Computation using noise-based logic: efficient string verification over a slow communication channel

Utilizing the hyperspace of noise-based logic, we show two string verification methods with low communication complexity. One of them is based on continuum noise-based logic. The other one utilizes noise-based logic with random telegraph signals where a mathematical analysis of the error probability is also given. The last operation can also be interpreted as computing universal hash functions with noise-based logic and using them for string comparison. To find out with 10^-25 error probability that two strings with arbitrary length are different (this value is similar to the error probability of an idealistic gate in today's computer) Alice and Bob need to compare only 83 bits of the noise-based hyperspace.     

Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system

The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from “on” → “off” of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching “off” → “on”. A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified.     

Computing with spins: from classical to quantum computing

This article reviews the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the bistable spin polarization of a single electron confined in a quantum dot and subjected to a weak magnetic field. The spin orientation can be either parallel or anti-parallel to the field, so that it becomes a binary variable which can encode logic 0 and logic 1. Coherent superposition of these two polarizations can represent a qubit for quantum computing. By engineering the exchange interaction between closely spaced spins in neighboring quantum dots, it is possible to implement either classical or quantum logic gates.     

On the noisiness of steady state and intermittent noises

An experiment was designed to investigate the effects of sound level (L_A), number of single noises (N), level of total energy (L_T) and mean energy level ($\text{dB(A)}$) on the noisiness of steady state and intermittent noises. With the level and duration of pink noise controlled with a sound system called “Programmable Sound Control System”, 16 kinds of intermittent noises and 22 kinds of steady state noises were prepared. Seven subjects judged the noisiness of these stimuli by magnitude estimation. Their judgments were converted into the corresponding sound level (point of subjective equality, abbreviated PSE) by using the power function obtained between sound level and magnitude estimation for the seven kinds of steady state noises. As a result, the level of total energy and mean energy level were found inappropriate to evaluate the noisiness of intermittent noises though they showed high correlation with the noisiness of steady state noises. PSE's of the intermittent noises showed good correspondence with L_N, which is expressed by the equation $\text{L}{}_{\mathrm{N}}\text{=}\text{dB(A)}\text{+ 10}\text{log}\text{N}$. L_N could also be applied to steady state noises if it was assumed that a steady state noise with a duration of D_T is equal to a 2000 ms noise presented $\text{N (}\text{D}{}_{\mathrm{T}}\text{2000}\text{)}$ times. This result suggests that L_N is a good measure of the noisiness of both steady state and intermittent noises.     

Noise-driven synchronization of a FitzHugh-Nagumo ring with phase-repulsive coupling: A perspective from the system’s nonequilibrium potential

We study a one-dimensional array of N autonomous units with excitable FitzHugh-Nagumo dynamics coupled in phase-repulsive way to form a ring, and submitted to a common subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. By varying η, two macroscopic regimes are observed. For some value of noise intensity, a transition from the rest state to an activated one-with almost half of the neurons excited forming an “...-activated-inhibited-activated-... ” structure along the ring-takes place. For larger values of η, the inverse transition is also observed, and both states alternate in a synchronized way with the signal. Moreover, measures of activation and coherent behavior become maximal for intermediate values of η. The origin of these collective effects is explained in terms of the system’s nonequilibrium potential. In particular, the levels of noise for activation and synchronization are theoretically estimated.     

A scheme of developing frequency encoded tristate logic operations exploiting nonlinear character of PPLN waveguide and RSOA

In binary logic the information is represented by two distinct states only (0 and 1 state). The major disadvantage of the binary or Boolean logic operation is due to its limitation of large information handling capacity. It is established that tristate operations can be accommodated with optics in data processing, as this type of operation can enhance the operation speed very much as well as information capacity. Here in this communication the authors propose a new concept to implement all-optical different logic gates with tristate mechanism using frequency-encoding principle. For this purpose, co-propagating beams having different frequencies in C-band have used for generating cascaded sum and difference frequency, exploiting the nonlinear response character of periodically poled LiNbO₃ waveguide (PPLN). The highly reflecting property of optical add and drop multiplexer (ADM) and high wavelength conversion property of reflecting semiconductor optical amplifiers (RSOA) have been exploited here to implement the desired AND, NAND,OR and NOR logic operations with tristate. As NAND and NOR are the universal logic operation, so any other member of this logic family may be implemented with these.     

Nonequilibrium potential for arbitrary-connected networks of FitzHugh-Nagumo elements

We study an array of N units with FitzHugh-Nagumo dynamics linearly coupled. The system is submitted to a subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. In the limit of adiabatic driving, we analytically calculate the system’s nonequilibrium potential for arbitrary linear coupling. We illustrate its applicability by investigating noise-induced effects in an excitable regular network with extended antiphase coupling. In particular, the levels of noise for short-wavelength phase-instability, network’s synchronization and depinning of “defects” (groups of contiguous inhibited neurons on an antiphase background) are theoretically predicted and numerically confirmed. The origin of these collective effects and the dependence with parameters of the most probable length of defects are explained in terms of the system’s nonequilibrium potential.     

Spectral shifts of partially coherent radial array beams passing through ABCD optical systems

The expressions for the spectral intensity of partially coherent Gaussian Schell-model (GSM) radial array beams for both the correlated and uncorrelated superpositions passing through ABCD optical systems have been derived by using the extended Huygens-Fresnel diffraction integral. The effects of the normalized radius R, the number of beamlets N, the spatial coherent parameter of array beamlets β and the optical system parameters on the on-axis and off-axis relative spectral shifts for the two types of superposition have been discussed in detail. The results show that for the correlated superposition, the on-axis spectral intensity in free space and the off-axis spectral intensity on the geometrical focal plane depends on the source spectral density S⁰(ω), the spatial coherent parameter of array beamlets β, the generalized Fresnel number of the system F, the normalized radius R and the number of beamlets N, whereas the spectral intensity for the uncorrelated superposition is independent of the number of beamlets N. Furthermore, as for on the actual focal plane, the off-axis spectral intensity for the two types of superposition is closely related to N.     

An intelligent approach for engine fault diagnosis based on Hilbert–Huang transform and support vector machine

Based on the techniques of Hilbert–Huang transform (HHT) and support vector machine (SVM), a noise-based intelligent method for engine fault diagnosis (EFD), so-called HHT–SVM model, is developed in this paper. The noises of a sample engine under normal and several fault states are first measured and denoised by using the wavelet packet threshold method to initially lower the noise level with negligible signal distortion. To extract fault features of the engine, then, the HHT is selected and applied to the measured noise signals. A nine-dimensional vector, which consists of seven intrinsic mode functions (IMFs) from the empirical mode decomposition (EMD), maximum value of HHT marginal spectrum and its corresponding frequency component, is specified to represent each engine fault feature. Finally, an optimal SVM model is established and trained for engine failure classification by using the fault feature vectors of the noise signals. Cross-validation results show that the proposed noise-based HHT–SVM method is accurate and effective for engine fault diagnosis. Due to outstanding time–frequency characteristics and pattern recognition capacity of the HHT and SVM, the newly proposed HHT–SVM can be used to deal with both the stationary and nonstationary signals, and even the transient ones. In the view of applications, the HHT–SVM technique may be suggested not only to detect the abnormal states of vehicle engines, but also to be extended to other fields for failure diagnosis in engineering.     

Modified signed-digit addition by using binary logic operations and its optoelectronic implementation

In this work, a three-step modified signed-digit (MSD) addition by using binary logic operations is proposed. Each input digit is encoded with two binary bits. Through binary logic operations, all of the weight and transfer digits and the final sum digits represented with the same encoding scheme will be generated. The operations can be performed at each digit position in parallel. In our suggested optical arithmetic and logic unit (ALU), a single electron trapping (ET) device is employed to serve as the binary logic device. This technique based on ET logic possesses the advantage of high signal-to-noise ratio (SNR). The optoelectronic system can be constructed in a simple, compact and general-purpose form.     

Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Practical implementation of an acoustic-based modal filtering sensing technique for active noise control

To accurately measure the global radiated sound power from a large noise source a significant number of sensors, either acoustic of vibration sensors, are required. In this paper a sensing system containing 128 acoustic sensors, a number beyond the capabilities of current large sensing systems, is experimentally implemented and investigated in real-time. At the heart of the sensing strategy is the development of orthogonal acoustic radiating shapes, orthogonal patterns which can be applied to any noise source, structural or non-structural. The aim of the sensing strategy is to then decompose the large number of sensor signals into a smaller number of signals, which accurately represent a global quantity. The decomposition uses frequency independent weights over a wide frequency band (20–800 Hz) to calculate radiated sound power, thus reducing the filtering process to simple multiplication and addition. To complete the filtering task, custom built electronics capable of 128 inputs and outputs sampling at 5.5 kHz has been developed. This paper examines the capabilities of the modal filtering device and contains a detailed examination of the multipole decomposition itself. Experimental analysis has been carried out on a simply supported panel, however should the technique give an accurate estimate of power, it is applicable beyond structures to any noise source.     

Frozen entanglement and quantum correlations of one-parameter qubit−qutrit states under classical noise effects

We provide a detailed analysis of the dynamics of entanglement and quantum correlations for one-parameter qubit-qutrit states under independent or common classical noises influence. Namely the static noise, the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise. Independently of the intrinsic features of the noises, entanglement measured by negativity and quantum correlations measured by measured-induced disturbance (MID) vanish after a finite time under the effects of independent noise environments. In a common environment setup, we show the existence of specific and very important features of perfect insulation of the systems quantum properties from noise effects, for suitable range of the entanglement parameter. We refer these phenomena to as frozen entanglement and frozen quantum correlations. The dichotomy between entanglement (separability) and quantum correlations is strengthened by our results, with the robustness of MID over entanglement and existence of separable qubit-qutrit states with non-zero quantum correlations.     

Noise-induced transport in a periodic system driven by Gaussian white noises with intensive cross-correlation

An analytical investigation of overdamped Brownian particle in a periodic system driven by intensive cross-correlated Gaussian white noises is presented. The center idea of this Letter is to construct an exact soluble model to exhibit the possible new effect of the cross-correlated Gaussian white noises on the noise-induced transport. The model clearly shows the following new aspects of this transport: (1) There is one and only extreme in the J–Q curve for the case of weakly cross-correlated noises here J and Q denote the current and multiplicative noise intensity, respectively. (2) When the two noises are intensive correlative, the J–Q curve behaves three extrema. (3) The J–Q curve exhibits a giant suppression plateau between the two maxima as the noise correlation coefficient is increased further. (4) The direction of the current is controlled by two parameters.     

A reduced gradient description of stochastic-resonant spatiotemporal patterns in a FitzHugh–Nagumo ring with electric inhibitory coupling

We study the synchronization (sync) properties of a ring of N units with excitable FitzHugh–Nagumo dynamics, when the inhibitor fields of nearest-neighbor units are coupled diffusively (electric coupling). The system is submitted to a common subthreshold adiabatic signal $S(t)$, and independent Gaussian white noises with common variance η. By running numerical integrations with increasing η, we observe the excitation activity to become spatiotemporally self-organized, until η is so strong that spoils sync. By means of a two-cell model and projecting the dynamics along the slow manifolds, we obtain a (signal-dependent) potential landscape which explains qualitatively the sync regime, and whose barrier heights give a good estimate of the optimal noise intensity.     

Stochastic bifurcation in FitzHugh-Nagumo ensembles subjected to additive and/or multiplicative noises

We have studied the dynamical properties of finite N-unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. In the AMM, original 2N-dimensional stochastic equations are transformed to eight-dimensional deterministic ones, and the dynamics is described in terms of averages and fluctuations of local and global variables. The stochastic bifurcation is discussed by a linear stability analysis of the deterministic AMM equations. The bifurcation transition diagram of multiplicative noise is rather different from that of additive noise: the former has the wider oscillating region than the latter. The synchronization in globally-coupled FN ensembles is also investigated. Results of the AMM are in good agreement with those of direct simulations (DSs).     

Time reversible evolution via nonadiabatic coupling in adiabatic dark subspace

We propose a method for the creation of arbitrary superposition of N atomic states using generalized stimulated Raman adiabatic passage (STIRAP) techniques with laser fields coupling each one of N lower states to a single upper state in a (N+1)-level atomic system. (N-1) dark states that are composed of N lower states span a dark subspace. In the adiabatic limit, the dark and bright subspaces are decoupled, thus the nonadiabatic interaction within this dark subspace dominates the evolution of the system. Different from general methods to create our required coherent superposition state, in a reverse way, here we consider the required state as the starting point of evolution dynamics, and utilize laser fields to drive it into a single lower state step by step. Time reverse pulses of laser fields return the single lower state back to our required coherent superposition state based on time reversal symmetry. In principle, the computationally simple method allows the case with a large value of N. Based on the STIRAP techniques, it is robust against small variations of parameters of laser pulses and is immune to spontaneous radiation.     

An increase in the sensitivity of the saturated absorption method in the multimode regime

A possibility for an increase in the signal-to-noise ratio in the laser spectroscopy that is free of Doppler broadening and is based on the saturated absorption is considered. The application of the counter-propagating laser beams in the multimode regime is proposed. The number of atoms that effectively interact with the field, and, hence, the intensity of a narrow resonance in the line shape can be increased due to the interaction of the counterpropagating modes with different frequencies. It is demonstrated that, for the intrinsic photon noise, the signal-to-noise ratio can be increased by a factor of √N, where N is the number of modes. For the remaining noises (fluctuations of the radiation power, noise of photodetector, etc.), the signal-to-noise ratio can be increased by a factor of N.     

Experimental behaviour of noise indices as a function of averaging time

The behaviour of noise indices as a function of averaging time has been investigated. Measurements were made on 13 noise samples selected as representative of noises of industrial origin which are rapidly varying in time.It was found that log χ² distributions well represent the SPL distributions of the noises; moreover an equivalence between the integration time (T) and the time constant (τ) was achieved when T = 2τ. For noises of rapid time variation the choice of the averaging time is of some importance, while for traffic noise it is fairly uncritical. As regards fluctuation measurements the indices L_DI and σ_L show a similar behaviour for high time constants and slowly varying noises. On the contrary, for short time constants and rapidly varying noises they have a somewhat different trend.