and theta information flow while simultaneously increasing feedback excitation within CA1. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs.

A memory efficient implementation scheme of Gauss error function in a Laguerre-Volterra network for neuroprosthetic devices

Cognitive neural prosthesis is a manmade device which can be used to restore or compensate for lost human cognitive modalities. The generalized Laguerre-Volterra (GLV) network serves as a robust mathematical underpinning for the development of such prosthetic instrument. In this paper, a hardware implementation scheme of Gauss error function for the GLV network targeting reconfigurable platforms is reported. Numerical approximations are formulated which transform the computation of nonelementary function into combinational operations of elementary functions, and memory-intensive look-up table (LUT) based approaches can therefore be circumvented. The computational precision can be made adjustable with the utilization of an error compensation scheme, which is proposed based on the experimental observation of the mathematical characteristics of the error trajectory. The precision can be further customizable by exploiting the run-time characteristics of the reconfigurable system. Compared to the polynomial expansion based implementation scheme, the utilization of slice LUTs, occupied slices, and DSP48E1s on a Xilinx XC6VLX240T field-programmable gate array has decreased by 94.2%, 94.1%, and 90.0%, respectively. While compared to the look-up table based scheme, 1.0×10¹⁷ bits of storage can be spared under the maximum allowable error of 1.0×10^-3. The proposed implementation scheme can be employed in the study of large-scale neural ensemble activity and in the design and development of neural prosthetic device.

Effective connectivity matrix for neural ensembles

In this paper, we present an efficient framework to study the directional interactions within the multiple-input multiple-output (MIMO) biological neural network from spiketrain data. We used an efficient generalized linear model (GLM) with Laguerre basis functions to model a MIMO neural system, and developed an Effective Connectivity Matrix (ECM) to visualize excitatory and inhibitory connections within the neural network. A new causality representation was developed based on system dynamics. Statistical test was applied to identify the significance of the measured causality. We tested ECM on both common-input model and random networks. The results showed that ECM could (1) solve the common-input problem; (3) recover the causality among random neural networks with different connection probabilities and sizes of networks; and (3) identify the excitatory and inhibitory connections among neuronal populations accurately.

Decoding memory features from hippocampal spiking activities using sparse classification models

To understand how memory information is encoded in the hippocampus, we build classification models to decode memory features from hippocampal CA3 and CA1 spatio-temporal patterns of spikes recorded from epilepsy patients performing a memory-dependent delayed match-to-sample task. The classification model consists of a set of B-spline basis functions for extracting memory features from the spike patterns, and a sparse logistic regression classifier for generating binary categorical output of memory features. Results show that classification models can extract significant amount of memory information with respects to types of memory tasks and categories of sample images used in the task, despite the high level of variability in prediction accuracy due to the small sample size. These results support the hypothesis that memories are encoded in the hippocampal activities and have important implication to the development of hippocampal memory prostheses.

Monte Carlo validation of spike-timing-dependent plasticity identification from spiking activity

As increasingly complex non-stationary models become possible to be identified from neural data, rigorous validation approaches must be developed to rule out overfitting and the potential to identify features by chance. Specifically, identification of spike-timing-dependent plasticity (STDP) from recorded spontaneous in vivo spike timing is a potentially powerful tool to quantify activity-dependent plasticity. In previous work, we presented a methodology to perform this STDP identification from spike timing alone and successfully identified a generative model. Validation was straightforward with the generative model because the underlying model was known, but becomes challenging when applied to experimental data. Here, we introduce a set of null hypothesis tests that can be performed with Monte Carlo (MC) simulations of null models to rule out cases of overfitting with experimental data. We demonstrate the identification of these null models and null hypothesis testing on a generative model in two test cases, one with and one without overfitting. Importantly, we show that it is possible to distinguish an identified STDP rule from a null case where there are similar weight fluctuations which are activity-independent. With the development of the null hypothesis tests described here, STDP identification can be effectively applied to experimental data recordings.

Reconstruction of neural network topology using spike train data: Small-world features of hippocampal network

As the amount of experimental data made publicly accessible has gradually increased in recent years, it is now possible to reconsider many of the longstanding questions in neuroscience. In this paper, we present an efficient frame-work for reconstructing the functional connectivity from the spike train data curated from the Collaborative Research in Computational Neuroscience (CRCNS) program. We used a modified generalized linear model (GLM) framework with L1 norm penalty to investigate 10 datasets. These datasets contain spike train data collected from the hippocampal region of rats performing various tasks. Analysis of the reconstructed network showed that the neural network in the hippocampal region of well-trained rats demonstrated significant small-world features.

Sparse Large-Scale Nonlinear Dynamical Modeling of Human Hippocampus for Memory Prostheses

In order to build hippocampal prostheses for restoring memory functions, we build sparse multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from hippocampal CA3 and CA1 regions of epileptic patients performing a variety of memory-dependent delayed match-to-sample (DMS) tasks. Using CA3 and CA1 spike trains as inputs and outputs respectively, sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the CA3-CA1 spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains during multiple memory events, e.g., sample presentation, sample response, match presentation and match response, of the DMS task, and thus will serve as the computational basis of human hippocampal memory prostheses.

Identification of Stable Spike-Timing-Dependent Plasticity from Spiking Activity with Generalized Multilinear Modeling

Characterization of long-term activity-dependent plasticity from behaviorally driven spiking activity is important for understanding the underlying mechanisms of learning and memory. In this letter, we present a computational framework for quantifying spike-timing-dependent plasticity (STDP) during behavior by identifying a functional plasticity rule solely from spiking activity. First, we formulate a flexible point-process spiking neuron model structure with STDP, which includes functions that characterize the stationary and plastic properties of the neuron. The STDP model includes a novel function for prolonged plasticity induction, as well as a more typical function for synaptic weight change based on the relative timing of input-output spike pairs. Consideration for system stability is incorporated with weight-dependent synaptic modification. Next, we formalize an estimation technique using a generalized multilinear model (GMLM) structure with basis function expansion. The weight-dependent synaptic modification adds a nonlinearity to the model, which is addressed with an iterative unconstrained optimization approach. Finally, we demonstrate successful model estimation on simulated spiking data and show that all model functions can be estimated accurately with this method across a variety of simulation parameters, such as number of inputs, output firing rate, input firing type, and simulation time. Since this approach requires only naturally generated spikes, it can be readily applied to behaving animal studies to characterize the underlying mechanisms of learning and memory.

Implementing spiking neuron model and spike-timing-dependent plasticity with generalized Laguerre-Volterra models

To perform large-scale simulations of the brain or build biologically-inspired cognitive architectures, it is essential to have a succinct and flexible model of spiking neurons. The model should be able to capture the nonlinear dynamical properties of various types of neurons and the nonstationary properties such as the spike-timing-dependent plasticity (STDP). In this paper, we propose a generalized Laguerre-Volterra modeling approach for such a task. Due to its built-in nonlinear dynamical terms, the generalized Laguerre-Volterra model (GLVM) can capture various biological processes/mechanisms. Using Laguerre expansion of Volterra kernel technique, the model is fully represented with a small set of coefficients. The calculation of the model variables can be expressed recursively based on only the current and the one-step-before values and thus can be performed efficiently. In addition, we show that, using the same methodology, STDP can be implemented as a specific form of second-order Volterra kernel describing the causal relationship between pairs of input-output spikes and the changes of the feedforward kernels in the GLVMs.

A cognitive prosthesis for memory facilitation by closed-loop functional ensemble stimulation of hippocampal neurons in primate brain

Very productive collaborative investigations characterized how multineuron hippocampal ensembles recorded in nonhuman primates (NHPs) encode short-term memory necessary for successful performance in a delayed match to sample (DMS) task and utilized that information to devise a unique nonlinear multi-input multi-output (MIMO) memory prosthesis device to enhance short-term memory in real-time during task performance. Investigations have characterized how the hippocampus in primate brain encodes information in a multi-item, rule-controlled, delayed match to sample (DMS) task. The MIMO model was applied via closed loop feedback micro-current stimulation during the task via conformal electrode arrays and enhanced performance of the complex memory requirements. These findings clearly indicate detection of a means by which the hippocampus encodes information and transmits this information to other brain regions involved in memory processing. By employing the nonlinear dynamic multi-input/multi-output (MIMO) model, developed and adapted to hippocampal neural ensemble firing patterns derived from simultaneous recorded multi-neuron CA1 and CA3 activity, it was possible to extract information encoded in the Sample phase of DMS trials that was necessary for successful performance in the subsequent Match phase of the task. The extension of this MIMO model to online delivery of electrical stimulation patterns to the same recording loci that exhibited successful CA1 firing in the DMS Sample Phase provided the means to increase task performance on a trial-by-trial basis. Increased utility of the MIMO model as a memory prosthesis was exhibited by the demonstration of cumulative increases in DMS task performance with repeated MIMO stimulation over many sessions. These results, reported below in this article, provide the necessary demonstrations to further the feasibility of the MIMO model as a memory prosthesis to recover and/or enhance encoding of cognitive information in humans with memory disruptions resulting from brain injury, disease or aging.

An Asynchronous Recurrent Network of Cellular Automaton-Based Neurons and Its Reproduction of Spiking Neural Network Activities

Modeling and implementation approaches for the reproduction of input-output relationships in biological nervous tissues contribute to the development of engineering and clinical applications. However, because of high nonlinearity, the traditional modeling and implementation approaches encounter difficulties in terms of generalization ability (i.e., performance when reproducing an unknown data set) and computational resources (i.e., computation time and circuit elements). To overcome these difficulties, asynchronous cellular automaton-based neuron (ACAN) models, which are described as special kinds of cellular automata that can be implemented as small asynchronous sequential logic circuits have been proposed. This paper presents a novel type of such ACAN and a theoretical analysis of its excitability. This paper also presents a novel network of such neurons, which can mimic input-output relationships of biological and nonlinear ordinary differential equation model neural networks. Numerical analyses confirm that the presented network has a higher generalization ability than other major modeling and implementation approaches. In addition, Field-Programmable Gate Array-implementations confirm that the presented network requires lower computational resources.

Evaluating the Small-World-Ness of a Sampled Network: Functional Connectivity of Entorhinal-Hippocampal Circuitry

The amount of publicly accessible experimental data has gradually increased in recent years, which makes it possible to reconsider many longstanding questions in neuroscience. In this paper, an efficient framework is presented for reconstructing functional connectivity using experimental spike-train data. A modified generalized linear model (GLM) with L1-norm penalty was used to investigate 10 datasets. These datasets contain spike-train data collected from the entorhinal-hippocampal region in the brains of rats performing different tasks. The analysis shows that entorhinal-hippocampal network of well-trained rats demonstrated significant small-world features. It is found that the connectivity structure generated by distance-dependent models is responsible for the observed small-world features of the reconstructed networks. The models are utilized to simulate a subset of units recorded from a large biological neural network using multiple electrodes. Two metrics for quantifying the small-world-ness both suggest that the reconstructed network from the sampled nodes estimates a more prominent small-world-ness feature than that of the original unknown network when the number of recorded neurons is small. Finally, this study shows that it is feasible to adjust the estimated small-world-ness results based on the number of neurons recorded to provide a more accurate reference of the network property.

Estimation of a large-scale generalized Volterra model for neural ensembles with group lasso and local coordinate descent

Estimation of neural models based on observed spike timing faces challenges as the amount of recorded units increases, especially when identifying detailed model features. Given that neural regions are generally sparsely connected, input selection is a critical step in model estimation but oftentimes computationally and theoretically challenging. In this paper, we detail an efficient methodology for estimating a sparse, nonlinear dynamical multiple-input, single-output model (MISO) applicable to large-scale (n > 50) single-unit recorded activity. The main contribution of this paper is the complete implementation of a principled group-lasso and local coordinate descent (LCD) algorithm into a generalized Volterra model (GVM) framework to achieve efficient sparse model estimation. Input selection is achieved with group-lasso by simultaneously selecting groups of parameters that are associated with each input. LCD yields efficient computation as the amount of inputs and parameters increase. We investigate and validate the performance of this estimation procedure with the application to a 64 input simulated model.

Understanding spike-triggered covariance using Wiener theory for receptive field identification

Receptive field identification is a vital problem in sensory neurophysiology and vision. Much research has been done in identifying the receptive fields of nonlinear neurons whose firing rate is determined by the nonlinear interactions of a small number of linear filters. Despite more advanced methods that have been proposed, spike-triggered covariance (STC) continues to be the most widely used method in such situations due to its simplicity and intuitiveness. Although the connection between STC and Wiener/Volterra kernels has often been mentioned in the literature, this relationship has never been explicitly derived. Here we derive this relationship and show that the STC matrix is actually a modified version of the second-order Wiener kernel, which incorporates the input autocorrelation and mixes first- and second-order dynamics. It is then shown how, with little modification of the STC method, the Wiener kernels may be obtained and, from them, the principal dynamic modes, a set of compact and efficient linear filters that essentially combine the spike-triggered average and STC matrix and generalize to systems with both continuous and point-process outputs. Finally, using Wiener theory, we show how these obtained filters may be corrected when they were estimated using correlated inputs. Our correction technique is shown to be superior to those commonly used in the literature for both correlated Gaussian images and natural images.

Hippocampal closed-loop modeling and implications for seizure stimulation design

OBJECTIVE

Traditional hippocampal modeling has focused on the series of feedforward synapses known as the trisynaptic pathway. However, feedback connections from CA1 back to the hippocampus through the entorhinal cortex (EC) actually make the hippocampus a closed-loop system. By constructing a functional closed-loop model of the hippocampus, one may learn how both physiological and epileptic oscillations emerge and design efficient neurostimulation patterns to abate such oscillations.

APPROACH

Point process input-output models where estimated from recorded rodent hippocampal data to describe the nonlinear dynamical transformation from CA3 → CA1, via the schaffer-collateral synapse, and CA1 → CA3 via the EC. Each Volterra-like subsystem was composed of linear dynamics (principal dynamic modes) followed by static nonlinearities. The two subsystems were then wired together to produce the full closed-loop model of the hippocampus.

MAIN RESULTS

Closed-loop connectivity was found to be necessary for the emergence of theta resonances as seen in recorded data, thus validating the model. The model was then used to identify frequency parameters for the design of neurostimulation patterns to abate seizures.

SIGNIFICANCE

Deep-brain stimulation (DBS) is a new and promising therapy for intractable seizures. Currently, there is no efficient way to determine optimal frequency parameters for DBS, or even whether periodic or broadband stimuli are optimal. Data-based computational models have the potential to be used as a testbed for designing optimal DBS patterns for individual patients. However, in order for these models to be successful they must incorporate the complex closed-loop structure of the seizure focus. This study serves as a proof-of-concept of using such models to design efficient personalized DBS patterns for epilepsy.

An Application Specific Instruction Set Processor (ASIP) for Adaptive Filters in Neural Prosthetics

Neural coding is an essential process for neuroprosthetic design, in which adaptive filters have been widely utilized. In a practical application, it is needed to switch between different filters, which could be based on continuous observations or point process, when the neuron models, conditions, or system requirements have changed. As candidates of coding chip for neural prostheses, low-power general purpose processors are not computationally efficient especially for large scale neural population coding. Application specific integrated circuits (ASICs) do not have flexibility to switch between different adaptive filters while the cost for design and fabrication is formidable. In this research work, we explore an application specific instruction set processor (ASIP) for adaptive filters in neural decoding activity. The proposed architecture focuses on efficient computation for the most time-consuming matrix/vector operations among commonly used adaptive filters, being able to provide both flexibility and throughput. Evaluation and implementation results are provided to demonstrate that the proposed ASIP design is area-efficient while being competitive to commercial CPUs in computational performance.

Laguerre-Volterra identification of spike-timing-dependent plasticity from spiking activity: a simulation study

This paper presents a Laguerre-Volterra methodology for identifying a plasticity learning rule from spiking neural data with four components: 1) By analyzing input-output spiking data, the effective contribution of an input on the output firing probability can be quantified with weighted Volterra kernels. 2) The weight of these Volterra kernels can be tracked over time using the stochastic state point processing filtering algorithm (SSPPF) 3) Plasticity system Volterra kernels can be estimated by treating the tracked change in weight over time as the plasticity system output and the spike timing data as the input. 4) Laguerre expansion of all Volterra kernels allows for minimization of open parameters during estimation steps. A single input spiking neuron with Spike-timing-dependent plasticity (STDP) and prolonged STDP induction is simulated. Using the spiking data from this simulation, the amplitude of the STDP learning rule and the time course of the induction is accurately estimated. This framework can be applied to identify plasticity for more complicated plasticity paradigms and is applicable to in vivo data.

An Extended TAM to Explore Behavioural Intention of Consumers to Use M-Commerce

This study proposes a research framework that integrates personal innovativeness, perceived risk, cost and enjoyment with the technology acceptance model (TAM). We used the proposed model to explore the antecedents of consumer behavioural intention (BI) to adopt mobile commerce (m-commerce). Excluding missing answers and invalid questionnaires, 477 valid responses were collected. In addition to confirmatory factor analysis (CFA), we used structural equation modelling (SEM) to examine the relationships among the constructs in the proposed model. Our findings indicated that the younger group (under 30) had lower stickiness to m-commerce. Among the constructs, perceived enjoyment (PE) had the most significant influence on BI, followed by attitude, perceived ease of use (PEOU), perceived usefulness (PU) and perceived risk. Our research results could be used as a guide and reference for m-commerce service providers to improve and operate their services.