Threshold-diversity-induced resonance

The effect of diversity on a system of coupled threshold elements is investigated, where each element is driven by a common periodic signal. Diversity is introduced to the system by assuming that the thresholds of all units are heterogeneous, e.g. the thresholds follow a Gaussian or other distribution. A combined numerical and analytical approach shows that the response of the system to the input signal is maximized at a moderate value of the diversity amplitude, which is similar to the well-known stochastic resonance phenomenon induced by noise. Our findings exhibit that the diversity, a kind of spatial disorder, may play a similar role to noise as a kind of temporal disorder.     

Stochastic resonance in threshold devices

Summary We consider the transmission of a periodic signal by noisy threshold devices. A general expression for the input-output characteristic is developed and applied to two particular threshold devices. It is shown that the amplitude of the signal output shows in the subthreshold regime a maximum as a function of the noise strength—the fingerprint of stochastic resonance. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba 5–10 June 1994.     

基于分数阶可停振动系统的周期未知微弱信号检测方法

本文建立了分数阶可停振动系统, 其可停振动状态的改变对周期策动力敏感, 对零均值随机微小扰动不敏感, 这事实上为周期未知微弱信号检测提供了一种新的高效检测方法和判别标准. 与现有的利用混沌系统的大尺度周期状态变化检测周期未知弱信号的方法 需逐一尝试设置不同频率内置信号以便期望与待检周期信号发生共振不同, 利用分数阶可停振动系统的可停振动状态变化检测周期未知微弱信号的方法, 除了同样具有因为状态变化对周期信号的敏感性而能够实现极低检测门限的特点外, 还具有混沌系统信号检测所不具有的优点: 1)无需预先估计待检信号的周期; 2)无需计算系统状态的临界阈值; 3)可停振动状态可由本文设计的指数波动函数可靠地进行判断; 4)通过系统微分阶数的变化, 将检测系统层次化, 从而可得到比整数阶检测系统更低的检测门限, 特别是在色噪声环境下, 通过选取合适的微分阶数, 基于分数阶可停振动系统的微弱周期信号检测法能够大幅度的降低检测门限, 在本文的仿真试验中, 检测门限可达-182 dB. 关键词： 分数阶非线性系统 Duffing振子 弱信号检测     

Spatiotemporal stochastic resonance in a bistable FitzHugh-Nagumo ring with phase-repulsive coupling

In this paper, we numerically study a ring of bistable FitzHugh-Nagumo elements coupled in a phase-repulsive way, which are externally driven by a weak periodic signal and noises, and focus on the system’s response. A novel type of spatiotemporal stochastic resonance of antiphase state is uncovered, namely, for an intermediate strength of individual noise, the elements can form an “...-upper-lower-upper-lower-...” antiphase structure along the ring, and the global activation oscillates nearly synchronously with the weak periodic signal. Meanwhile, the system response undergoes a resonant behavior with the intensity of noise. It is shown that the combinative effects of the periodic signal, noise, and coupling are of importance for its appearance. The influences of common and individual noises are also investigated.     

Non-Gaussian,non-dynamical stochastic resonance

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the “most” periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.     

Hysteresis studies in a noisy autoassociative neural network

We define magnetization for a noisy autoassociative neural network driven by an external periodic field. Numerical simulations are carried out to investigate the effect of drive amplitude and frequency and noise strength on the area of the hysteresis loop. We observe that in the presence of weak periodic signal, the network exhibits a maximum in the hysteresis loop area at a nonzero noise intensity indicating maximum synchronization between the periodic signal and the response. It also goes through a maximum as a function of signal frequency.     

Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter

Stochastic resonance (SR) has become a well-known phenomenon that can enhance weak periodic signals with the help of noise. SR is an interesting phenomenon when applied to signal processing. Although it has been proven that SR does not always improve the signal-to-noise ratio (SNR), in a strongly nonlinear system such as simple threshold system, SR does in fact improve SNR for noisy pulsed signals at appropriate noise strength. However, even in such cases, when noise is weak, the SNR is degraded. Since the noise strength cannot be known in advance, it is difficult to apply SR to real signal processing. In this paper, we focused on the shape of the threshold at which SR did not degrade the SNR when noise was weak. To achieve output change when noise was weak, we numerically analyzed a sigmoid function threshold system. When the slope around the threshold was appropriate, SNR did not degrade when noise was weak and instead was improved at suitable noise strength. We also demonstrated SNR improvement for noisy pulsed voltages using a CMOS inverter, a very common threshold device. The input-output property of a CMOS inverter resembles the sigmoid function. By inputting the noisy signal voltage to a CMOS inverter, we measured the input and output voltages and analyzed the SNRs. The results showed that SNR was effectively improved over a wide range of noise strengths.     

基于BP神经网络的图像质量评价参数优化

 在基于噪声图像的无参考峰值信噪比质量评价方法中,为了得到最优的阈值参数,提出以图像块均方误差阈值threshold1、噪声检测阈值threshold2为输入因子, 以Pearson相关系数和Spearman等级相关系数为输出因子, 以实验值为样本建立［2 7 2］单隐层BP神经网络模型,应用BP神经网络的泛化能力实现对相关阈值参数的预测优化,为阈值参数的选择提供理论依据。实验结果表明,所建立的数学模型可靠,预测结果与试验值的偏差小,训练好的BP神经网络能够比较准确地预测不同阈值参数下的相关系数。优化后,选取threshold1=101,threshold2=4,Pearson相关系数达到了-0.895 0,Spearman等级相关系数达到了-0.913 6,评价效果得到提高,且节省大量时间。     

Stochastic resonance in a nonequilibrium electron-hole plasma

A photogenerated electron-hole plasma, heated in the process of Auger recombination, is studied. It is shown that in the plasma near the threshold for the appearance of uniform relaxational self-excited oscillations, weak noise transforms into a stochastic sequence of large-amplitude spikes. An additional optical periodic signal with amplitude approximately five times smaller than the noise variance, depending on the form of this signal, transforms these stochastic oscillations into low-amplitude quasiharmonic oscillations or into periodic spike self-excited oscillations of enormous amplitude. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 422–427 (10 October 1999)     

Coherence and stochastic resonance in threshold crossing detectors with delayed feedback

We consider the dynamical behavior of threshold systems driven by external periodic and stochastic signals and internal delayed feedback. Specifically, the effect of positive delayed feedback on the sensitivity of a threshold crossing detector (TCD) to periodic forcing embedded in noise is investigated. The system has an intrinsic ability to oscillate in the presence of positive feedback. We first show conditions under which such reverberatory behavior is enhanced by noise, which is a form of coherence resonance (CR) for this system. Further, for input signals that are subthreshold in the absence of feedback, the open-loop stochastic resonance (SR) characteristic can be sharply enhanced by positive delayed feedback. This enhancement is shown to depend on the stimulus period, and is maximal when this period is matched to an integer multiple of the delay. Reverberatory oscillations, which are particularly prominent after the offset of periodic forcing, are shown to be eliminated by a summing network of such TCDs with local delayed feedback. Theoretical analysis of the crossing rate dynamics qualitatively accounts for the existence of CR and the resonant behavior of the SR effect as a function of delay and forcing frequency.     

Noise reduction in pulse-code-modulated images by optical regenerative repeaters

Digital signal transmission in electronic communication links provides the possibility of periodic reshaping of the electronic pulses by so-called regenerative repeaters, thereby keeping the signal above the noise level. This concept of noise minimization is applied to the optical transmission of pulse-coded images. Optical elements are described which correspond to the regenerative repeaters used in electronic transmission systems. They are based on holographic as well as incoherent methods. Examples illustrating the basic idea are provided.     

Propagation of firing rate in a feed-forward neuronal network

Propagation of the firing rate and synchronous firings in a 10-layer feed-forward neuronal network are studied. When neurons in layer 1 are subject to white noise, synchrony can be built up in deep layers and the firing rate can be propagated. A network with 6 layers is found to be enough for such behavior. A periodic signal with frequencies of 30-80 Hz can be selectively transmitted through the network. These abilities in information processing due to synchrony can be modulated by noise and the operating mode of neurons, and our results are relevant to experimental findings.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

混沌背景中微弱信号检测的神经网络方法

基于复杂非线性系统相空间重构理论，提出了混沌背景中微弱信号检测的神经网络方法，利用神经网络强大的学习和非线性处理能力，建立了混沌背景噪声的一步预测模型，从预测误差中检测淹没在混沌背景噪声中的微弱目标信号(包括周期信号和瞬态信号)，研究了混沌背景中存在白噪声时该方法的检测能力，指出了目标信号为瞬态信号和周期信号时检测原理的异同点，最后以Lorenz系统作为混沌背景噪声进行了仿真实验，实验表明该方法能有效地将混沌背景中极其微弱的信号检测出来. 关键词： 混沌 神经网络 信号检测     

调制与解调用于随机共振的微弱周期信号检测

提出了调制随机共振方法，实现了在大参数条件下从强噪声中检测微弱周期信号.将混于噪声中的较高频率的弱信号经调制变为一差频的低频信号作用于随机共振体系，该低频信号满足绝热近似理论，因而能产生随机共振；再经解调可获得埋于噪声中的原较高频率的弱信号.对埋于噪声中的未知频率，可采用连续改变调制振荡器的频率，以获得一个适当的差频信号输入到随机共振体系，根据输出信号共振谱峰的变化经解调而得待检弱信号的未知频率.该方法应具有较高的应用前景. 关键词： 调制与解调 非线性双稳系统 随机共振 微弱信号检测     

Comparative Analysis of Different Statistics for Detecting Spatial Signals in the Case of Short Samples

In this paper, we perform comparative analysis of several algorithms for signal processing in an antenna array used for determining multidimensional Gaussian complex signals with an a priori unknown spatial covariance matrix against the background of Gaussian noise. All the studied decision statistics are obtained on the basis of generalized likelihood ratio for arbitrary-size samples. Depending on the available a priori information on the received signal and noise, we consider three cases of noise background, namely, nonuniform noise over the antenna elements with unknown power, uniform noise with unknown power, and uniform noise with known (unit) power. To determine the threshold values of the decision statistics, their probability densities are expanded in a series in terms of orthogonal Jacobi polynomials. Detection curves are constructed for all considered cases on the basis of obtained thresholds. The obtained results are valid for short samples whose size is comparable with the number of elements in the receiving antenna.     

Temporal gap resolution in narrow-band noises with center frequencies from 6000-14000 Hz

Temporal resolution was examined in normal-hearing subjects using a broadband noise and five narrow-band noises with center frequencies (fc) spaced 2 kHz apart between 6 and 14 kHz. Bandwidths of the narrow-band signals were equal to 0.16 fc, and broadband noise maskers with spectral notches were used to restrict the listening bands. Subjects used a Békésy procedure to track the minimum signal level required to keep a periodic temporal gap of fixed duration at threshold. Gap durations from 25 ms to the smallest trackable value were tested with each signal to generate performance curves, which showed the relationship between gap resolution and signal level in the low-to-moderate intensity range. Results showed that gap resolution improved progressively with increased signal level to about 35 dB SL, where minimum gap thresholds of about 3 ms were observed for all signals. These results, when combined with previous low-frequency data, indicate that gap threshold decreases systematically with increased signal frequency to about 5 kHz, and asymptotes at 2-3 ms for higher frequencies. In the context of functional models, the frequency effect is qualitatively consistent with the notion that both the auditory filter and a sensory integrator operate in series to govern temporal resolution in audition.     

基于随机共振原理的分段线性模型的理论分析与实验研究

提出了一种分段线性双稳态模型, 推导了模型的解析关系及其输出信噪比, 通过对该模型与连续双稳态模型的对比分析和仿真实验, 证明了该模型的优越性.该模型具有参数之间相互独立、易于调节的特点. 在对模型分析与数值仿真的基础上, 通过电路对强噪声背景下的微弱周期信号检测进行了实验研究. 结果表明分段线性随机共振模型能够有效实现对微弱周期信号的检测, 并能显著增强输出信噪比.     

时滞与噪声影响 Notch信号通路动力学的模型化研究

本文基于Hill动力学与Michaelis-Menten方程,建立理论模型研究时滞与噪声影响Notch信号通路动力学.研究发现,her1、her7基因转录的时滞性在很大程度上调控着Notch信号通路的动力学行为.由于时滞性的调控,Notch系统动力学经历Hopf分岔,由稳态转变为周期演化特性.通过考察Notch信号通路的噪声效应,我们发现,由于噪声的扰动,Notch系统周期振荡动力学改变.在较小噪声幅值条件下,Notch信号通路中改变的周期节律性可以通过时滞得以平衡恢复,由此表明了her1、her7转录的时滞性促进了Notch信号通路的周期振荡.对于较强噪声环境,时滞效应很难改变Notch信号的巨大突变,其信号通路动力学行为被噪声影响.理论结果符合实验,并揭示了时滞与噪声对Notch信号通路动力学的一种调控机制,可为设计阻止Notch功能异常导致的多种疾病和癌症的通路治疗方案提供理论依据.     

Sensitive signal detection using a feed-forward oscillator network

We present the results of an experimental investigation of a network of nonlinear coupled oscillators which are coupled in feed-forward mode. By exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point, we have found remarkable amplification of small signals over a narrow bandwidth with a large dynamic range. The effect is exploited to extract a small amplitude periodic signal from an input time series which is dominated by noise. Specifically, we have used this relatively simple experimental system to measure responses with a bandwidth of approximately 1% of the central frequency, amplifications of approximately 60 dB, and a dynamic range of approximately 80 dB and can extract signals from a time series with a signal to noise ratio of approximately -50 dB.