Messages of oscillatory correlograms: a spike train model

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.     

神经元膜电位对信息的编码

神经元膜电位的放电活动是神经编码的基础。然而,目前对于神经元电活动对神经信息的编码方式,至今尚未形成一个完整的认识。传统的编码理论认为神经系统以离散的动作电位放电序列进行信息的表达和传递,主要研究动作电位的发放频率和放电活动的时间模式。基于该理论,对神经元放电序列所携带的信息已经出现了一些定量的计算方法,但这些方法还很难应用到大规模神经元网络的计算当中。本研究以神经元的膜电位为研究对象,展示了如何量化膜电位序列所携带的信息,并将该计算结果与传统放电序列方沣的计算结果进行了对比分析,其结果取得了很好的一致性。本研究为神经活动信息量的定量计算提供了一种新的思路和方法。     

Resampling methods for ranked set samples

When measuring units are expensive or time consuming, while ranking them can be done easily, it is known that ranked set sampling (RSS) is preferred to simple random sampling (SRS). Available results for RSS are developed under specific parametric assumptions or are asymptotic in nature, with few results available for finite size samples when the underlying distribution of the observed data is unknown. We investigate the use of resampling techniques to draw inferences on population characteristics. To obtain standard error and confidence interval estimates we discuss and compare three methods of resampling a given ranked set sample. Chen et al. (2004. Ranked Set Sampling: Theory and Applications. Springer, New York) suggest a natural method to obtain bootstrap samples from each row of a RSS. We prove that this method is consistent for a location estimator. We propose two other methods that are designed to obtain more stratified resamples from the given sample. Algorithms are provided for these methods. We recommend a method that obtains a bootstrap RSS from the observations. We prove several properties of this method, including consistency for a location parameter. We define two types of L-estimators for RSS and obtain expressions for their exact moments. We discuss an application to obtain confidence intervals for the Winsorized mean of a RSS.     

Classification of stationary neuronal activity according to its information rate

We propose a measure of the information rate of a single stationary neuronal activity with respect to the state of null information. The measure is based on the Kullback-Leibler distance between two interspike interval distributions. The selected activity is compared with the Poisson model with the same mean firing frequency. We show that the approach is related to the notion of specific information and that the method allows us to judge the relative encoding efficiency. Two classes of neuronal activity models are classified according to their information rate: the renewal process models and the first-order Markov chain models. It has been proven that information can be transmitted changing neither the spike rate nor the coefficient of variation and that the increase in serial correlation does not necessarily increase the information gain. We employ the simple, but powerful, Vasicek's estimator of differential entropy to illustrate an application on the experimental data coming from olfactory sensory neurons of rats.     

Statistical smoothing of neuronal data

The purpose of smoothing (filtering) neuronal data is to improve the estimation of the instantaneous firing rate. In some applications, scientific interest centres on functions of the instantaneous firing rate, such as the time at which the maximal firing rate occurs or the rate of increase of firing rate over some experimentally relevant period. In others, the instantaneous firing rate is needed for probability-based calculations. In this paper we point to the very substantial gains in statistical efficiency from smoothing methods compared to using the peristimulus-time histogram (PSTH), and we also demonstrate a new method of adaptive smoothing known as Bayesian adaptive regression splines (DiMatteo 1, Genovese C R and Kass R E 2001 Biometrika 88 1055-71). We briefly review additional applications of smoothing with non-Poisson processes and in the joint PSTH for a pair of neurons.     

Estimating spiking irregularities under changing environments

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. A gamma distribution is a natural extension of the Poisson process taking the effect of a refractory period into account. The model is specified by two parameters: a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes over time, observed data are generated from a model with a time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation. We suggest a measure of spiking irregularity based on the estimating function, which may be useful for characterizing individual neurons in changing environments.     

Replicating receptive fields of simple and complex cells in primary visual cortex in a neuronal network model with temporal and population sparseness and reliability

We propose a new principle for replicating receptive field properties of neurons in the primary visual cortex. We derive a learning rule for a feedforward network, which maintains a low firing rate for the output neurons (resulting in temporal sparseness) and allows only a small subset of the neurons in the network to fire at any given time (resulting in population sparseness). Our learning rule also sets the firing rates of the output neurons at each time step to near-maximum or near-minimum levels, resulting in neuronal reliability. The learning rule is simple enough to be written in spatially and temporally local forms. After the learning stage is performed using input image patches of natural scenes, output neurons in the model network are found to exhibit simple-cell-like receptive field properties. When the output of these simple-cell-like neurons are input to another model layer using the same learning rule, the second-layer output neurons after learning become less sensitive to the phase of gratings than the simple-cell-like input neurons. In particular, some of the second-layer output neurons become completely phase invariant, owing to the convergence of the connections from first-layer neurons with similar orientation selectivity to second-layer neurons in the model network. We examine the parameter dependencies of the receptive field properties of the model neurons after learning and discuss their biological implications. We also show that the localized learning rule is consistent with experimental results concerning neuronal plasticity and can replicate the receptive fields of simple and complex cells.     

Detection of hidden structures in nonstationary spike trains

We propose an algorithm for simultaneously estimating state transitions among neural states and nonstationary firing rates using a switching state-space model (SSSM). This algorithm enables us to detect state transitions on the basis of not only discontinuous changes in mean firing rates but also discontinuous changes in the temporal profiles of firing rates (e.g., temporal correlation). We construct estimation and learning algorithms for a nongaussian SSSM, whose nongaussian property is caused by binary spike events. Local variational methods can transform the binary observation process into a quadratic form. The transformed observation process enables us to construct a variational Bayes algorithm that can determine the number of neural states based on automatic relevance determination. Additionally, our algorithm can estimate model parameters from single-trial data using a priori knowledge about state transitions and firing rates. Synthetic data analysis reveals that our algorithm has higher performance for estimating nonstationary firing rates than previous methods. The analysis also confirms that our algorithm can detect state transitions on the basis of discontinuous changes in temporal correlation, which are transitions that previous hidden Markov models could not detect. We also analyze neural data recorded from the medial temporal area. The statistically detected neural states probably coincide with transient and sustained states that have been detected heuristically. Estimated parameters suggest that our algorithm detects the state transitions on the basis of discontinuous changes in the temporal correlation of firing rates. These results suggest that our algorithm is advantageous in real-data analysis.     

Kernel current source density method

Local field potentials (LFP), the low-frequency part of extracellular electrical recordings, are a measure of the neural activity reflecting dendritic processing of synaptic inputs to neuronal populations. To localize synaptic dynamics, it is convenient, whenever possible, to estimate the density of transmembrane current sources (CSD) generating the LFP. In this work, we propose a new framework, the kernel current source density method (kCSD), for nonparametric estimation of CSD from LFP recorded from arbitrarily distributed electrodes using kernel methods. We test specific implementations of this framework on model data measured with one-, two-, and three-dimensional multielectrode setups. We compare these methods with the traditional approach through numerical approximation of the Laplacian and with the recently developed inverse current source density methods (iCSD). We show that iCSD is a special case of kCSD. The proposed method opens up new experimental possibilities for CSD analysis from existing or new recordings on arbitrarily distributed electrodes (not necessarily on a grid), which can be obtained in extracellular recordings of single unit activity with multiple electrodes.     

Marking optimization of stochastic timed event graphs using IPA

This paper addresses the marking optimization of stochastic timed event graphs, where the transition firing times are generated by random variables with general distributions. The marking optimization problem consists of obtaining a given cycle time while minimizing a p-invariant criterion. We propose two heuristic algorithms, both starting from the optimal solution to the associated deterministic problem and iteratively adding tokens to adequate places as long as the given cycle time is not obtained. Infinitesimal perturbation analysis of the average cycle time with respect to the transition firing times is used to identify the appropriate places in which new tokens are added at each iteration. Numerical results show that the heuristic algorithms provide solutions better than the ones obtained by the existing methods.     

Inferring input nonlinearities in neural encoding models

We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus. The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs. In one case, the nonlinear transform is the same at all filter lag-times. Thus, this "input nonlinearity" converts the initial numerical representation of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties.     

基于大脑神经元放电的脑-机接口技术

基于大脑运动皮层神经元放电的脑-机接口通过记录大脑运动皮层神经元的放电信号控制瘫痪肢体或假肢运动,其软硬件核心为神经元群体解码和神经元放电活动的检测。解码方法分为推理算法和分类器方法,检测方法通过在大脑运动皮层区植入长效电极记录单个或群体神经元的放电活动。分析表明,脑-机接口技术应在更多脑区域上植入长效电极达到更好控制设备的目的,各类解码算法应通过联合并加入反馈信号提高对神经元信号的解码效果。     

TEXTUAL ARTICLE CLUSTERING IN NEWSPAPER PAGES

In the analysis of a newspaper page an important step is the clustering of various text blocks into logical units, i.e., into articles. We propose three algorithms based on text processing techniques to cluster articles in newspaper pages. Based on the complexity of the three algorithms and experiments on actual pages from the Italian newspaper L'Adige, we select one of the algorithms as the preferred choice to solve the textual clustering problem.     

On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.     

Stable propagation of activity pulses in populations of spiking neurons

We investigate the propagation of pulses of spike activity in a neuronal network with feedforward couplings. The neurons are of the spike-response type with a firing probability that depends linearly on the membrane potential. After firing, neurons enter a phase of refractoriness. Spike packets are described in terms of the moments of the firing-time distribution so as to allow for an analytical treatment of the evolution of the spike packet as it propagates from one layer to the next. Analytical results and simulations show that depending on the synaptic coupling strength, a stable propagation of the packet with constant waveform is possible. Crucial for this observation is neither the existence of a firing threshold nor a sigmoidal gain function--both are absent in our model--but the refractory behavior of the neurons.     

A network of coincidence detector neurons with periodic and chaotic dynamics

We propose a simple neural network model to understand the dynamics of temporal pulse coding. The model is composed of coincidence detector neurons with uniform synaptic efficacies and random pulse propagation delays. We also assume a global negative feedback mechanism which controls the network activity, leading to a fixed number of neurons firing within a certain time window. Due to this constraint, the network state becomes well defined and the dynamics equivalent to a piecewise nonlinear map. Numerical simulations of the model indicate that the latency of neuronal firing is crucial to the global network dynamics; when the timing of postsynaptic firing is less sensitive to perturbations in timing of presynaptic spikes, the network dynamics become stable and periodic, whereas increased sensitivity leads to instability and chaotic dynamics. Furthermore, we introduce a learning rule which decreases the Lyapunov exponent of an attractor and enlarges the basin of attraction.     

Supposed maximum information for comprehensible representations in SOM

In this paper, we propose a new information-theoretic method to simplify the computation of information and to unify several methods in one framework. The new method is called “supposed maximum information,” used to produce humanly comprehensible representations in competitive learning by taking into account the importance of input units. In the new learning method, by supposing the maximum information of input units, the actual information of input units is estimated. Then, the competitive network is trained with the estimated information in input units. The method is applied not to pure competitive learning, but to self-organizing maps, because it is easy to demonstrate visually how well the new method can produce more interpretable representations. We applied the method to three well-known sets of data, namely, the Kohonen animal data, the SPECT heart data and the voting data from the machine learning database. With these data, we succeeded in producing more explicit class boundaries on the U-matrices than did the conventional SOM. In addition, for all the data, quantization and topographic errors produced by our method were lower than those by the conventional SOM.     

Recurrent infomax generates cell assemblies, neuronal avalanches, and simple cell-like selectivity

Recently multineuronal recording has allowed us to observe patterned firings, synchronization, oscillation, and global state transitions in the recurrent networks of central nervous systems. We propose a learning algorithm based on the process of information maximization in a recurrent network, which we call recurrent infomax (RI). RI maximizes information retention and thereby minimizes information loss through time in a network. We find that feeding in external inputs consisting of information obtained from photographs of natural scenes into an RI-based model of a recurrent network results in the appearance of Gabor-like selectivity quite similar to that existing in simple cells of the primary visual cortex. We find that without external input, this network exhibits cell assembly-like and synfire chain-like spontaneous activity as well as a critical neuronal avalanche. In addition, we find that RI embeds externally input temporal firing patterns to the network so that it spontaneously reproduces these patterns after learning. RI provides a simple framework to explain a wide range of phenomena observed in in vivo and in vitro neuronal networks, and it will provide a novel understanding of experimental results for multineuronal activity and plasticity from an information-theoretic point of view.     

Cooperative information maximization with Gaussian activation functions for self-organizing maps

In this paper, we propose a new information-theoretic method to produce explicit self-organizing maps (SOMs). Competition is realized by maximizing mutual information between input patterns and competitive units. Competitive unit outputs are computed by the Gaussian function of distance between input patterns and competitive units. A property of this Gaussian function is that, as distance becomes smaller, a neuron tends to fire strongly. Cooperation processes are realized by taking into account the firing rates of neighboring neurons. We applied our method to uniform distribution learning, chemical compound classification and road classification. Experimental results confirmed that cooperation processes could significantly increase information content in input patterns. When cooperative operations are not effective in increasing information, mutual information as well as entropy maximization is used to increase information. Experimental results showed that entropy maximization could be used to increase information and to obtain clearer SOMs, because competitive units are forced to be equally used on average.