Noise-induced phase transition in the Vicsek model through eigen microstate methodology

This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.

Research on the generation method of seawater sound velocity model based on Perlin noise

In the processing of conventional marine seismic data,seawater is often assumed to have a constant velocity model.However,due to static pressure,temperature difference and other factors,random disturbances may often frequently in seawater bodies.The impact of such disturbances on data processing results is a topic of theoretical research.Since seawater sound velocity is a difficult physical quantity to measure,there is a need for a method that can generate models conforming to seawater characteristics.This article will combine the Munk model and Perlin noise to propose a two-dimensional dynamic seawater sound velocity model generation method,a method that can generate a dynamic,continuous,random seawater sound velocity model with some regularity at large scales.Moreover,the paper discusses the influence of the inhomogeneity characteristics of seawater on wave field propagation and imaging.The results show that the seawater sound velocity model with random disturbance will have a significant influence on the wave field simulation and imaging results.

Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Simulation and Modeling of Common Mode EMI Noise in Planar Transformers

The transformer is the key circuit component of the common-mode noise current when an isolated converter is working.The highfrequency characteristics of the transformer have an important influence on the common-mode noise of the converter.Traditionally,the measurement method is used for transformer modeling,and a single lumped device is used to establish the transformer model,which cannot be predicted in the transformer design stage.Based on the transformer common-mode noise transmission mechanism,this paper derives the transformer common-mode equivalent capacitance under ideal conditions.According to the principle of experimental measurement of the network analyzer,the electromagnetic field finite element simulation software three-dimensional(3D)modeling and simulation method is used to obtain the two-port parameters of the transformer,extract the high-frequency parameters of the transformer,and establish its electromagnetic compatibility equivalent circuit model.Finally,an experimental prototype is used to verify the correctness of the model by comparing the experimental measurement results with the simulation prediction results.

A novel approach to conductive EMI noise source modeling

A new approach to conductive electromagnetic interference （EMI） noise source modeling, i. e. the source internal impedance extraction, is presented. First, the impedance magnitude is achieved through an exciting probe and a detecting probe, or through calculations based on insertion loss measurement results when inserting a series nigh-value known impedance or a shunt low-value known impedance in the circuit. Then the impedance phase is extracted by the Hilbert transform （HT） of the logarithm of the obtained impedance magnitude. Performance studies show that the estimated phase error can increase greatly at a zero frequency in the Hilbert transform because of the existence of a singular point, and this effect can be eliminated by introducing a zero-point when the noise source does not include a series-connected capacitive component. It is also found that when the frequency is nigher than 150 kHz, the estimated phase error is not sensitive to the inductive source but sensitive to the capacitive source. Finally, under the conditions of the same measurement accuracies for impedance magnitude, the accuracy of complex impedance based on the HT can be improved about 10 times when compared with the accuracy of estimated parameters based on the impedance magnitude fitting method （IMFM）.

Stochastic modeling and analysis of hepatitis and tuberculosis co-infection dynamics

Several mathematical models have been developed to investigate the dynamics of tuberculosis(TB)and hepatitis B virus(HBV).Numerous current models for TB,HBV,and their co-dynamics fall short in capturing the important and practical aspect of unpredictability.It is crucial to take into account a stochastic co-infection HBV–TB epidemic model since different random elements have a substantial impact on the overall dynamics of these diseases.We provide a novel stochastic co-model for TB and HBV in this study,and we establish criteria on the uniqueness and existence of a nonnegative global solution.We also looked at the persistence of the infections as long its dynamics are governable by the proposed model.To verify the theoretical conclusions,numerical simulations are presented keeping in view the associated analytical results.The infections are found to finally die out and go extinct with certainty when L´evy intensities surpass the specified thresholds and the related stochastic thresholds fall below unity.The findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given population.Our results provide insights into effective intervention strategies,ultimately aiming to improve the management and control of TB and HBV co-infections.

Fault diagnosis using noise modeling and a new artificial immune system based algorithm

A new fault classification/diagnosis method based on artificial immune system (AIS) algorithms for the structural systems is proposed. In order to improve the accuracy of the proposed method, i.e., higher success rate, Gaussian and non-Gaussian noise generating models are applied to simulate environmental noise. The identification of noise model, known as training process, is based on the estimation of the noise model parameters by genetic algorithms (GA) utilizing real experimental features. The proposed fault classification/diagnosis algorithm is applied to the noise contaminated features. Then, the results are compared to that obtained without noise modeling. The performance of the proposed method is examined using three laboratory case studies in two healthy and damaged conditions. Finally three different types of noise models are studied and it is shown experimentally that the proposed algorithm with non-Gaussian noise modeling leads to more accurate clustering of memory cells as the major part of the fault classification procedure.

HBT's High Frequency Noise Modeling and Analysis

A T equivalent high frequency heterojunction bipolar transistor (HBT) noise model is reported.This model is derived from Hawkins noise model commonly used in Si BJT.The main modifications include the influence of the ideality factor,emitter resistance,intrinsic base collector capacitance,extrinsic base collector capacitance and other parasitic elements of HBT represented in equivalent circuit topology.In order to calculate accurate noise parameters from the equivalent circuit,the noise correlation matrix method is used to avoid any simplifications generated in circuit transformations and complex noise measurements.The analysis of the influence of the equivalent circuit elements on the minimum noise figure is reported,the results of analysis agree well with the physics explanations.By means of the formulae derived from device physics of HBT,the influence of device parameters on the minimum noise figure is also represented.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.

Time Domain Modeling of Powerline Impulsive Noise at Its Source

Noise characteristics of an indoor power line network strongly influence the link capability to achieve high data rates. The appliances shared with PLC modems in the same powerline network generate different types of noises, among them the impulsive noises are the main source of interference resulting in signal distortions and bit errors during data transmission. With regard to impulsive noise many models were proposed in the literature and shared the same impulsive noise definition: “unpredictable noises measured in the receiver side”. Authors are, consequently, confronted to model thousands of impulsive noises whose plurality would very likely come from the diversity of paths that the original impulsive noise took. In this paper, an innovative modelling approach is applied to impulsive noises which are studied here directly at their sources. Noise at receiver would be simply the noise model at source convolved by powerline channel block. In the new analytical model, the impulsive noise at source is described by a succession of short pulses, each modeled by a phase-shifted Gaussian. Noises at source are classified into 6 different classes [1], and a noise generator is established for each class.

Modeling and Analysis of Low Frequency Noise in Ion-Field-Effect Transistors Sensors

Ions Sensitive Field Effect Transistors (ISFETs) are becoming the platform sensors for important chemical and biomedical applications. However, the accuracy of ISFET output measurement is greatly affected by the presences of low-frequency noise, drift and slow response of the device. This requires more safety in measured results and the tools of analysis. In this paper, we present fundamental limits on the sensitivity of ISFETs micro-sensors, arising from intrinsic and extrinsic noise sources. We developed an algorithm in MATLAB in order to model the frequency analysis of the 1/f noise in ISFET sensor using Hooge theory. We have shown that the 1/f noise of the ISFETs sensors is due to both the electrochemical system (pH solution) and the MOS component (canal size, insulator thickness). The temperature effect on the ISFET noise and the signal conditioning are also performed.

Robust Parametric Modeling of Speech in Additive White Gaussian Noise

In estimating the linear prediction coefficients for an autoregressive spectral model, the concept of using the Yule-Walker equations is often invoked. In case of additive white Gaussian noise (AWGN), a typical parameter compensation method involves using a minimal set of Yule-Walker equation evaluations and removing a noise variance estimate from the principal diagonal of the autocorrelation matrix. Due to a potential over-subtraction of the noise variance, however, this method may not retain the symmetric Toeplitz structure of the autocorrelation matrix and thereby may not guarantee a positive-definite matrix estimate. As a result, a significant decrease in estimation performance may occur. To counteract this problem, a parametric modelling of speech contaminated by AWGN, assuming that the noise variance can be estimated, is herein presented. It is shown that by combining a suitable noise variance estimator with an efficient iterative scheme, a significant improvement in modelling performance can be achieved. The noise variance is estimated from the least squares analysis of an overdetermined set of p lower-order Yule-Walker equations. Simulation results indicate that the proposed method provides better parameter estimates in comparison to the standard Least Mean Squares (LMS) technique which uses a minimal set of evaluations for determining the spectral parameters.

Effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model

The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.

Combined Novel Gate Level Model and Critical Primary Input Sharing for Genetic Algorithm Based Maximum Power Supply Noise Estimation

A gate level maximum power supply noise （PSN） model is defined that captures both IR drop and di/dt noise effects. Experimental results show that this model improves PSN estimation by 5.3% on average and reduces computation time by 10.7% compared with previous methods. Furthermore,a primary input critical factor model that captures the extent of primary inputs＇ PSN contribution is formulated. Based on these models,a novel niche genetic algorithm is proposed to estimate PSN more effectively. Compared with general genetic algorithms, this novel method can achieve up to 19.0% improvement on PSN estimation with a much higher convergence speed.

Model/data comparison of typhoon-generated noise

Ocean noise recorded during a typhoon can be used to monitor the typhoon and investigate the mechanism of the wind- generated noise. An analytical expression for the typhoon-generated noise intensity is derived as a function of wind speed. A ＂bi-peak＂ structure was observed in an experiment during which typhoon-generated noise was recorded. Wind speed dependence and frequency dependence were also observed in the frequency range of 100 Hz-1000 Hz. The model/data comparison shows that results of the present model of 500 Hz and 1000 Hz are in reasonable agreement with the exper- imental data, and the typhoon-generated noise intensity has a dependence on frequency and a power-law dependence on wind speed.

Model of wind-generated ambient noise in stratified shallow water

In order to build a rapid ocean ambient noise model adapted for a stratified shallow water, a hybrid model of normal mode method (for far field) and ray method (for near field) is suggested which combines the advantages of both methods. Since the near field of wind-generated noise is not sensitive to the sound speed pro- file, the sound speed profile is regarded as a constant; which makes the model rapid and accurate. The simulation results are in agreement with those of the wave model.

A Probabilistic Trust Model and Control Algorithm to Protect 6G Networks against Malicious Data Injection Attacks in Edge Computing Environments

Future 6G communications are envisioned to enable a large catalogue of pioneering applications.These will range from networked Cyber-Physical Systems to edge computing devices,establishing real-time feedback control loops critical for managing Industry 5.0 deployments,digital agriculture systems,and essential infrastructures.The provision of extensive machine-type communications through 6G will render many of these innovative systems autonomous and unsupervised.While full automation will enhance industrial efficiency significantly,it concurrently introduces new cyber risks and vulnerabilities.In particular,unattended systems are highly susceptible to trust issues:malicious nodes and false information can be easily introduced into control loops.Additionally,Denialof-Service attacks can be executed by inundating the network with valueless noise.Current anomaly detection schemes require the entire transformation of the control software to integrate new steps and can only mitigate anomalies that conform to predefined mathematical models.Solutions based on an exhaustive data collection to detect anomalies are precise but extremely slow.Standard models,with their limited understanding of mobile networks,can achieve precision rates no higher than 75%.Therefore,more general and transversal protection mechanisms are needed to detect malicious behaviors transparently.This paper introduces a probabilistic trust model and control algorithm designed to address this gap.The model determines the probability of any node to be trustworthy.Communication channels are pruned for those nodes whose probability is below a given threshold.The trust control algorithmcomprises three primary phases,which feed themodel with three different probabilities,which are weighted and combined.Initially,anomalous nodes are identified using Gaussian mixture models and clustering technologies.Next,traffic patterns are studied using digital Bessel functions and the functional scalar product.Finally,the information coherence and content are analyzed.The noise content and abnormal information sequences are detected using a Volterra filter and a bank of Finite Impulse Response filters.An experimental validation based on simulation tools and environments was carried out.Results show the proposed solution can successfully detect up to 92%of malicious data injection attacks.

LINEAR FILTERING FOR VASICEK TERM STRUCTURE MODEL WITH SEQUENTIALLY CORRELATED NOISE

When Kalman filter is used in the estimation of Vasicek term structure of interest rates,it is usual to assume that the measurement noise is uncorrelated.Study results are more favorable to the assumption of correlated measurement noise.An augmented state Kalman filter form for Vasicek model is proposed to optimally estimate the unobservable state variable with the assumption of correlated measurement noise.Empirical results indicate that the model with sequentially correlated measurement noise can more accurately describe the dynamics of the term structure of interest rates.

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussianα-stable Lévy noise

Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models.We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussianα-stable Lévy noise.More explicitly,firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers–Moyal formulas.Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process.Three examples are then given to demonstrate the feasibility.This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.