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This study presents the performance of the auto-correlation methods for detecting weak signals, where the signal level is much less than the noise level. Double and triple auto-correlation techniques are used to improve the detection performance compared with the single autocorrelation. Simulation results obtained by MATLAB programs show that the multiple correlation techniques outperform the single correlation in terms of probability of detection and probability of false alarm versus signal to noise ratio SNR.

Stochastic resonance can detect weak periodic signals from strong background noise without loss of signal energy. However, the classical bistable stochastic resonance has the inherent outp...

Particles moving in confined regions with bistable potential driven by weak signal and fluctuations may present a similar stochastic resonance (SR). This similar SR is called entropic stochastic resonance (ESR). The phenomenon of ESR in a confined asymmetrical bistable potential driven by a transverse periodic force is investigated when a non-Gaussian fluctuation is considered in the system. The left potential of the bistable system can be adjusted by introducing the asymmetrical ratio α. By the functional analysis and two-state theory, the approximate Signal-to-Noise ratio (SNR) is derived. It is found that there is a global maximum in the SNR curves when the asymmetrical ratio α and the noise intensity D are changed. It is also shown that the noise correlation time τ will suppress the ESR of the system and the departure q can obviously change the position of peak in the SNR. The above clues are helpful in achieving weak signal detection under irregular, small-scale systems.

This paper presents a minimum signal model via the AC small-signal model and the uncertainty principle, which reveals the minimum AC signal that can be amplified by a bipolar transistor. The Ebers—Moll model (EM3) can describe the small signal amplification process, but it is difficult to define the minimum amplifiable signal of the bipolar transistor. In this study, the correspondence relationship between the non-equilibrium carrier and the electric injection is proved, and the relationship between the life of the non-equilibrium carrier and the measurable signal is proposed by the uncertainty principle. Next, the limit of perceived minimum voltage is also derived in this paper. Then, combining with EM3 model, the minimum AC signal model of bipolar transistor is presented to calculate the minimum voltage signal of bipolar transistor that can be amplified. Finally, a number of the simulation and experiment results show that when the minimum signal in the model is used as input, the carrier concentration of the bipolar transistor does not change and the base electrode cannot perceive the signal, which verifies the validity of the minimum AC signal model.

The kinetic behavier of the Duffing system is analyzed. The state changes of the Duffing system are studied. The main process is composed of the inner orbits state, the bifurcation state, the chaotic state, the chaotic critical state and the large-scale periodic state. Let the weak signal of the noise be the trigger condition that change the inner state of the Duffing system, the Duffing system applied in the weak signal detection is discussed. At last, the validity of this method is validated by the simulation.

This paper investigates the propagation of the weak aperiodic signal in a parallel array of FitzHugh–Nagumo (FHN) neurons with heterogenous aperiodic high-frequency (HAHF) disturbances. Different from the traditional vibrational resonance, where the optimal amplitudes of the HF driving signal should be tuned for individual elements, the ability of the proposed averaging parallel array network for weak signal detection can be optimized at a fixed amplitude of the HAHF disturbance, regardless of the nature of the input signal. Local connections in the parallel array network are found to be important for the propagation of weak signal in parallel array. Besides, the characteristics of high-frequency signal such as heterogeneity and frequency, can also modulate the propagation of aperiodic signal in parallel array.

Stochastic resonance (SR), as a typical noise-assisted signal processing method, has been extensively studied in weak signal detection by virtue of the advantage of using noise to enhance the feature of periodic signal. And how to better apply the SR method in engineering signal processing has always been the research hotspot. In this paper, a novel adaptive SR method based on coupled bistable systems (ACBSR) is proposed to further improve the performance of SR method for weak signal detection. Compared with the cascaded bistable SR system, the suggested coupled bistable SR (CBSR) system can enhance the target signal while suppressing the low-frequency and high-frequency interferences, whose output behavior exhibits good bandpass filtering characteristic. In addition, a weighted spectral peak signal-to-noise ratio (WPSNR) index is constructed by using spectral peak SNR, spectral correlation coefficient and zero-crossing ratio to serve as the measurement index of SR for periodic signal detection. The constructed WPSNR index is simple in form and easy to calculate, which can quantitatively evaluate the resonance effect of periodic signal, even though the target signal frequency cannot be estimated accurately. And the combination of WPSNR index and the CBSR system is beneficial to improve the performance of SR method in rolling bearing fault diagnosis. Experiments and engineering application are performed to verify the effectiveness and superiority of the proposed ACBSR method in comparison with the traditional SR method.

To efficiently extract the features of aeroengine intershaft bearing faults with weak signal, the variational mode decomposition (VMD) method based on the tolerant adaptive genetic algorithm (TAGA) (TAGA-VMD) is proposed by introducing the idea of tolerance into the traditional adaptive genetic algorithm in this paper. In this method, the tolerant genetic algorithm was adopted to find the optimum empirical parameters K and α of VMD. A fault simulation experiment system of intershaft bearings was built for the inner ring fault and outer ring fault of bearings to verify the proposed TAGA-VMD method. The results show that the proposed method can effectively extract the fault feature frequency of intershaft bearings, and the error between the extracted fault feature frequency and the theoretical value of fault frequency is less than 0.1%. The efforts of this study provide one promising fault feature extraction approach for aeroengine intershaft bearing fault diagnosis with weak signal.

In this study, Stochastic resonance phenomenon in Morris-Lecar neurons was investigated. Obtained results showed that Stochastic resonance occurs in all classes of Morris-Lecar neuron. It is also observed that the weak signal detection performance of Type I neurons are significantly high compared the weak signal detection performance of Type II and III neurons at the optimal noise intensity. In addition, it is seen that the signal detection frequency range of Morris-Lecar neurons are similar for all classes. However, it was noticed that the threshold of amplitude ensuring firing in Type III neurons was higher than Type I and II neurons.

The normal diffusion effect is introduced as a new regulating factor into the established diffusive coupling model for bistable oscillator networks. We find that the response of the system to the weak signal is substantially enhanced by the anormal diffusion, which is termed anormal-diffusion-induced resonance. We also reveal that the diffusive coupling-induced transition, which changes the system from a bistable to a monostable state, is of fundamental importance for the occurrence of resonance. The proposed approach is validated using simulation studies and theoretical analyses. Our results suggest that diffusion induced resonance can be more easily observed in nonlinear oscillator networks.

A recently proposed deconvolution method applied to conventional beamforming (CBF) shows a much higher array gain (AG) than CBF in theory, thereby providing the possibility for detecting a weak signal with a much lower signal-to-noise ratio (SNR). However, simulated data processing shows an effective AG that decreases with decreasing SNR. The reason for the performance loss is analyzed. A method based on deconvolution of the signal subspace of the CBF outputs is shown to recover most of the AG loss. It is used to trace a weak signal in bearing and time.

The existing Duffing oscillator weak signal detection method will lead to the degradation of detection performance when the noise is strong. In order to reduce detection signal-to-noise ratio and improve the detection performance, a weak signal detection method based on Duffing oscillator phase transition rate is proposed. This method uses the phase transition rate of Duffing oscillator to judge, which can effectively reduce the detection error caused by pure noise, and further improve the performance of weak signal detection. Compared with the existing methods, the lower limit of detection signal-to-noise ratio is reduced by 2dB.

We study the alignment of radio galaxies axes using the FIRST catalogue. we impose several cuts in order to select the candidates which are most likely to be free of systematic bias. In our study we primarily focus on testing for alignment among sources within a certain angular separation from one another since for most sources redshift information is not available. We find a very significant effect for angular distances less than 1 degrees. The distance scale of alignment is found to be roughly 28 Mpc, in agreement with earlier estimates, assuming that these sources are dominantly at redshift of 0.8. However we are not able to entirely rule out the possibility of systematic bias in data. We also perform a full three dimensional analysis using a smaller data sample for which redshift information is available. In this case we only find a very weak signal at much larger distances., Comment: 7 pages, 10 figures, to appear in MNRAS

This paper proposes a new system whose potential function is with three types of asymmetric potential wells, driven by trichotomous noise. Firstly, the three types of asymmetric bistable system are described in detail, and the changes of asymmetric bistable system potential function under different asymmetric factors are analyzed. Secondly, the effect of potential function parameters, asymmetric factorα, noise intensity D, and the probability of particle transition q is discussed, using numerical simulation. The detection effects of traditional symmetric SR and three types of asymmetric SR are observed and compared under the driving of trichotomous noise and periodic signals. The mean of signal-to-noise ratio gain is the indicator of the system's effectiveness on enhancing weak signal. The results indicate that it can make the detection effect of the asymmetric system better than that of the traditional bistable system by adjusting the parameters of the asymmetric stochastic resonance system and trichotomous noise.

Forty years ago saw the introduction of stochastic resonance — the counter-intuitive idea that noise may help a nonlinear system respond to a weak signal.

This paper develops a prototype signal readout system based on the physical mechanism and signal-to-noise ratio of the ultralow voltage signal characteristics of a bolometer. The preamplifier module is one of the key difficulties of the prototype: the internal resistance is as high as one hundred MΩ, the signal frequency band is susceptible to low-frequency noise, and the high energy resolution requires a high signal-to-noise ratio that is matching the input impedance to design a preamplifier with a good common-mode rejection ratio and low inherent noise. Therefore, the preamplifier circuit is designed with an instrument amplifier. At present, the energy resolution of the bolometer is 500 ~ 1000 nV (root mean square, rms) at the input of the signal readout system. According to the calculation, the theoretical value of the inherent noise at the input end is 394 nVrms, including a theoretical value for the equivalent input voltage noise of 166 nVrms, while the actual measurement value is less than 180 nVrms, which is basically consistent with the theoretical value. In addition, the signal gain (10,000) and frequency response of the prototype are experimentally verified. The experimental results show that the gain is 9400, and the frequency and waveform are not distorted within the allowable error range; all of these parameters meet the design requirement.

We investigate a system of globally coupled bistable oscillators subjected to a common weak signal, where the couplings are oscillator dependent with random signs: positive or negative. We find that neither purely positive nor purely negative couplings are optimal for signal amplification of the system; a mixture of both positive and negative couplings is more beneficial for the signal amplification. Our numerical results further show that different from the fully synchronous state caused by purely positive couplings or asynchronous state caused by purely negative couplings, the mixed positive and negative couplings can generate a clustering synchronous state, which allows the system to generate a resonancelike response to the weak signal, and thus, amplifies the signal. We finally propose a reduced model to analyze the mechanism underlying this resonancelike behavior, and find a complementary effect of these two types of couplings in signal amplification.

In radio-based physics experiments, sensitive analysis techniques are often required to extract signals at or below the level of noise. For a recent experiment at the SLAC National Accelerator Laboratory to test a radar-based detection scheme for high energy neutrino cascades, such a sensitive analysis was employed to dig down into a spurious background and extract a putative signal. In this technique, the backgrounds are decomposed into an orthonormal basis, into which individual data vectors (signal + background) can be expanded. This expansion is a filter that can extract signals with amplitudes $\sim$1 % of the background. This analysis technique is particularly useful for applications when the exact signal characteristics (spectral content, duration) are not known. In this proceeding we briefly present the results of this analysis in the context of test-beam experiment 576 (T576) at SLAC., Prepared for the ACAT2019 conference. Submitted on behalf of the T576 collaboration

Planetary gearbox is an important part of the mechanical devices, but the fault-induced impulses that induced by the fault and submerged in strong noise are too weak to be detected. Stochastic resonance (SR) can improve the weak signal with the help of noise, which suits the detection of the weak signal. Bi-stable SR (BSR) is the most classical SR and has been used for the mechanical fault diagnosis. Varying-stable SR (VSR), whose potential is the varying-stable potential, is proposed for the planetary gearbox diagnosis. Unlike the bi-stable potential, the number of varying-stable potential well is different under different parameters, which enhances the SR effect. To verify the proposed method, two planted fault tests of the planetary gearbox are carried out. For comparison, the fault signals are analyzed by BSR and VSR respectively. The results prove that VSR is feasible for the planetary gearbox diagnosis and more effective than BSR.

The correlation detection and adaptive line spectrum enhancement(ALE) algorithm in weak signal detection is presented. Aiming at the problem that the traditional ALE has no obvious effect of line spectrum enhancement at low signal-to-noise ratio(SNR), we propose a modified ALE algorithm based on coherent integrator. Combining this ALE and sliding window correlation, the effect of ALE is clearly improved. The simulation results show that the weak signal receiving ability can be improved by 8 dB under the same line spectrum condition.

Вибрано та адаптовано метод аналізу ієрархій для оцінювання сигналів впливу на підприємство. Запропоновано обчислення узагальненого інтегрального сигналу впливу на підприємство здійснювати шляхом скалярного множення вектора локальних пріоритетів груп сигналів на вектор глобальних пріоритетів сигналів у кожній групі. Розроблено метод виявлення слабких сигналів, який ґрунтується на порівнянні порогової величини, яка визначається експериментальним шляхом, з різницею між біжучим та прогнозованим значеннями узагальненого інтегрального сигналу впливу на підприємство. Показано, що використання методу управляння за слабкими сигналами забезпечує підприємству завчасне нарощування запасу гнучкості для усунення небезпек на ранніх стадіях їх виникнення.

It has been found that a triple-node feed-forward motif has a function of signal amplification, where two input nodes receive the external weak signal and jointly modulate the response of the third output node [Liang et al., Phys. Rev. E 88 (2013) 012910]. We here show that the signal amplification can be further enhanced by adding a link between the two input nodes in the feed-forward motif. We further reveal that the coupling strength of the link regulates the enhancement of signal amplification in the modified feed-forward motif. We finally analyze the mechanism of signal amplification of such simple structure.

Since the traditional detection methods cannot accurately detect, determine and extract weak signals, the extreme sensitivity of chaotic systems to initial values is used for weak signal detection using a memristor-based chaotic system. Then, in order to find out all kinds of static nonlinear circuits suitable for Chua’s circuit with identical parameters, a comparative research platform is designed to generate five kinds of nonlinearity by taking advantage of the active short-circuit line method using the memristor-involved chaotic Chua’s circuit. The comparative research platform consists of three parts: a linear circuit unit, multiple nonlinear static function circuits and a nonlinear characteristic curve measurement unit connected by an electronic switch. By pressing the space bar, the switch between the active short-circuit line and the physical short-circuit line can be realized. The diffeomorphism between them is proved by comparing the memristive nonlinearity shape and the trilinear amplitude limiting the nonlinearity in the chaotic systems. Accordingly, hardware circuit experiments are carried out to verify the effectiveness and feasibility of the comparative research platform with various nonlinearity for Chua’s circuit. A good agreement is shown between the numerical simulations and the experimental results.

Weak signals detection plays an important role in industrial production. We propose the space-coiling gradient acoustic grating to control the sound wave transmission and realize the acoustic enhancement. The numerical results show that the acoustic pressure amplitude can be amplified more than 240 times, and the corresponding frequency can be reduced to 500Hz. Besides, we optimize properties of the space-coiling acoustic grating and apply it into the field of weak signals detection. For periodic impulse signals, the amplitude of characteristic frequency is effectively enlarged, which make the detection of the characteristic frequency is much easier.

This study presents a weak-signal detection system based on a strongly coupled Duffing-Van der Pol (DVP) oscillator. The simulation shows that under all noise conditions with different noise varian...

The classical bistable stochastic resonance (CBSR) has the disadvantage of output saturation, which limits the enhancement capability for weak signal detection. To break the limitation of output saturation, a novel unsaturated piecewise non-linear bistable stochastic resonance (PNBSR) method is proposed. Because the trichotomous noise exists in practical engineering, the PNBSR under trichotomous noise is explored in this paper. The performance of PNBSR is evaluated by the index, i.e., the mean of [Formula: see text] times signal-to-noise ratio increase (MSNRI). The double-peak phenomenon of SR is observed under trichotomous noise. Experiments reveal that the proposed PNBSR method performs best on extracting characteristic components from a strong noise background, compared with the CBSR method and the traditional digital filter. Then, the PNBSR is applied to the fault diagnosis of rolling element bearings. The paper focuses on solving practical engineering problems with mathematical methods.

In this paper, chaotic system is applied to identify and extract the weak signals of bearing early fault which are often submerged in strong background noise. Chaotic system is an effective method in weak signal detection because of its properties of noise immunity and sensitivity to the weak periodic signal. However, chaotic system is not completely immune to noise in critical chaotic state. Aiming at this problem, four indicators are used to evaluate the detection performance of Duffing oscillators. Then, the influence of Duffing oscillator parameters on the four indicators is studied in detail and a new method is proposed to improve the detection performance of Duffing oscillator. The simulation and experimental results show that the proposed method can accurately obtain the characteristic signals of early bearing fault in a lower signal-to-noise ratio (SNR) situation.

Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

Water exists in two forms, para and ortho, that have nuclear spin states with different symmetries. Here we report the conversion of fullerene-encapsulated para water to ortho water. The enrichment of para water at low temperatures is monitored via changes in the electrical polarizability of the material. Upon rapid dissolution of the material in toluene the excess para water converts to ortho water. In ${\mathrm{H}}_{2}^{16}\mathrm{O}@{\mathrm{C}}_{60}$ the conversion leads to a slow increase in the NMR signal. In ${\mathrm{H}}_{2}^{17}\mathrm{O}@{\mathrm{C}}_{60}$ the conversion gives rise to weak signal enhancements attributed to quantum-rotor-induced nuclear spin polarization. The time constants for the para-to-ortho conversion of fullerene-encapsulated water in ambient temperature solution are estimated as $30\ifmmode\pm\else\textpm\fi{}4\text{ }\text{ }\mathrm{s}$ for the $^{16}\mathrm{O}$ isotopolog of water, and $16\ifmmode\pm\else\textpm\fi{}3\text{ }\text{ }\mathrm{s}$ for the $^{17}\mathrm{O}$ isotopolog.

In this paper, we originally present a memristor-based chaotic oscillator which comes from the classical Chua circuit and is devoted to weak signal detection application. On this basis, a non-autonomous memristor-based chaotic oscillator is proposed to estimate the amplitude of weak character signals at diverse frequency, enhance signal-to-noise ratio (SNR) and especially implement square wave signals detection. The detection properties utilizing the proposed oscillator and those of the traditional chaotic oscillators have been compared to demonstrate that this novel oscillator has superior detection performance on strong anti-noise characteristics, detection sensitivity and so on. As a result, the proposed memristor-based chaotic oscillator for weak signal detection has a wide range of engineering applications.

In our former work developed by Yang et al. (2017, “Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators,” ASME J. Comput. Nonlinear Dyn., 12(5), p. 051011), we put forward the rescaled vibrational resonance (VR) method in fractional duffing oscillators to amplify a weak signal with arbitrary high frequency. In the present work, we propose another method named as twice sampling VR to achieve the same goal. Although physical processes of two discussed methods are different, the results obtained by them are identical completely. Besides the two external signals excitation case, the validity of the new proposed method is also verified in the system that is excited by an amplitude modulated signal. Further, the dynamics of the system reveals that the resonance performance, i.e., the strength and the pattern, depends on the fractional order closely.

We propose a new way to correct for finite centrality bin width effect i.e. participant fluctuations in fluctuation analysis in high energy nucleus-nucleus collisions. The MMCP method allows to separate participant fluctuations and obtain fluctuations from one participant - a source - from a combination of the experimentally measured first four moments. The EPOS model is used for the numerical check of the MMCP for the net electric charge fluctuations in the forward rapidity region in Ar+Sc reactions at beam momentum 150 GeV/c. We show that using the existing methods - decreasing a centrality bin width, or using the Centrality Bin Width Correction procedure, one may still leave some residual participant fluctuations in the sample. Moreover, we show that the Centrality Bin Width Correction procedure may alter the fluctuation measures. The most important advantage of the MMCP is it's precision even when the amount of measured events does not allow to decrease the centrality bin width, or the experimental determination of participants is difficult, e.g. in collider experiments. Even for the largest centrality bin in the considered case, $c=0-20\%$, the relative error of the MMCP for the scaled variance of a source is below 2\%. It is especially important in determination of the base line of the fluctuations in the search for the QCD Critical Point and the signals of the QCD phase transition., Comment: We expand the derivation and justification of the MMCP, see Eqs.(12-37), (45), (46) in the revised version, and the corresponding text. A new figure with the estimation of the MMCP parameters is added, see Fig. 1 left. Misprints in the last column of Table I are corrected. 15 new references are added

Aselsan;et al.;Huawei;IEEE Signal Processing Society;IEEE Turkey Section;Netas, 26th IEEE Signal Processing and Communications Applications Conference, SIU 2018 -- 2 May 2018 through 5 May 2018 -- -- 137780, In this paper, effects of autapse on signal detection capacity of Izhikevich neuron in feed-forward-loop network motifs are investigated. Obtained results showed that autapse significantly enchances singal detection of Izhikevich neuron at proper autaptic time delay values compared without autapse. Also, it is seen that feed-forward-loop motifs have significant effects on signal detection ability of Izhikevich neuron. It is obtained that signal detection of Izhikevich neuron are best in T1 feed-forward-loop motif. © 2018 IEEE.

In this paper, the influences of system parameters on stochastic resonance output effect is analyzed, which takes the multi-stable stochastic resonance system as the model. That is, the vibration condition of multi-stable stochastic resonance system, and weak signal detection method based on the multi-stable stochastic resonance under α stable noise is investigated. Then considering the real-time detection of weak signals in practical engineering, the multi-stable stochastic resonance system parameters a, b, c are optimized by particle swarm optimization(PSO), which takes the output signal-to-noise ratio(SNR out ) as the fitness function. Finally, multi-frequency weak signals detection with α stable noise is achieved, and the above method is applied to the vibration fault diagnosis of turbine. Both simulation and experiment results show that this method can quickly and effectively detect multi-frequency weak signals submerged in strong noise background, which lays a foundation for its application in engineering practice.

Because of the strong background noise, the weak echo signal in diffuse reflection laser ranging is very difficult to detect in daylight, which limits the extensive application of diffuse reflection laser ranging. In this paper, the multi-hit method is proposed to solve the weak signal detection problem of diffuse reflection laser ranging in daylight. First of all, a fast performance prediction method for multi-hit Geiger-mode avalanche photodiode (GM-APD) is introduced. Then, taking the typical parameters of the diffuse reflection laser ranging system, the detection probability of the echo signal is analysed under different firing times. Furthermore, effective detection ratio is defined to evaluate the extraction cost of the echo signal. The theoretical analysis shows that processing only a few firings in one gate window can result in large increase of detection probability for diffuse reflection laser ranging in daylight. Meanwhile the optimization of the firing time for GM-APD can increase the effective detection ratio and reduce the extraction cost of the echo signal. Finally, the correctness of the theoretical analysis is verified by the system simulation. Therefore, the multi-hit method is one of the feasible ways to detect the weak echo signal of the diffuse reflection laser ranging in daylight.

We present a quantum receiver for weak signals of the pulse position modulation (PPM) and its modification, multi-pulse PPM, which approaches the Helstrom limit. The adaptive detection strategy is performed by Bayes criterion derived from the records of an on-off single photon detector (SPD).

The gain of the output signal-to-noise ratio (SNR) is insufficient in traditional stochastic resonance (SR) method to detect weak signals. In order to obtaining a higher SNR gain, a kind of signal detection method of adaptive stochastic resonance that use cascade system is proposed. To achieve the optimal output, stochastic resonance parameters adjustment is transformed into the multi-parameter optimization of particle swarm optimization. The optimal result in weak signal detection can be reached by adjusting the parameters of two layers subsystem. The weak signal submerged in strong noise background can be extracted through this simple method that has a fast convergence speed. The threshold of the weak signal detection is lowered by this method, and the applicable scope of stochastic resonance can be enlarged.

When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than 1 rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In this work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional order, and the reduction scale are important factors for the strength of VR.

Aims. We aim to systematically study the properties of the different transitions of the dense molecular gas tracer HC3N in galaxies. Methods. We have conducted single-dish observations of HC3N emission lines towards a sample of nearby gas-rich galaxies. HC3N(J=2-1) was observed in 20 galaxies with Effelsberg 100-m telescope. HC3N(J=24-23) was observed in nine galaxies with the 10-m Submillimeter Telescope (SMT). Results. HC3 N 2-1 is detected in three galaxies: IC 342, M 66 and NGC 660 (> 3 {\sigma}). HC3 N 24-23 is detected in three galaxies: IC 342, NGC 1068 and IC 694. This is the first measurements of HC3N 2-1 in a relatively large sample of external galaxies, although the detection rate is low. For the HC3 N 2-1 non-detections, upper limits (2 {\sigma}) are derived for each galaxy, and stacking the non-detections is attempted to recover the weak signal of HC3N. But the stacked spectrum does not show any significant signs of HC3N 2-1 emission. The results are also compared with other transitions of HC3N observed in galaxies. Conclusions. The low detection rate of both transitions suggests low abundance of HC3N in galaxies, which is consistent with other observational studies. The comparison between HC3N and HCN or HCO+shows a large diversity in the ratios between HC3N and HCN or HCO+. More observations are needed to interpret the behavior of HC3N in different types of galaxies., Comment: A&A (Research Note) accepted

In Chapter 35, we showed that inhibition can become less powerful when it is made rhythmic. More precisely, a weak signal can elicit a response more easily when the inhibition in the receiving network oscillates. The opposite effect is seen for a strong signal. Here we will argue that excitation can become more powerful when it is made rhythmic. More precisely, weak signals benefit from being made rhythmic, while strong ones become less effective when made rhythmic.

The traditional weak signal chaotic detection system still restricts some technical issues in the situation of the signal with noise, such as poor denoising ability and low detection precision. In this paper, we propose a novel weak signal chaotic detection system based on an improved wavelet transform algorithm. First, the traditional wavelet transform algorithm domain variables have been transformed and discretized to eliminate the redundant transform. Then, based on the discrete optimization, the wavelet coefficients have been optimized by threshold compromise strategy. The improved wavelet transform algorithm is applied in the weak signal chaotic detection system. The noise signal after finite discrete processing is treated as a perturbation of cycle power and put into a chaotic system for detecting weak signal under the noise conditions. The simulation experiments show that the proposed improved wavelet transform algorithm has a better denoising effect than the traditional wavelet transform algorithm. Moreover, the improved algorithm shows better accuracy and higher robustness in the weak signal chaotic detection system.

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.

We propose a scheme to realize the manipulation of a weak signal pulse by ultraslow optical soliton in a coherent inverted-Y-type atomic system via double electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations, we derive nonlinear equations governing the spatial-temporal evolution of the probe and signal pulse envelopes. We show the giant enhancement of optical Kerr nonlinearity can be obtained under the condition of the double EIT, which results in the generation of a (2+1)-dimension optical soliton and can realize the manipulation of a weak signal pulse. Applying a far-detuned laser field to the system, we find that a weak signal pulse can be trapped by a (3+1)-dimension light bullet. In particular, the trajectories of the light bullet and trapped signal pulse can be manipulated and controlled by introducing a Stern–Gerlach gradient magnetic field. The results predicted here may not only open a route for the study of weak-light nonlinear optics but also have potential applications in the precision measurements and optical information processing and transmission.