Noise induced amplification of sub-threshold pulses in multi-thread excitable semiconductor ‘neurons’

We report on the transmission of electrical pulses through a semiconductor structure which emulates biological neurons. The ‘neuron’ emits bursts of electrical spikes whose coherence we study as a function of the amplitude and frequency of a sine wave stimulus and noise. Noise is found to enhance the transmission of pulses below the firing threshold of the neuron. We demonstrate stochastic resonance when the power of the output signal passes through a maximum at an optimum noise value. Under appropriate conditions, we observe coherence resonance and stochastic synchronization. Data are quantitatively explained by modelling the FitzHugh–Nagumo equations derived from the electrical equivalent circuit of the soma. We have therefore demonstrated a physically realistic neuron structure that provides first principles feedback on mathematical models and that is well suited to building arborescent networks of pulsing neurons.     

Stochastic resonance at the periphery of auditory system: A simulation experiment

An auditory nerve fiber model is studied. The model includes the formation of the response of the basilar membrane, formation of the receptor potential of the internal hair cell, formation of the synaptic potential of the auditory nerve fiber, and transformation of the synaptic potential into a sequence of spikes. The role of this transformation, as well as the role of changes in the excitability of the fiber after the spike generation in the coding of amplitude-modulated signals is revealed for the cases of signals of medium (i.e., corresponding to the sloping part of the curve representing the mean firing rate of an auditory nerve fiber as a function of the stimulus level) and subthreshold levels. Simulated experiments show that the coding of the envelope of a medium-level amplitude-modulated signal is a dynamic process, which includes fine tuning (adaptation) of the threshold of the auditory nerve fiber to the stimulus level. The coding of the signal envelope is little affected by the slope of the dependence of the mean firing rate on the stimulus level. However, fibers with steep input-output characteristics may exhibit stochastic resonance properties. Owing to these properties, such fibers are capable of reproducing the envelope of a subthreshold modulated signal when weak noise is added to it. Ways are considered for extending the range of subthreshold signal and noise levels within which the envelope of a modulated signal is reproduced (or the phenomenon of stochastic resonance is observed).     

Markov analysis of stochastic resonance in a periodically driven integrate-and-fire neuron

We model the dynamics of the leaky integrate-and-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.     

Response of Hodgkin–Huxley stochastic bursting neuron to single-pulse stimulus

We investigate Hodgkin–Huxley neuron model with external Gaussian noise in the range of parameters where it exhibits bistability of silent and firing states, and noise-induced bursts occur. We study the response of the system to brief single pulse of current. When noise amplitude increases, the delay time between the stimulus and the first spike decreases substantially even for subthreshold stimulus. The mean number of spikes in a post-stimulus burst has a maximum in a certain range of noise amplitudes. Therefore, we found that Hodgkin–Huxley neuron in the stochastic bursting regime has more improved sensitivity to single-pulse stimulus than in the silent one.     

Discrimination of modulation depth of sinusoidal amplitude modulation (SAM) noise

The detection of sinusoidal amplitude modulation (SAM) provides a lower bound on the degree to which temporal information in the envelope of complex waveforms is encoded by the auditory system. The extent to which changes in the amount of modulation are discriminable provides additional information on the ability of the auditory system to utilize envelope fluctuations. Results from an experiment on the discrimination of modulation depth of broadband noise are presented. Discrimination thresholds, expressed as differences in modulation power, increase monotonically with the modulation depth of the standard, but do not obey Weber's law. The effects of carrier level and of modulation frequency are consistent with those observed in modulation detection: Changes in carrier level have little effect on modulation discrimination; changes in modulation frequency also have little effect except for standards near the modulation detection threshold. The discrimination of modulation depth is consistent with the leaky-integrator model of modulation detection for standards below--10 dB (20 log ms); for standards greater than--10 dB, the leaky integrator predicts better performance than that observed behaviorally.     

Spectro-temporal processing in the envelope-frequency domain

The frequency selectivity for amplitude modulation applied to tonal carriers and the role of beats between modulators in modulation masking were studied. Beats between the masker and signal modulation as well as intrinsic envelope fluctuations of narrow-band-noise modulators are characterized by fluctuations in the "second-order" envelope (referred to as the "venelope" in the following). In experiment 1, masked threshold patterns (MTPs), representing signal modulation threshold as a function of masker-modulation frequency, were obtained for signal-modulation frequencies of 4, 16, and 64 Hz in the presence of a narrow-band-noise masker modulation, both applied to the same sinusoidal carrier. Carrier frequencies of 1.4, 2.8, and 5.5 kHz were used. The shape and relative bandwidth of the MTPs were found to be independent of the signal-modulation frequency and the carrier frequency. Experiment 2 investigated the extent to which the detection of beats between signal and masker modulation is involved in tone-in-noise (TN), noise-in-tone (NT), and tone-in-tone (TT) modulation masking, whereby the TN condition was similar to the one used in the first experiment. A signal-modulation frequency of 64 Hz, applied to a 2.8-kHz carrier, was tested. Thresholds in the NT condition were always lower than in the TN condition, analogous to the masking effects known from corresponding experiments in the audio-frequency domain. TT masking conditions generally produced the lowest thresholds and were strongly influenced by the detection of beats between the signal and the masker modulation. In experiment 3, TT masked-threshold patterns were obtained in the presence of an additional sinusoidal masker at the beat frequency. Signal-modulation frequencies of 32, 64, and 128 Hz, applied to a 2.8-kHz carrier, were used. It was found that the presence of an additional modulation at the beat frequency hampered the subject's ability to detect the envelope beats and raised thresholds up to a level comparable to that found in the TN condition. The results of the current study suggest that (i) venelope fluctuations play a similar role in modulation masking as envelope fluctuations do in spectral masking, and (ii) envelope and venelope fluctuations are processed by a common mechanism. To interpret the empirical findings, a general model structure for the processing of envelope and venelope fluctuations is proposed.     

最小神经元模型放电起始动态控制与分析

本文采用最小神经元模型,从生理学角度设计wash-out滤波器,实现了不同放电起始动态机理之间的转换,并证明wash-out滤波器控制通过影响阈下电流的竞争结果改变了神经元的放电起始动态机理. 关键词： 放电起始动态机理 阈下电流竞争 最小神经元模型 wash-out滤波器     

Second-order temporal modulation transfer functions

Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181-1196 (2000)].     

Modulation masking produced by beating modulators.

This study examined whether "modulation masking" could be produced by temporal similarity of the probe and masker envelopes, even when the masker envelope did not contain a spectral component close to the probe frequency. Both masker and probe amplitude modulation were applied to a single 4-kHz sinusoidal or narrow-band noise carrier with a level of 70 dB SPL. The threshold for detecting 5-Hz probe modulation was affected by the presence of a pair of masker modulators beating at a 5-Hz rate (40 and 45 Hz, 50 and 55 Hz, or 60 and 65 Hz). The threshold was dependent on the phase of the probe modulation relative to the beat cycle of the masker modulators; the threshold elevation was greatest (12-15 dB for the sinusoidal carrier and 9-11 dB for the noise carrier, expressed as 20 log m) when the peak amplitude of the probe modulation coincided with a peak in the beat cycle. The maximum threshold elevation of the 5-Hz probe produced by the beating masker modulators was 7-12 dB greater than that produced by the individual components of the masker modulators. The threshold elevation produced by the beating masker modulators was 2-10 dB greater for 5-Hz probe modulation than for 3- or 7-Hz probe modulation. These results cannot be explained in terms of the spectra of the envelopes of the stimuli, as the beating masker modulators did not produce a 5-Hz component in the spectra of the envelopes. The threshold for detecting 5-Hz probe modulation in the presence of 5-Hz masker modulation varied with the relative phase of the probe and masker modulation. The pattern of results was similar to that found with the beating two-component modulators, except that thresholds were highest when the masker and probe were 180 degrees out of phase. The results are consistent with the idea that nonlinearities within the auditory system introduce distortion in the internal representation of the envelopes of the stimuli. In the case of two-component beating modulators, a weak component is introduced at the beat rate, and it has an amplitude minimum when the beat cycle is at its maximum. The results could be fitted well using two models, one based on the concept of a sliding temporal integrator and one based on the concept of a modulation filter bank.     

相位噪声诱发神经放电的单次或两次相干共振

神经元电活动可以从静息通过Hopf分岔到放电,放电频率有固定周期;也可以从静息通过鞍-结分岔到放电,放电频率接近零.在具有周期性的相位噪声作用下的Hopf分岔和鞍-结分岔点附近,都会产生相干共振.噪声的周期小于Hopf分岔点附近的放电的周期时,相位噪声可以引起神经系统产生一次相干共振,位于系统内在的固有频率附近;噪声的周期大于系统的固有周期时,相位噪声可以引起双共振,对应低噪声强度的共振产生在噪声频率附近,对应高噪声强度的共振产生在系统的固有频率附近;并对双共振的产生原因进行了解释.在鞍-结分岔点附近,无论噪声的周期是大是小,都只会引起一次共振,研究结果不仅揭示了相位噪声作用下平衡点分岔点相干共振的动力学特性和对应于两类分岔的两类神经兴奋性的差别,还对近期的相位噪声诱发产生单或双共振的不同研究结果给出了解释.     

色关联噪声驱动下非线性神经元模型的相干共振

研究了关联的加性离子通道噪声和乘性突触噪声共同作用下非线性积分发放神经元模型中的相干共振现象.运用绝热近似理论和统一色噪声近似方法,得到了神经元首次点火概率分布和神经元放电峰峰间隔的变差系数的近似表达式.研究表明,首次点火概率分布和变差系数是突触噪声强度、离子通道噪声强度、乘性色噪声自相关时间和噪声关联强度的函数,适当的噪声强度、噪声自相关时间和噪声关联强度可以减小神经元发放峰峰间隔的变差系数,使系统的相干性达到最大值,从而引起神经元出现相干共振现象.同时讨论了离子通道噪声强度、突触噪声强度、乘性色噪声自相关时间和噪声关联强度对系统相干共振的影响.     

Spectral modulation detection as a function of modulation frequency, carrier bandwidth, and carrier frequency region

The present study investigates the nature of spectral envelope perception using a spectral modulation detection task in which sinusoidal spectral modulation is superimposed upon a noise carrier. The principal goal of this study is to characterize spectral envelope perception in terms of the influence of modulation frequency (cycles/octave), carrier bandwidth (octaves), and carrier frequency region (defined by lower and upper cutoff frequencies in Hz). Spectral modulation detection thresholds measured as a function of spectral modulation frequency result in a spectral modulation transfer function (SMTF). The general form of the SMTF is bandpass in nature, with a minimum modulation detection threshold in the region between 2 to 4 cycles/octave. SMTFs are not strongly dependent on carrier bandwidth (ranging from 1 to 6 octaves) or carrier frequency region (ranging from 200 to 12 800 Hz), with the exception of carrier bands restricted to very low audio frequencies (e.g., 200-400 Hz). Spectral modulation detection thresholds do not depend on the presence of random level variations or random modulation phase across intervals. The SMTFs reported here and associated excitation pattern computations are considered in terms of a linear systems approach to spectral envelope perception and potential underlying mechanisms for the perception of spectral features.     

Intrinsic envelope fluctuations and modulation-detection thresholds for narrow-band noise carriers

A model is presented which calculates the intrinsic envelope power of a bandpass noise carrier within the passband of a hypothetical modulation filter tuned to a specific modulation frequency. Model predictions are compared to experimentally obtained amplitude modulation (AM) detection thresholds. In experiment 1, thresholds for modulation rates of 5, 25, and 100 Hz imposed on a bandpass Gaussian noise carrier with a fixed upper cutoff frequency of 6 kHz and a bandwidth in the range from 1 to 6000 Hz were obtained. In experiment 2, three noises with different spectra of the intrinsic fluctuations served as the carrier: Gaussian noise, multiplied noise, and low-noise noise. In each case, the carrier was spectrally centered at 5 kHz and had a bandwidth of 50 Hz. The AM detection thresholds were obtained for modulation frequencies of 10, 20, 30, 50, 70, and 100 Hz. The intrinsic envelope power of the carrier at the output of the modulation filter tuned to the signal modulation frequency appears to provide a good estimate for AM detection threshold. The results are compared with predictions on the basis of the more complex auditory processing model by Dau et al.     

An analysis of quasi-frequency-modulated noise and random-sideband noise as comparisons for amplitude-modulated noise

Experiments were performed to determine under what conditions quasi-frequency-modulated (QFM) noise and random-sideband noise are suitable comparisons for AM noise in measuring a temporal modulation transfer function (TMTF). Thresholds were measured for discrimination of QFM from random-sideband noise and AM from QFM noise as a function of sideband separation. In the first experiment, the upper spectral edge of the noise stimuli was at 2400 Hz and the bandwidth was 1600 Hz. For sideband separations up to 256 Hz, at threshold sideband levels for discriminating AM from QFM noise, QFM was indiscriminable from random-sideband noise. For the largest sideband separation used (512 Hz), listeners may have used within-stimulus envelope correlation in the QFM noise to discriminate it from the random-sideband noise. Results when stimulus bandwidth was varied suggest that listeners were able to use this cue when the carrier was wider than a critical band, and the sideband separation approached the carrier bandwidth. Within-stimulus envelope correlation was also present in AM noise, and thus QFM noise was a suitable comparison because it made this cue unusable and forced listeners to use across-stimulus envelope differences. When the carrier bandwidth was less than a critical band or was wideband, QFM noise and random-sideband noise were equally suitable comparisons for AM noise. When discrimination thresholds for QFM and random-sideband noise were converted to modulation depth and modulation frequency, they were nearly identical to those for discrimination of AM from QFM noise, suggesting that listeners were using amplitude modulation cues in both cases.     

动态突触、神经耦合与时间延迟对神经元发放的影响

神经元膜电位的受激发放在神经系统的信息传递中起着重要作用.基于一个受动态突触刺激的突触后神经元发放模型,采用数值模拟和傅里叶变换分析的方法研究了动态突触、神经耦合与时间延迟对突触后神经元发放的影响.结果发现:突触前神经元发放频率与Hodgkin-Huxley神经元的固有频率发生共振决定了突触后神经元发放的难易,特定频率范围内的电流刺激有利于神经元激发,动态突触输出的随机突触电流中这些电流刺激所占的比率在很大程度上影响了突触后神经元的发放次数;将突触后神经元换成神经网络后,网络中神经元之间的耦合可以促进神经元的发放,耦合中的时间延迟可以增强这种促进作用,但是不会改变神经耦合对神经元发放的促进模式.     

Temporal interactions between pure tones and amplitude-modulated noise

An auditory interaction between the temporal fine structure of a low-frequency tone and the envelope of a high-frequency waveform was observed at very large frequency separations. Thresholds for detection of sinusoidal amplitude modulation of a high-frequency, narrow-band noise were measured as a function of the relative phase between the modulator and a pure tone with the same frequency as the modulator. These "phase functions" were determined at various intensities of the noise and tone for three different modulation frequencies. In general, the phase functions show that low-frequency stimulation has a cyclic effect on the sensitivity to amplitude modulation; over a limited range of relative phases, the modulation threshold is lower than that measured without low-frequency stimulation whereas over a broader range of relative phases, the modulation threshold is much higher. The difference between minimum and maximum modulation thresholds was observed to be as great as 23 dB. Despite this substantial degree of temporal interaction, little, if any, masking by the low-frequency tone of the high-frequency noise was observed.     

累积放电模型及其符号动力学研究

基于累积释放模型提出了一种累积放电模型.相比于累积释放模型, 累积放电模型无须变化的阈值调制, 即可出现多种状态, 例如混沌态、锁频等. 利用符号动力学对其进行研究, 发现在一定的参数条件下, 模型的输出符号序列可以被用于监测模型参数的变化, 而且与神经系统的测量相似, 都具有很高的分辨率. 计算机仿真和电路实验得到的结果也验证了上述说法. 电路实验结果显示模型的输出符号序列对输入频率的分辨率最高可以达到0.05 Hz, 对电流幅值的分辨率可达到1 μA, 并且都具有很大的动态范围. 关键词： 符号动力学 混沌 累积释放模型 非线性电路     

Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus

We present results from a novel experimental paradigm to investigate the influence of spatial correlations of stimuli on electrosensory neural network dynamics. Further, a new theoretical analysis for the dynamics of a model network of stochastic leaky integrate-and-fire neurons with delayed feedback is proposed. Experiment and theory for this system both establish that spatial correlations induce a network oscillation, the strength of which is proportional to the degree of stimulus correlation at constant total stimulus power.     

Predicting speech intelligibility based on the signal-to-noise envelope power ratio after modulation-frequency selective processing

A model for predicting the intelligibility of processed noisy speech is proposed. The speech-based envelope power spectrum model has a similar structure as the model of Ewert and Dau [(2000). J. Acoust. Soc. Am. 108, 1181-1196], developed to account for modulation detection and masking data. The model estimates the speech-to-noise envelope power ratio, SNR(env), at the output of a modulation filterbank and relates this metric to speech intelligibility using the concept of an ideal observer. Predictions were compared to data on the intelligibility of speech presented in stationary speech-shaped noise. The model was further tested in conditions with noisy speech subjected to reverberation and spectral subtraction. Good agreement between predictions and data was found in all cases. For spectral subtraction, an analysis of the model's internal representation of the stimuli revealed that the predicted decrease of intelligibility was caused by the estimated noise envelope power exceeding that of the speech. The classical concept of the speech transmission index fails in this condition. The results strongly suggest that the signal-to-noise ratio at the output of a modulation frequency selective process provides a key measure of speech intelligibility.