Identification and estimation algorithm for stochastic neural system

An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.     

State-space analysis of time-varying higher-order spike correlation for multiple neural spike train data

Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.     

Spike train metrics

Quantifying similarity and dissimilarity of spike trains is an important requisite for understanding neural codes. Spike metrics constitute a class of approaches to this problem. In contrast to most signal-processing methods, spike metrics operate on time series of all-or-none events, and are, thus, particularly appropriate for extracellularly recorded neural signals. The spike metric approach can be extended to multineuronal recordings, mitigating the 'curse of dimensionality' typically associated with analyses of multivariate data. Spike metrics have been usefully applied to the analysis of neural coding in a variety of systems, including vision, audition, olfaction, taste and electric sense.     

Stimulus dependent neural correlations in the auditory midbrain of the grassfrog (Rana temporaria L.)

Few-unit recordings were obtained using metal microelectrodes. Separation into single-unit spike trains was based on differences in spike amplitude and spike waveform. For that purpose a hardware microprocessor based spike waveform analyser was designed and built. Spikes are filtered by four matched filters and filter outputs at the moments of spike occurrence are read by a computer and used for off-line separation and spike waveform reconstruction. Thirty-one double unit recordings were obtained and correlation between the separated spike trains was determined. After stimulus correction correlation remained in only 8 of the double unit records. It appeared that in most cases this neural correlation was stimulus dependent. Continuous noise stimulation resulted in the strongest neural correlation remaining after correction for stimulus coupling, stimulation with 48 ms duration tonepips presented once per second generally did not result in a significant neural correlation after the correction procedure for stimulus lock. The usefulness of the additive model for neural correlation and the correction procedure based thereupon is discussed.     

Computing Complex Visual Features with Retinal Spike Times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.     

Adjusted regularization of cortical covariance

It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an \(L_{1}\) penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.     

自发和诱发神经放电序列的内在时序特性

运用Fano因子分析法,考察豚鼠听神经单纤维的自发放电序列、小鼠海马CAl区神经元的自发放电序列以及蟾蜍缝匠肌肌梭传入神经的诱发放电序列的时序特性,结果显示自发和诱发放电时间序列均存在Fano因子随计算窗口时间的增大而持续增长的特点,而原始数据的随机重排替代数据则没有这一特性,说明这些神经放电时间序列与一般的随机点过程不同,存在长时程相关性,在时序上具有某种结构特征。进一步的研究表明,这一时序结构特征可以通过将随机产生的一维正态分布序列数据,与神经放电时间序列数据进行跟随排序后而体现,提示这一特征与放电间隔的分布特点无关。     

Fitting of dynamic recurrent neural network models to sensory stimulus-response data

We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Nonlinear principal components analysis of neuronal spike train data

Many recent approaches to decoding neural spike trains depend critically on the assumption that for low-pass filtered spike trains, the temporal structure is optimally represented by a small number of linear projections onto the data. We therefore tested this assumption of linearity by comparing a linear factor analysis technique (principal components analysis) with a nonlinear neural network based method. It is first shown that the nonlinear technique can reliably identify a neuronally plausible nonlinearity in synthetic spike trains. However, when applied to the outputs from primary visual cortical neurons, this method shows no evidence for significant temporal nonlinearities. The implications of this are discussed. Received: 29 November 1996 / Accepted in revised form: 1 July 1997     

A Granger causality measure for point process models of ensemble neural spiking activity

The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the directional interactions between multiple sets of continuous-valued data, but cannot be applied to neural spike train recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood function to relate a neuron's spiking probability to possible covariates, such as its own spiking history and the concurrent activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process data, and has the potential to provide unique physiological insights when applied to neural spike trains.     

Partial correlation analysis for the identification of synaptic connections

In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can be attributed to linear relationships with recorded spike trains from other neurons. As an alternative to the common frequency domain approach based on the partial spectral coherence we propose a new statistic in the time domain. The new scaled partial covariance density provides additional information on the direction and the type, excitatory or inhibitory, of the connectivities. In simulation studies, we investigated the power and limitations of the new statistic. The simulations show that the detectability of various connectivity patterns depends on various parameters such as connectivity strength and background activity. In particular, the detectability decreases with the number of neurons included in the analysis and increases with the recording time. Further, we show that the method can also be used to detect multiple direct connectivities between two neurons. Finally, the methods of this paper are illustrated by an application to neurophysiological data from spinal dorsal horn neurons.     

The refractory periods and threshold potentials of sequential spikes measured by whole-cell recording

Neurons in the central nervous system are thought to program neural language via firing sequential spikes for guiding animal behaviors. The quantitative profiles of spike intrinsic properties are critically important to understand spike programming. We developed approaches with whole-cell recordings to measure the threshold potentials and refractory periods (RPs) of sequential spikes, and to analyze the relationships of these factors with spike timing precision and capacity at the regular-spiking and fast-spiking neurons in cortical slice. The RPs and threshold potentials of sequential spikes at these two groups of neurons are different and are linearly correlated with spike timing precision and capacity. These data suggest that RPs and threshold potentials essentially navigate the spike programming for the precise and loyal encoding of meaningful neural signals. Our study provides the avenues for decoding the spectrum of the neural signals quantitatively.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

Spike-sorting analysis of neural electrical signals evoked by acupuncture based on model

Acupuncturing the Zusanli (ST 36) point with different types of manual acupuncture manipulations (MAs) and different frequencies can evoke a lot of neural response activities in spinal dorsal root neurons. The action potential is the basic unit of communication in the neural response process. With the rapid development of the electrode acquisition technology, we can simultaneously obtain neural electrical signals of multiple neurons in the target area. So it is crucial to extract spike trains of each neuron from raw recorded data. To solve the problem of variability of the spike waveform, this paper adopts a optimization algorithm based on model to improve the wave-cluster algorithm, which can provide higher accuracy and reliability. Further, through this optimization algorithm, we make a statistical analysis on spike events evoked by different MAs. Results suggest that numbers of response spikes under reinforcing manipulations are far more than reducing manipulations, which mainly embody in synchronous spike activities.     

脑电信号数据压缩及棘波识别的小波神经网络方法

本文在对小波神经网络及其算法研究的基础上,提出了一种对脑电信号压缩表达和痫样脑电棘波识别的新方法。实验结果显示,小波网络在大量压缩数据的同时,能够较好的恢复原有信号,另外,在脑电信号的时频谱等高线图上,得到了易于自动识别的棘波和棘慢复合波特征,说明此方法在电生理信号处理和时频分析方面有着光明的应用前景。     

Synaptic convergence regulates synchronization-dependent spike transfer in feedforward neural networks

Correlated neural activities such as synchronizations can significantly alter the characteristics of spike transfer between neural layers. However, it is not clear how this synchronization-dependent spike transfer can be affected by the structure of convergent feedforward wiring. To address this question, we implemented computer simulations of model neural networks: a source and a target layer connected with different types of convergent wiring rules. In the Gaussian-Gaussian (GG) model, both the connection probability and the strength are given as Gaussian distribution as a function of spatial distance. In the Uniform-Constant (UC) and Uniform-Exponential (UE) models, the connection probability density is a uniform constant within a certain range, but the connection strength is set as a constant value or an exponentially decaying function, respectively. Then we examined how the spike transfer function is modulated under these conditions, while static or synchronized input patterns were introduced to simulate different levels of feedforward spike synchronization. We observed that the synchronization-dependent modulation of the transfer function appeared noticeably different for each convergence condition. The modulation of the spike transfer function was largest in the UC model, and smallest in the UE model. Our analysis showed that this difference was induced by the different spike weight distributions that was generated from convergent synapses in each model. Our results suggest that, the structure of the feedforward convergence is a crucial factor for correlation-dependent spike control, thus must be considered important to understand the mechanism of information transfer in the brain.     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.