Shigeru Shinomoto

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.

Differences in spiking patterns among cortical neurons

Spike sequences recorded from four cortical areas of an awake behaving monkey were examined to explore characteristics that vary among neurons. We found that a measure of the local variation of interspike intervals, LV, is nearly the same for every spike sequence for any given neuron, while it varies significantly among neurons. The distributions of LV values for neuron ensembles in three of the four areas were found to be distinctly bimodal. Two groups of neurons classified according to the spiking irregularity exhibit different responses to the same stimulus. This suggests that neurons in each area can be classified into different groups possessing unique spiking statistics and corresponding functional properties.

Local and Grobal Self-Entrainments in Oscillator Lattices

By computer simulations of an active rotator model, it is found that 1-, 2and 3-dimensional oscillator lattices with distributed natural frequencies exhibit peculiar clustering patterns due to local entrainment. A simple theory suggests that some of such self-entrained clusters mayor may not develop into macroscopic size depending on system dimension, and this fact consistently explains our numerically obtained order parameter curves.

Relating Neuronal Firing Patterns to Functional Differentiation of Cerebral Cortex

It has been empirically established that the cerebral cortical areas defined by Brodmann one hundred years ago solely on the basis of cellular organization are closely correlated to their function, such as sensation, association, and motion. Cytoarchitectonically distinct cortical areas have different densities and types of neurons. Thus, signaling patterns may also vary among cytoarchitectonically unique cortical areas. To examine how neuronal signaling patterns are related to innate cortical functions, we detected intrinsic features of cortical firing by devising a metric that efficiently isolates non-Poisson irregular characteristics, independent of spike rate fluctuations that are caused extrinsically by ever-changing behavioral conditions. Using the new metric, we analyzed spike trains from over 1,000 neurons in 15 cortical areas sampled by eight independent neurophysiological laboratories. Analysis of firing-pattern dissimilarities across cortical areas revealed a gradient of firing regularity that corresponded closely to the functional category of the cortical area; neuronal spiking patterns are regular in motor areas, random in the visual areas, and bursty in the prefrontal area. Thus, signaling patterns may play an important role in function-specific cerebral cortical computation.

A benchmark test for a quantitative assessment of simple neuron models

Several methods and algorithms have recently been proposed that allow for the systematic evaluation of simple neuron models from intracellular or extracellular recordings. Models built in this way generate good quantitative predictions of the future activity of neurons under temporally structured current injection. It is, however, difficult to compare the advantages of various models and algorithms since each model is designed for a different set of data. Here, we report about one of the first attempts to establish a benchmark test that permits a systematic comparison of methods and performances in predicting the activity of rat cortical pyramidal neurons. We present early submissions to the benchmark test and discuss implications for the design of future tests and simple neurons models.

Four types of learning curves

If machines are learning to make decisions given a number of examples, the generalization error (t) is defined as the average probability that an incorrect decision is made for a new example by a machine when trained with t examples. The generalization error decreases as t increases, and the curve (t) is called a learning curve. The present paper uses the Bayesian approach to show that given the annealed approximation, learning curves can be classified into four asymptotic types. If the machine is deterministic with noiseless teacher signals, then (1) at-1 when the correct machine parameter is unique, and (2) at-2 when the set of the correct parameters has a finite measure. If the teacher signals are noisy, then (3) at-1/2 for a deterministic machine, and (4) c + at-1 for a stochastic machine.

Made-to-order spiking neuron model equipped with a multi-timescale adaptive threshold

Information is transmitted in the brain through various kinds of neurons that respond differently to the same signal. Full characteristics including cognitive functions of the brain should ultimately be comprehended by building simulators capable of precisely mirroring spike responses of a variety of neurons. Neuronal modeling that had remained on a qualitative level has recently advanced to a quantitative level, but is still incapable of accurately predicting biological data and requires high computational cost. In this study, we devised a simple, fast computational model that can be tailored to any cortical neuron not only for reproducing but also for predicting a variety of spike responses to greatly fluctuating currents. The key features of this model are a multi-timescale adaptive threshold predictor and a nonresetting leaky integrator. This model is capable of reproducing a rich variety of neuronal spike responses, including regular spiking, intrinsic bursting, fast spiking, and chattering, by adjusting only three adaptive threshold parameters. This model can express a continuous variety of the firing characteristics in a three-dimensional parameter space rather than just those identified in the conventional discrete categorization. Both high flexibility and low computational cost would help to model the real brain function faithfully and examine how network properties may be influenced by the distributed characteristics of component neurons.

The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex

Cortical neurons of behaving animals generate irregular spike sequences. Recently, there has been a heated discussion about the origin of this irregularity. Softky and Koch (1993) pointed out the inability of standard single-neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible. Shadlen and Newsome (1994), on the other hand, demonstrated that a standard leaky integrate-and-fire model can reproduce the irregularity if the inhibition is balanced with the excitation. Motivated by this discussion, we attempted to determine whether the Ornstein-Uhlenbeck process, which is naturally derived from the leaky integration assumption, can in fact reproduce higher-order statistics of biological data. For this purpose, we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher-order statistics of the interspike intervals. Consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient, which are, respectively, a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution. It is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values. This fact suggests that the leaky integrate-and-fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons.

Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons

There has been controversy over whether the standard neuro-spiking models are consistent with the irregular spiking of cortical neurons. In a previous study, we proposed examining this consistency on the basis of the high-order statistics of the inter-spike intervals (ISIs), as represented by the coefficient of variation and the skewness coefficient. In that study we found that a leaky integrate-and-fire model incorporating the assumption of temporally uncorrelated inputs is not able to account for the spiking data recorded from a monkey prefrontal cortex. In the present paper, we attempt to revise the neuro-spiking model so as to make it consistent with the biological data. Here we consider the correlation coefficient of consecutive ISIs, which was ignored in previous studies. Considering three statistical coefficients, we conclude that the leaky integrate-and-fire model with temporally correlated inputs does account for the biological data. The correlation time scale of the inputs needed to explain the biological statistics is found to be on the order of 100ms. We discuss possible origins of this input correlation.

Mutual Entrainment in Oscillator Lattices with Nonvariational Type Interaction

On etudie un systeme modele pour des oscillateurs cycle limite distribues sur un reseau cubique a d dimensions