噪声改善码元传输

文中运用随机共振来改善码元的传输。对于由字符构成的文本,通过编码生成一系列的码元作为系统输入信号,经过带有噪声的系统传输后,进行译码得到接收文本。文中使用的噪声为高斯型的加性与乘性噪声,逐渐增加噪声强度,接收文本中出错字符比例先降低再增高,从而存在最佳噪声强度,此时出错比例最小,系统性能最好。另外,乘性噪声在改善信号传输时,表现出了一定的鲁棒性。最后,讨论了阈值单元数目与系统阈值的变化对系统性能的影响。     

Stochastic Resonance and Coincidence Detection in Single Neurons

We demonstrate that a realistic neuron model expressed by the Hodgkin-Huxley equations shows a stochastic resonance phenomenon, by computing cross-correlation between input and output spike timing when the neuron receives both aperiodic signal input of spike packets and background random noise of both excitatory and inhibitory spikes. We consider that such a signal detection is realized because the neuron with active properties is sensitive to fluctuation caused by a sharp increase just after a sudden dip of excitatory noise spikes and a gradual decrease of inhibitory noise spikes. We also show that the model generates highly irregular firing of output spikes on the basis of the modulation detecting property.     

语音信号传输过程中的阈上随机共振现象

对利用阈上随机共振现象来改善语音信号的传输进行了研究.在理论上,选取输入输出互相关系数作为测度,用拉普拉斯信号模拟语音信号,研究了拉普拉斯信号在多阈值系统中受到加性高斯噪声和乘性高斯噪声作用下的阈上随机共振现象.在实际应用中,同样选取输入输出互相关系数作为测度,用真实的语音信号作为输入信号,在受到加性高斯噪声和乘性高斯...     

Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Theta neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Theta neuron model is obtained only in the Stratonovich interpretation of the stochastic Theta neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.     

Optical neuron by use of a laser diode with injection seeding andexternal optical feedback

We present an all-optical neuron by use of a multimode laser diode that is subjected to external optical feedback and light injection. The shape of the threshold function, that is needed for neural operation, is controlled by adjusting the external feedback level for two longitudinal cavity modes of the laser diode individually. One of the two modes corresponds to the output of the neuron, light injection at the wavelength of this mode provides excitatory input. Light injection in the other mode provides inhibitory input. When light corresponding to two input signals is injected in the same mode, summation of input signals can be achieved. A rate-equation model is used to explain the operating principle theoretically. The proposed injection seeding neuron is built using free-space optics to demonstrate the concept experimentally. The results are in good agreement with the predictions from the rate-equation model. Some experimental results show threshold functions that are preferable from a neural-network point of view. These results agree well with injection locking theory and experiments reported in literature.     

神经元网络模型的弱信号随机共振检测研究

基于FitzHugh-Nagumo可兴奋细胞耦合后形成的神经元网络模型,对生物神经系统的弱周期信号随机共振检测机制进行研究。以加和网络的双层FHN神经元模型为例,对周期随机共振现象分别进行研究,并应用信噪比、互信息率对比评价方法,结合输出神经元动作电位的发放频率和幅值,从多个角度进行了定量和定性的描述和比较。实验结果表明,双层FHN神经元网络的随机共振响应优于单神经元的FHN模型,且具有更好的稳定性,可以在一定的噪声强度范围内对输入信号进行有效地检测。     

Adaptive stochastic resonance in noisy neurons based on mutual information

Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This work presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.     

离散时间系统中随机谐振研究

摘要：基于一种新的信噪比的定义讨论了在四种经典噪声下在离散时间系统中的随机谐振现象。当输入信号是阈上信号时,噪声总是在恶化信号的传输,即随着噪声强度增加,输出信噪比呈现单调递减的趋势。然而当输入信号是阈下信号时。适当的噪声能够引起系统最优反应,即随着噪声强度的增加,输出信噪比达到一个最大峰值,也即存在明显的随机谐振现象。随着非线性系统中阈值的增加,随机谐振现象的明显度降低,当最佳噪声强度在增加时,输出信噪比的最优值却在减少。文中结果也说明,基于新的信噪比的定义是可以用来度量一个离散时间系统的随机谐振现象,且随机谐振对噪声具有一定的鲁棒性,拓广了随机谐振在信息传输领域的应用。     

突触噪声作用下的IF阈值神经元模型的随机共振

基于带阈值的积分放电模型研究了神经元在突触递质噪声和周期信号驱动下的随机共振现象.利用平均法得到系统输出幅值增益的精确表达式,考察了输出幅值增益与信号频率、噪声强度、相关时间及非对称度的关系.发现输出幅值增益随着这些参量的演化曲线在一定条件下呈非单调的,这些都表明在突触递质噪声和周期信号驱动下的神经发放确实存在随机共振现象.     

双稳随机共振系统信号调制噪声效应用于弱信号检测

通过对双稳系统随机共振模型的数值分析，得出在双稳系统输出信号中，有一个正弦信号成分和一个表现为维纳过程的噪声成分分别与输入的正弦信号和白噪声相对应。通过选择合适的系统参数，可以减小系统输出中信号和噪声之间的耦合效应。该系统可以大大抑制噪声，并在双稳系统中产生信号调制噪声效应。然后对双稳系统的输出信号作功率谱分析。不但可以辨识出淹没在白噪声中的微弱正弦信号的频率，还可以较精确地估算出微弱正弦信号的幅值。数值仿真表明，双稳系统的信号调制噪声效应可用于多个微弱正弦信号的检测。     

Precision constrained stochastic resonance in a feedforward neural network

Stochastic resonance (SR) is a phenomenon in which the response of a nonlinear system to a subthreshold information-bearing signal is optimized by the presence of noise. By considering a nonlinear system (network of leaky integrate-and-fire (LIF) neurons) that captures the functional dynamics of neuronal firing, we demonstrate that sensory neurons could, in principle harness SR to optimize the detection and transmission of weak stimuli. We have previously characterized this effect by use of signal-to-noise ratio (SNR). Here in addition to SNR, we apply an entropy-based measure (Fisher information) and compare the two measures of quantifying SR. We also discuss the performance of these two SR measures in a full precision floating point model simulated in Java and in a precision limited integer model simulated on a field programmable gate array (FPGA). We report in this study that stochastic resonance which is mainly associated with floating point implementations is possible in both a single LIF neuron and a network of LIF neurons implemented on lower resolution integer based digital hardware. We also report that such a network can improve the SNR and Fisher information of the output over a single LIF neuron.     

Noise in integrate-and-fire neurons: from stochastic input to escape rates

We analyze the effect of noise in integrate-and-fire neurons driven by time-dependent input and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a gaussian dependence on the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.     

基于神经元阈上非周期随机共振机制的语音复原技术研究

应用随机共振机制.通过噪声能量来加强语音信号,改善低信噪比语音的输出质量.对FitzHugh-Nagumo(FHN)神经元模型中存在的阈上非周期随机共振现象进行了分析,根据其阈值特性,此二维神经元模型可被等价为两状态的阈值跨越非线性动力学系统.因此对含噪语音信号添加噪声,产生阈值化后的二值输出,经迭代收敛进入阈上非周期随机共振状态.在一个非零添加噪声强度上,含噪语音输出的互相关系数将达到最大值.通过语音复原的结果表明,本文方法对噪声的变化有更好的鲁棒性,尤其在强背景噪声下,随机共振方法较其他传统方法有更佳的复原效果.     

极大并联阈值网络中噪声改善信号的相关性

讨论了极大并联阈值网络中噪声改善信号相关性问题。当输入噪声为单峰高斯噪声时，输入信号在阈下时噪声才能改善信号的相关性，即随机谐振现象存在。而当输入噪声为双峰高斯混合噪声时，不仅输入信号在阈下时随机谐振现象有时存在，而且输入信号在阈上时噪声往往也能改善信号的相关性，即阈上随机谐振现象存在。噪声改善信号相关性随着网络中单元数的调整而改善。这些结果进一步说明了随机谐振或阈上随机谐振对噪声分布的依赖性，同时也拓广了随机谐振或阈上随机谐振在数字信号处理方面的应用。     

Dynamics of the firing probability of noisy integrate-and-fire neurons

Cortical neurons in vivo undergo a continuous bombardment due to synaptic activity, which acts as a major source of noise. Here, we investigate the effects of the noise filtering by synapses with various levels of realism on integrate-and-fire neuron dynamics. The noise input is modeled by white (for instantaneous synapses) or colored (for synapses with a finite relaxation time) noise. Analytical results for the modulation of firing probability in response to an oscillatory input current are obtained by expanding a Fokker-Planck equation for small parameters of the problem - when both the amplitude of the modulation is small compared to the background firing rate and the synaptic time constant is small compared to the membrane time constant. We report here the detailed calculations showing that if a synaptic decay time constant is included in the synaptic current model, the firing-rate modulation of the neuron due to an oscillatory input remains finite in the high-frequency limit with no phase lag. In addition, we characterize the low-frequency behavior and the behavior of the high-frequency limit for intermediate decay times. We also characterize the effects of introducing a rise time to the synaptic currents and the presence of several synaptic receptors with different kinetics. In both cases, we determine, using numerical simulations, an effective decay time constant that describes the neuronal response completely.     

Competition and cooperation in neuronal processing

A new type of model neuron is introduced as a building block of an associative memory. The neuron, which has a number of receptor zones, processes both the amplitude and the frequency of input signals, associating a small number of features encoded by those signals. Using this two-parameter input in our model compared to the one-dimensional inputs of conventional model neurons (e.g., the McCulloch Pitts neuron) offers an increased memory capacity. In our model, there is a competition among inputs in each zone with a subsequent cooperation of the winners to specify the output. The associative memory consists of a network of such neurons. A state-space model is used to define the neurodynamics. We explore properties of the neuron and the network and demonstrate its favorable capacity and recall capabilities. Finally, the network is used in an application designed to find trademarks that sound alike.     

Stochastic Resonance and Optimal Detection of Pulse Trains by Threshold Devices

The nonlinear detection by a threshold device of a periodic train of soliton-like pulses embedded in arbitrarily distributed white noise is studied. A theoretical model is developed which provides expressions for the signal-to-noise ratio at the output of the detector and for the input–output gain in signal-to-noise ratio. We analyze the properties and conditions of optimality for these quantities as functions of the parameters of the process. Especially, specific nonlinear properties not shared by linear devices are established, among which are the possibility of an input–output amplification of the signal-to-noise ratio and the demonstration that through nonlinear coupling the noise can be beneficial to the signal detection and that adding noise may result in improved performance via a mechanism known as stochastic resonance.     

带输入饱和的不确定非线性系统自适应模糊触发式补偿控制

针对一类带有输入饱和特性的不确定非线性系统,为了在保证系统跟踪性能的同时最大限度节省系统通讯资源,结合Backstepping技术,提出一种自适应模糊触发式补偿控制方法.由于安全需求或者物理限制等因素,输入饱和特性往往不可避免地存在于实际物理系统中,给系统的控制性能和稳定性造成不利影响.为有效解决该问题,将光滑的双曲正切函数融入自适应控制设计过程,以实现对系统输入饱和约束的补偿.此外,由于实际系统模型难以精确建立,系统描述中难免会存在未知不确定部分,对此,利用模糊逻辑系统对系统的未知不确定部分进行逼近处理.为节省系统的通讯资源,引入一种基于相对阈值的事件触发控制策略,以减小系统传输压力.通过Lyapunov 稳定性理论分析,系统的所有信号都是半全局一致最终有界的.仿真结果验证了所提出方法的有效性.     

Reconstruction of chaotic dynamics via a network of stochastic resonance neurons and its application to speech

Recently, a great deal of attention has been paid tostochastic resonance as a new framework to understand sensory mechanisms of biological systems. Stochastic resonance explains important properties of sensory neurons that accurately detect weak input stimuli by using a small amount of internal noise. In particular, Collins et al. reported that a network of stochastic resonance neurons gives rise to a robust sensory function for detecting a variety of complex input signals. In this study, we investigate effectiveness of such stochastic resonance neural networks to chaotic input signals. Using the Rössler equations, we analyze the network's capability to detect chaotic dynamics. We also apply the stochastic resonance network systems to speech signals, and examine a plausibility of the stochastic resonance neural network as a possible model for the human auditory system.     

一种基于非周期随机共振的微弱信号检测方法

随机共振滤波器能够在强噪声背景中跟踪微弱信号(非周期或周期信号)波形,并将幅度放大,这正好弥补了匹配滤波器在强噪声背景下检测性能的严重不足。本文给出了FHN随机共振的简化模型及计算方法,在深入分析FHN随机共振模型参数对其滤波性能影响的基础上,结合随机共振滤波器和匹配滤波器,提出了一种基于FHN随机共振模型检测确知信号的方法。首先将接收信号经FHN随机共振滤波器进行滤波,再进行匹配滤波,最后将滤波结果和门限进行比较判断信号是否存在。经过实验验证,该方法具有较好的效果。