Hideaki Shimazaki

A Method for Selecting the Bin Size of a Time Histogram

The time histogram method is the most basic tool for capturing a time dependent rate of neuronal spikes. Generally in the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers. Here, we propose a method for objectively selecting the bin size from the spike count statistics alone, so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate. For a small number of spike sequences generated from a modestly fluctuating rate, the optimal bin size may diverge, indicating that any time histogram is likely to capture a spurious rate. Given a paucity of data, the method presented here can nevertheless suggest how many experimental trials should be added in order to obtain a meaningful time-dependent histogram with the required accuracy.

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.

Social conflict resolution regulated by two dorsal habenular subregions in zebrafish

How to win a fish fight When to cease aggression and escape is an important decision that fighting animals must make. Chou et al. characterized the role of two nuclei in a brain area of the zebrafish called the dorsal habenula (dHb) during social aggression (see the Perspective by Desban and Wyart). Silencing the lateral dHb reduced the likelihood of winning a fight, whereas silencing the medial dHb increased the likelihood of winning. Thus, these two nuclei antagonistically control the threshold for surrender. Science, this issue p. 87; see also p. 42 The neuronal basis for keeping the aggression of fighting fish in check is elucidated. [Also see Perspective by Desban and Wyart] When animals encounter conflict they initiate and escalate aggression to establish and maintain a social hierarchy. The neural mechanisms by which animals resolve fighting behaviors to determine such social hierarchies remain unknown. We identified two subregions of the dorsal habenula (dHb) in zebrafish that antagonistically regulate the outcome of conflict. The losing experience reduced neural transmission in the lateral subregion of dHb (dHbL)–dorsal/intermediate interpeduncular nucleus (d/iIPN) circuit. Silencing of the dHbL or medial subregion of dHb (dHbM) caused a stronger predisposition to lose or win a fight, respectively. These results demonstrate that the dHbL and dHbM comprise a dual control system for conflict resolution of social aggression.

Similarity in Neuronal Firing Regimes across Mammalian Species

The architectonic subdivisions of the brain are believed to be functional modules, each processing parts of global functions. Previously, we showed that neurons in different regions operate in different firing regimes in monkeys. It is possible that firing regimes reflect differences in underlying information processing, and consequently the firing regimes in homologous regions across animal species might be similar. We analyzed neuronal spike trains recorded from behaving mice, rats, cats, and monkeys. The firing regularity differed systematically, with differences across regions in one species being greater than the differences in similar areas across species. Neuronal firing was consistently most regular in motor areas, nearly random in visual and prefrontal/medial prefrontal cortical areas, and bursting in the hippocampus in all animals examined. This suggests that firing regularity (or irregularity) plays a key role in neural computation in each functional subdivision, depending on the types of information being carried. SIGNIFICANCE STATEMENT By analyzing neuronal spike trains recorded from mice, rats, cats, and monkeys, we found that different brain regions have intrinsically different firing regimes that are more similar in homologous areas across species than across areas in one species. Because different regions in the brain are specialized for different functions, the present finding suggests that the different activity regimes of neurons are important for supporting different functions, so that appropriate neuronal codes can be used for different modalities.

Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Representation of higher-order statistical structures in natural scenes via spatial phase distributions

Natural scenes contain richer perceptual information in their spatial phase structure than their amplitudes. Modeling phase structure of natural scenes may explain higher-order structure inherent to the natural scenes, which is neglected in most classical models of redundancy reduction. Only recently, a few models have represented images using a complex form of receptive fields (RFs) and analyze their complex responses in terms of amplitude and phase. However, these complex representation models often tacitly assume a uniform phase distribution without empirical support. The structure of spatial phase distributions of natural scenes in the form of relative contributions of paired responses of RFs in quadrature has not been explored statistically until now. Here, we investigate the spatial phase structure of natural scenes using complex forms of various Gabor-like RFs. To analyze distributions of the spatial phase responses, we constructed a mixture model that accounts for multi-modal circular distributions, and the EM algorithm for estimation of the model parameters. Based on the likelihood, we report presence of both uniform and structured bimodal phase distributions in natural scenes. The latter bimodal distributions were symmetric with two peaks separated by about 180°. Thus, the redundancy in the natural scenes can be further removed by using the bimodal phase distributions obtained from these RFs in the complex representation models. These results predict that both phase invariant and phase sensitive complex cells are required to represent the regularities of natural scenes in visual systems.

State-Space Analysis of an Ising Model Reveals Contributions of Pairwise Interactions to Sparseness, Fluctuation, and Stimulus Coding of Monkey V1 Neurons

In this study, we analyzed the activity of monkey V1 neurons responding to grating stimuli of different orientations using inference methods for a time-dependent Ising model. The method provides optimal estimation of time-dependent neural interactions with credible intervals according to the sequential Bayes estimation algorithm. Furthermore, it allows us to trace dynamics of macroscopic network properties such as entropy, sparseness, and fluctuation. Here we report that, in all examined stimulus conditions, pairwise interactions contribute to increasing sparseness and fluctuation. We then demonstrate that the orientation of the grating stimulus is in part encoded in the pairwise interactions of the neural populations. These results demonstrate the utility of the state-space Ising model in assessing contributions of neural interactions during stimulus processing.

Neural Engine Hypothesis

This chapter presents a hypothesis that the animal’s brain is acting analogously to a heat engine when it actively modulates incoming sensory information to achieve enhanced perceptual capacity. To articulate this hypothesis, we describe stimulus-evoked activity of a neural population based on the maximum entropy principle with constraints on two types of overlapping activities, one that is controlled by stimulus conditions and the other, termed internal activity, that is regulated internally in an organism. We demonstrate that modulation of the internal activity realizes gain control of stimulus response, and controls stimulus information. The model’s statistical structure common to thermodynamics allows us to construct the first law for neural dynamics, equation of state, and fluctuation-response relation. A cycle of neural dynamics is then introduced to model information processing by the neurons during which the stimulus information is dynamically enhanced by the internal gain-modulation mechanism. Based on the conservation law of entropy, we demonstrate that the cycle generates entropy ascribed to the stimulus-related activity using entropy supplied by the internal mechanism, analogously to a heat engine that produces work from heat. We provide an efficient cycle that achieves the highest entropic efficiency to retain the stimulus information. The theory allows us to quantify efficiency of the internal computation and its theoretical limit, which can be used to test the hypothesis.

Learning Complex Representations from Spatial Phase Statistics of Natural Scenes

Natural scenes contain higher-order statistical structures that can be encoded in their spatial phase information. Nevertheless, little progress has been made in modeling phase information of images in order to understand efficient representation of image phases in the brain. Based on recent findings of spatial phase structure in natural scenes, we introduce a generative model of the phase information in the visual systems according to the efficient coding hypothesis. In this model, we assume independent priors for the amplitude and phase of the coefficients, and model the phase using a non-uniform distribution, which extends existing models of independent component analysis for complex-valued signals. The parameters of the proposed model are then estimated under the maximum-likelihood principle. Using simulated data, we show that the proposed model outperforms conventional models with a uniform phase prior in blind source separation of complex-valued signals. We then apply the proposed model to natural scenes in the Fourier domain. The learning yields nonlinear features specified by a pair of similar Gabor-like filters in quadratic phase structure. These features predict properties of phase sensitive complex cells in the visual cortex, and indicate that the phase sensitive complex cells are essential for removing redundancy in natural scenes.

Approximate Inference Method for Dynamic Interactions in Larger Neural Populations

The maximum entropy method has been successfully employed to explain stationary spiking activity of a neural population by using fewer features than the number of possible activity patterns. Modeling network activity in vivo, however, has been challenging because features such as spike-rates and interactions can change according to sensory stimulation, behavior, or brain state. To capture the time-dependent activity, Shimazaki et al. (PLOS Comp Biol, 2012) previously introduced a state-space framework for the latent dynamics of neural interactions. However, the exact method suffers from computational cost; therefore its application was limited to only \({\sim }15\) neurons. Here we introduce the pseudolikelihood method combined with the TAP or Bethe approximation to the state-space model, and make it possible to estimate dynamic pairwise interactions of up to 30 neurons. These analytic approximations allow analyses of time-varying activity of larger networks in relation to stimuli or behavior.