Noise-Enhanced Detection of Subthreshold Signals With Carbon Nanotubes

Electrical noise can help pulse-train signal detection at the nanolevel. Experiments on a single-walled carbon nanotube transistor confirmed that a threshold exhibited stochastic resonance (SR) for finite-variance and infinite-variance noise: small amounts of noise enhanced the nanotube detector's performance. The experiments used a carbon nanotube field-effect transistor to detect noisy subthreshold electrical signals. Two new SR hypothesis tests in the Appendix also confirmed the SR effect in the nanotube transistor. Three measures of detector performance showed the SR effect: Shannon's mutual information, the normalized correlation measure, and an inverted bit error rate compared the input and output discrete-time random sequences. The nanotube detector had a threshold-like input-output characteristic in its gate effect. It produced little current for subthreshold digital input voltages that fed the transistor's gate. Three types of synchronized white noise corrupted the subthreshold Bernoulli sequences that fed the detector. The Gaussian, the uniform, and the impulsive Cauchy noise combined with the random input voltage sequences to help the detector produce random output current sequences. The experiments observed the SR effect by measuring how well an output sequence matched its input sequence. Shannon's mutual information used histograms to estimate the probability densities and computed the entropies. The correlation measure was a scalar inner product of the input and output sequences. The inverted bit error rate computed how often the bits matched between the input and output sequences. The observed nanotube SR effect was robust: it persisted even when infinite-variance Cauchy noise corrupted the signal stream. Such noise-enhanced signal processing at the nanolevel promises applications to signal detection in wideband communication systems and biological and artificial neural networks     

Optimal minimum variance‐entropy control of tumour growth processes based on the Fokker–Planck equation

The authors demonstrated an optimal stochastic control algorithm to obtain desirable cancer treatment based on the Gompertz model. Two external forces as two time‐dependent functions are presented to manipulate the growth and death rates in the drift term of the Gompertz model. These input signals represent the effect of external treatment agents to decrease tumour growth rate and increase tumour death rate, respectively. Entropy and variance of cancerous cells are simultaneously controlled based on the Gompertz model. They have introduced a constrained optimisation problem whose cost function is the variance of a cancerous cells population. The defined entropy is based on the probability density function of affected cells was used as a constraint for the cost function. Analysing growth and death rates of cancerous cells, it is found that the logarithmic control signal reduces the growth rate, while the hyperbolic tangent–like control function increases the death rate of tumour growth. The two optimal control signals were calculated by converting the constrained optimisation problem into an unconstrained optimisation problem and by using the real–coded genetic algorithm. Mathematical justifications are implemented to elucidate the existence and uniqueness of the solution for the optimal control problem.Inspec keywords: optimal control, genetic algorithms, cancer, Fokker‐Planck equation, cellular biophysics, stochastic systems, probability, tumours, entropy, medical control systemsOther keywords: cancer treatment, Gompertz model, time‐dependent functions, process input signals, external treatment agents, tumour growth rate, constrained optimisation problem, cost function, cancerous cells population, probability density function, logarithmic control signal, Fokker‐Planck equation, tumour growth process, optimal control signals, optimal control problem, optimal minimum variance‐entropy control, optimal stochastic control algorithm, tumour death rates, hyperbolic tangent‐like control function, unconstrained optimisation problem, real‐coded genetic algorithm     

Sparse electrocardiogram signals recovery based on solving a row echelon‐like form of system

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two‐stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon‐like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.Inspec keywords: electrocardiography, matrix algebra, medical signal processingOther keywords: sparse electrocardiogram signal recovery, row echelon‐like form of system, noise environment, biological data analysis, personalised medicine, dictionary learning algorithm, transformation matrices, sparse biomedical signal recovery     

Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing

An improved Hindmarsh–Rose (HR) neuron model, where the memristor is a bridge between membrane potential and magnetic flux, can be used to investigate the effect of periodic signals on autaptic regulation of neurons under electromagnetic radiation. Based on the improved HR model driven by periodic high–low‐frequency current and electromagnetic radiation, the responses of electrical autaptic regulation with diverse high–low‐frequency signals are investigated using bifurcation analysis. It is found that the electrical modes of neurons are determined by the selecting parameters of both periodic high and low‐frequency current and electromagnetic radiation, and the Hamiltonian energy depends on the neuronal firing modes. The effects of Gaussian white noise on the membrane potential are discussed using numerical simulations. It is demonstrated that external high–low‐frequency stimulus plays a significant role in the autaptic regulation of neural firing mode, and the electrical mode of neurons can be affected by the angular frequency of both high–low‐frequency forcing current and electromagnetic radiation. The mechanism of neuronal firing regulated by high–low‐frequency signal and electromagnetic radiation discussed here could be applied to research neuronal networks and synchronisation modes.Inspec keywords: bioelectric potentials, neural nets, bifurcation, synchronisation, memristors, neurophysiology, numerical analysis, white noiseOther keywords: synchronisation modes, external periodic signals, electromagnetic radiation, improved Hindmarsh–Rose neuron model, membrane potential, periodic high–low‐frequency current, electrical autaptic regulation, diverse high–low‐frequency signals, neuronal firing modes, external high–low‐frequency stimulus, high–low‐frequency forcing current, high–low‐frequency signal, research neuronal networks     

Comparison of adaptation motifs: temporal,stochastic and spatial responses

The cells’ ability to adapt to changes in the external environment is crucial for the survival of many organisms. There are two broad classes of signalling networks that achieve perfect adaptation. Both rely on complementary regulation of the response by an external signal and an inhibitory process. In one class of systems, inhibition comes about from the response itself, closing a negative feedback (NFB) loop. In the other, the inhibition comes directly from the external signal in what is referred to as an incoherent feedforward (IFF) loop. Although both systems show adaptive behaviour to constant changes in the level of the stimulus, their response to other forms of stimuli can differ. Here the authors consider the respective response to various such disturbances, including ramp increases, removal of the stimulus and pulses. The authors also consider the effect of stochastic fluctuations in signalling that come about from the interaction of the signalling elements. Finally, the authors consider the possible effect of spatially varying signals. The authors show that both the NFB and the IFF motifs can be used to sense static spatial gradients, under a local excitation, global inhibition assumption. The results may help experimentalists develop protocols that can discriminate between the two adaptation motifs.Inspec keywords: stochastic processes, microorganisms, cellular biophysicsOther keywords: adaptation motifs, temporal responses, spatial responses, stochastic responses, signalling networks, inhibitory process, negative feedback loop, incoherent feedforward loop, stochastic fluctuation effect, spatial varying signals, IFF motifs, NFB motifs     

双稳系统噪声特性的分析与弱信号检测的研究

研究了噪声通过双稳系统其能量向低频区集中的频谱特性，并根据绝热近似理论，得出只有在噪声能量集中的低频区域才能产生随机共振(SR)主谱峰的结论。提出频率压缩变换的SR方法，分析了绝热近似SR技术在大参数条件下从强噪声中检测弱信号的应用。仿真结果表明，只要双稳系统输入端的信噪比不低于-30 dB，且实测采样频率不小于弱周期信号频率的50倍，就可由双稳系统的响应谱得到弱周期信号频率处的SR谱峰值特征。达到识别弱信号的目的。     

Hilbert transform‐based time‐series analysis of the circadian gene regulatory network

In this work, the authors propose the Hilbert transform (HT)‐based numerical method to analyse the time series of the circadian rhythms. They demonstrate the application of HT by taking both deterministic and stochastic time series that they get from the simulation of the fruit fly model Drosophila melanogaster and show how to extract the period, construct phase response curves, determine period sensitivity of the parameters to perturbations and build Arnold tongues to identify the regions of entrainment. They also derive a phase model that they numerically simulate to capture whether the circadian time series entrains to the forcing period completely (phase locking) or only partially (phase slips) or neither. They validate the phase model, and numerics with the experimental time series forced under different temperature cycles. Application of HT to the circadian time series appears to be a promising tool to extract the characteristic information about circadian rhythms.Inspec keywords: time series, genetics, Hilbert transforms, stochastic processes, circadian rhythms, signal processing, medical signal processingOther keywords: phase model, experimental time series, circadian time series, circadian rhythms, circadian gene regulatory network, deterministic time series, stochastic time series, fruit fly model, phase response curves, period sensitivity, phase locking, phase slips, Hilbert transform, time‐series analysis, signal processing     

驱动输入白噪声对Duffing振子运动影响分析

强噪声背景下混沌弱信号检测是利用弱信号的周期扰动使系统运动状态发生改变实现的，研究了数值解算时计算步长和驱动输入白噪声对弱信号检测中Duffing振子运动特征的影响，重点研究了对Duffing振子混沌临界态和大尺度周期态的影响，结果表明采用数值解算的步长不同系统运动状态不相同，与统计意义下任何零均值噪声都不会改变系统原有运行轨迹不同，不同功率的驱动输入白噪声会导致系统状态改变，分析了产生原因。     

Deterministic inference for stochastic systems using multiple shooting and a linear noise approximation for the transition probabilities

Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the ‘multiple shooting for stochastic systems (MSS)’ method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least‐squares parameter estimation methods.Inspec keywords: stochastic systems, parameter estimation, probability, least squares approximationsOther keywords: deterministic inference, stochastic systems, multiple shooting, linear noise approximation, transition probabilities, systems biology, parameter estimation methods, likelihood function, normal distributions, intrinsic stochasticity effects, reversible jump techniques, approximative sampling, conventional least‐squares parameter estimation methods     

Effective sampling trajectory optimisation for sensitivity analysis of biological systems

Sensitivity analysis has been widely applied to study the biological systems, including metabolic networks, signalling pathways, and genetic circuits. The Morris method is a kind of screening sensitivity analysis approach, which can fast identify a few key factors from numerous biological parameters and inputs. The parameter or input space is randomly sampled to produce a very limited number of trajectories for the calculation of elementary effects. It is clear that the sampled trajectories are not enough to cover the whole uncertain space, which eventually causes unstable sensitivity measures. This paper presents a novel trajectory optimisation algorithm for the Morris‐based sensitivity calculation to ensure a good scan throughout the whole uncertain space. The paper demonstrates that this presented method gets more consistent sensitivity results through a benchmark example. The application to a previously published ordinary differential equation model of a cellular signalling network is presented. In detail, the parameter sensitivity analysis verifies the good agreement with data of the literatures.Inspec keywords: genetics, differential equations, sensitivity analysis, biology, sampling methods, optimisationOther keywords: biological systems, metabolic networks, genetic circuits, Morris‐based sensitivity calculation, ordinary differential equation, sampling trajectory optimisation, sensitivity analysis, parameter sensitivity analysis, cellular signalling network     

Comprehensive analysis of retroreflection in Papilio crino Fabricius, 1792 wings

Multilayer thin‐film structures in the wings of a butterfly; Papilio crino produce a colourful iridescence from reflected light. In this investigation, scanning electron microscope images show both the concave cover scales and pigmented air‐chamber ground scales. The microstructures with the concavities retroreflect incident light, thus causing the double reflection. This gives rise to both the colour mixing and polarisation conversion clearly depicted in the optical images. The result of the numerical and theoretical analysis via the CIELAB, and optical reflection and transmission of light through the multilayer stacks with the use of transfer method show that the emerging colouration on the Papilio crino is structural and is due to the combination of colours caused by multiple bounces within the concavities. The butterfly wing structure can be used as the template for designing the photonic device.Inspec keywords: bio‐optics, scanning electron microscopy, photodiodes, optical sensors, optical images, light reflection, reflectivity, colour, optical links, multilayers, optical multilayers, light polarisationOther keywords: pigmented air‐chamber ground scales, concavities, incident light, double reflection, colour mixing, polarisation conversion, optical images, numerical analysis, theoretical analysis, optical reflection, multilayer stacks, emerging colouration, butterfly wing structure, papilio crino fabricius, thin‐film structures, colourful iridescence, reflected light, electron microscope images, concave cover scales     

非线性分数阶双稳系统逻辑随机共振的研究

在整数阶逻辑随机共振的郎之万方程基础上构建了分数阶情况下的郎之万方程。对该方程描述的非线性分数阶双稳系统进行了仿真验证,分析分数阶阶次和系统参数的改变对逻辑随机共振现象的影响。结果表明当分数阶阶次小于临界值时,即使没有外加高斯白噪声或微弱周期信号也能观察到逻辑随机共振现象;当分数阶阶次大于临界值时,需要外加高斯白噪声或微弱周期信号才能实现逻辑随机共振,选择合适的噪声强度、微弱周期信号振幅、频率等可以提高逻辑输出的成功率。     

Sliding mode controller–observer pair for p53 pathway

A significant loss of p53 protein, an anti‐tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild‐type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non‐linear technique is presented for the drug design of a control‐oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero‐dynamics is also proved. To make the model‐based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced‐order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in‐silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.Inspec keywords: control system synthesis, tumours, variable structure systems, observers, cancer, robust control, drugs, proteins, medical control systemsOther keywords: wild‐type p53, nonlinear technique, drug design, control‐oriented p53 model, control input, drug infusion, smooth control signal, dynamic SMC, zero‐dynamics, model‐based control design, input disturbance, controlled drug administration, sliding mode controller–observer pair, cancerous cells, antitumour agent, molecule based drug     

Diagnosis of attention deficit hyperactivity disorder using non‐linear analysis of the EEG signal

Attention deficit hyperactivity disorder (ADHD) is a common behavioural disorder that may be found in 5%–8% of the children. Early diagnosis of ADHD is crucial for treating the disease and reducing its harmful effects on education, employment, relationships, and life quality. On the other hand, non‐linear analysis methods are widely applied in processing the electroencephalogram (EEG) signals. It has been proved that the brain neuronal activity and its related EEG signals have chaotic behaviour. Hence, chaotic indices can be employed to classify the EEG signals. In this study, a new approach is proposed based on the combination of some non‐linear features to distinguish ADHD from normal children. Lyapunov exponent, fractal dimension, correlation dimension and sample, fuzzy and approximate entropies are the non‐linear extracted features. For computing, the chaotic time series of obtained EEG in the brain frontal lobe (FP1, FP2, F3, F4, and Fz) need to be analysed. Experiments on a set of EEG signal obtained from 50 ADHD and 26 normal cases yielded a sensitivity, specificity, and accuracy of 98, 92.31, and 96.05%, respectively. The obtained accuracy provides a significant improvement in comparison to the other similar studies in identifying and classifying children with ADHD.Inspec keywords: feature extraction, time series, fractals, electroencephalography, medical disorders, neurophysiology, medical signal processing, entropy, signal classification, Lyapunov methodsOther keywords: nonlinear extracted features, chaotic time series, identifying classifying children, attention deficit hyperactivity disorder, nonlinear analysis methods, electroencephalogram signals, brain neuronal activity, chaotic behaviour, chaotic indices, EEG signals, nonlinear features, approximate entropies, common behavioural disorder, early diagnosis, life quality, ADHD     

Optimal choice of test signals for linear channel estimation using second order statistics

A time-varying acoustic channel may be estimated by an appropriate inference using the output from a periodic test signal. In this paper it is shown how to do this in a way that takes full account of the past history of the background noise and the past history of the channel. An explicit formula is obtained for the optimal linear estimator that may be used for rapid channel estimation for a given test signal when we know the autocovariance or power spectrum of the interfering noise and the autocovariance of the echo channel variation. Given this closed formula for the optimal estimator of the channel impulse response, an efficient method for determining the optimal test signal, subject to a constraint on the test signal power, given the history of the channel and the noise, is developed. We show that if the second order statistics of the channel or the noise are known, then the optimal test signal is not white. The method includes an explicit formula for the optimal test signal given a fixed estimator. A model of channel variation which is realistic while having less complexity than a full second-order statistical model, and therefore is more amenable to robust estimation, is used in the experiments which illustrate the performance of the optimal test signals and the channel estimation method. Matrix calculus identities required for the derivation of this expression for the optimal estimator are stated and proved in the Appendixes 1 and 2.     

Enhancing data rate of molecular communication system using Brownian motion

Inter‐symbol and co‐channel interferences restrict the capacity of molecular communication (MC) systems. In this study, the effect of these interferences on the data rate of MC systems is investigated to design an efficient MC system. To this end, the authors propose an analytical model for a diffusion‐based MC system comprised of two nanomachines when they exploit On/Off keying modulation. They model the Brownian motion of molecules in a one‐dimensional environment as a wiener process and the life expectancy of diffused molecules as an exponential process. First, they consider the inter‐symbol interference to derive the data rate of the MC system as a function of the receiver decision threshold and the symbol time duration. Hence, they propose an algorithm to obtain the optimal values of MC system parameters. Then, the effect of co‐channel interference is considered by assuming parallel MC systems. They propose a minimum distance between adjacent MC systems that their co‐channel interferences effect to be negligible. Moreover, they verify the accuracy of the analytical results by Monte–Carlo simulations. Results show a remarkable improvement in the data rate of MC systems. The derived results may find application in nanonetworks where nanomachines connect together to perform complex tasks.Inspec keywords: channel capacity, Monte Carlo methods, intersymbol interference, stochastic processes, Brownian motion, cochannel interferenceOther keywords: enhancing data rate, molecular communication system, Brownian motion, co‐channel interference, efficient MC system, diffusion‐based MC system, inter‐symbol interference, MC system parameters, parallel MC systems, adjacent MC systems, co‐channel interferences effect     

Multi‐bit Boolean model for chemotactic drift of Escherichia coli

Dynamic biological systems can be modelled to an equivalent modular structure using Boolean networks (BNs) due to their simple construction and relative ease of integration. The chemotaxis network of the bacterium Escherichia coli (E. coli ) is one of the most investigated biological systems. In this study, the authors developed a multi‐bit Boolean approach to model the drifting behaviour of the E. coli chemotaxis system. Their approach, which is slightly different than the conventional BNs, is designed to provide finer resolution to mimic high‐level functional behaviour. Using this approach, they simulated the transient and steady‐state responses of the chemoreceptor sensory module. Furthermore, they estimated the drift velocity under conditions of the exponential nutrient gradient. Their predictions on chemotactic drifting are in good agreement with the experimental measurements under similar input conditions. Taken together, by simulating chemotactic drifting, they propose that multi‐bit Boolean methodology can be used for modelling complex biological networks. Application of the method towards designing bio‐inspired systems such as nano‐bots is discussed.Inspec keywords: cell motility, microorganisms, Boolean functionsOther keywords: multibit Boolean approach, conventional BNs, high‐level functional behaviour, steady‐state responses, chemoreceptor sensory module, drift velocity, chemotactic drifting, multibit Boolean methodology, complex biological networks, bio‐inspired systems, multibit Boolean model, chemotactic drift, dynamic biological systems, equivalent modular structure, Boolean networks, simple construction, chemotaxis network, bacterium Escherichia coli, biological systems     

随机共振技术在齿轮箱故障检测中的应用

讨论了利用SR原理从强背景噪声中提取微弱周期特征信号的方法，给出了SR模型数值求解的新算法。在对齿轮箱故障进行数值仿真的基础上，将此方法用于某型直升机中间减速器齿轮点蚀故障的微弱特征信号提取，结果表明，该方法能有效提取出齿轮发生早期点蚀故障时的微弱特征信号，为直升机减速器齿轮箱的状态监测与早期故障检测提供了一条新途径。     

Control of depth of anaesthesia using fractional‐order adaptive high‐gain controller

This study presents a fractional‐order adaptive high‐gain controller for control of depth of anaesthesia. To determine the depth of anaesthesia, the bispectral index (BIS) is utilised. To attain the desired BIS, the propofol infusion rate (as the control signal) should be appropriately adjusted. The effect of the propofol on the human body is modelled with the pharmacokinetic–pharmacodynamic (PK/PD) model. Physical properties of the patient such as gender, age, height and a like determine the parameters of the PK/PD model. This necessitates us to employ an appropriate adaptive controller. To attain this goal, a fractional‐order adaptive high‐gain controller is constructed to solve the tracking problem for minimum phase systems with relative degree two (such as the PK/PD model). This leads to a time‐varying gain adjusting according to a fractional‐order adaptation mechanism. Simulation results performed on various patients (considering the external disturbance and the measurement noise) show the effectiveness of the proposed method.Inspec keywords: medical control systems, gain control, adaptive control, closed loop systems, time‐varying systemsOther keywords: fractional‐order adaptive high‐gain controller, control signal, pharmacokinetic–pharmacodynamic model, fractional‐order adaptation mechanism, anaesthesia depth control, bispectral index, PK‐PD model, propofol infusion rate, tracking problem, minimum phase systems, time‐varying gain, BIS