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Previous work assessing the effect of additive noise on the postural control system has found a positive effect of additive white noise on postural dynamics. This study covers two separate experiments that were run sequentially to better understand how the structure of the additive noise signal affects postural dynamics, while also furthering our knowledge of how the intensity of auditory stimulation of noise may elicit this phenomenon. Across the two experiments, we introduced three auditory noise stimulations of varying structure (white, pink, and brown noise). Experiment 1 presented the stimuli at 35 dB while Experiment 2 was presented at 75 dB. Our findings demonstrate a decrease in variability of the postural control system regardless of the structure of the noise signal presented, but only for high intensity auditory stimulation.

We report on efforts to improve the speed of low-G far-infrared transition-edged-sensed bolometers. We use a fabrication process that does not require any dry etch steps to reduce heat capacity on the suspended device and measure a reduction in the detector time constant. However, we also measure an increase in the temperature-normalized thermal conductance (G) and a corresponding increase in the noise-equivalent power (NEP). We employ a new near-IR photon-noise technique using a near-IR laser to calibrate the frequency-domain multiplexed AC system and compare the results to a well-understood DC circuit. We measure an NEP white noise level of 0.8 aW/rtHz with a 1/f knee below 0.1 Hz and a time constant of 3.2 ms. [ABSTRACT FROM AUTHOR]

Objective: Tuberculosis (TB) remains an important public health concern in western China. This study aimed to explore and analyze the spatial and temporal distribution characteristics of TB reported incidence in 12 provinces and municipalities in western China and to construct the optimal models for prediction, which would provide a reference for the prevention and control of TB and the optimization of related health policies. Methods: We collected monthly data on TB reported incidence in 12 provinces and municipalities in western China and used ArcGIS software to analyze the spatial and temporal distribution characteristics of TB reported incidence. We applied the seasonal index method for the seasonal analysis of TB reported incidence and then established the SARIMA and Holt-Winters models for TB reported incidence in 12 provinces and municipalities in western China. Results: The reported incidence of TB in 12 provinces and municipalities in western China showed apparent spatial clustering characteristics, and Moran's I was greater than 0 (p < 0.05) over 8 years during the reporting period. Among them, Tibet was the hotspot for TB incidence in 12 provinces and municipalities in western China. The reported incidence of TB in 12 provinces and municipalities in western China from 2004 to 2018 showed clear seasonal characteristics, with seasonal indices greater than 100% in both the first and second quarters. The optimal models constructed for TB reported incidence in 12 provinces and municipalities in western China all passed white noise test (p > 0.05). Conclusions: As a hotspot of reported TB incidence, Tibet should continue to strengthen government leadership and policy support, explore TB intervention strategies and causes. The optimal prediction models we developed for reported TB incidence in 12 provinces and municipalities in western China were different. [ABSTRACT FROM AUTHOR]

In this paper, the authors present a new transfer-learning-based robust technique for detection and classification of multi-type faults in low-voltage power distribution grids. Three-phase current and voltage signals were initially measured and sampled at a medium-voltage/low-voltage substation upon occurrence of a certain type of fault. Subsequently, a Hilbert–Huang transform was applied to the corresponding sampled fault signals to construct a time–frequency energy matrix as a 35 × 35 pixel matrix of the digital image after passing through a band-pass filter. Additionally, and for the sake of comprehensiveness, a residual network (ResNet) was designed as a fault detector and classifier to accurately identify the location and type of faults, while guaranteeing the robustness of the proposed technique against both white and connection noises. For the sake of evaluation, a three-phase 10 kV test system was implemented in the MATLAB/Simulink environment under different faulty operating conditions designs. The performance of the introduced technique was also examined in the Python environment. Based on simulation results, several conclusions can be drawn: (i) The ResNet outshines the neural architecture search network, Inception, and Xception by elevating the average accuracy by 2.23%; (ii) the ResNet-101 model is robust against white Gaussian noise and electromagnetic interference with values of 20, 30, and 40 dB; (iii) the proposed technique enhances functional coverage up to a radius of 30 km for fault detection along 14 points in the test system; and (iv) in the presence of distributed energy resources, the proposed technique is superior to other network architectures with an average of 5.44%. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics system forced by space-time white noise has been studied by physicists for decades, and the rigorous proof of its solution theory was recently established by Yamazaki (2023, Electron. J. Probab., 28 , 1–66). When an equation is well-posed, and it is approximated by replacing the differentiation operator by reasonable discretization schemes, it is widely believed that a solution of the approximating equation should converge to the solution of the original equation as the discretization parameter approaches zero. We prove otherwise for the three-dimensional magnetohydrodynamics system forced by space-time white noise. Specifically, we prove that the limit of the solution to the approximating system with an additional 32 drift terms solves the original system. These 32 drift terms depend on the choice of approximations, can be calculated explicitly and essentially represent a spatial version of Itô-Stratonovich correction terms. [ABSTRACT FROM AUTHOR]

Background: Newborns are exposed to varying degrees of stressful interventions due to procedures such as heel lancing used in routine metabolic screenings. It is an examination of the effects of white noise and kangaroo care on some physiological parameters and stress markers (cortisol and glucose-regulated protein 78-GRP78) in heel lancing in newborns. Methods: Randomized controlled study was conducted at a gynecology service of a hospital between January and September 2023. 90 babies were divided into three groups: 30 babies in the Kangaroo Care Group (KCG), 30 babies in the White Music Group (WMG), and 30 babies in the Control Group (CG). All babies were randomly divided into groups. Stress parameters were measured by saliva collection method and physiological parameters by saturation device. Results: A statistically significant difference was determined between the total crying time, pulse and saturation values ​​according to the groups (p < 0.001; p = 0.001). A statistically significant difference was determined between the mean values ​​of cortisol and GRP78 measurements according to group and time interaction (p < 0.001). KCG was more effective in reducing total crying time and stabilizing pulse, saturation, salivary cortisol, GRP-78 values compared to WNG and CG. Conclusion: It was concluded that white noise and kangaroo care help reduce newborns' stress in the case of heel lancing. Practical implications: The practice of kangaroo care and the use of white noise methods may assist healthcare professionals as supportive methods in stress management during invasive procedures. Trial Registration: NCT06278441, registered on 19/02/2024. [ABSTRACT FROM AUTHOR]

Understanding the mechanism by which the brain achieves relatively consistent information processing contrary to its inherent inconsistency in activity is one of the major challenges in neuroscience. Recently, it has been reported that the consistency of neural responses to stimuli that are presented repeatedly is enhanced implicitly in an unsupervised way, and results in improved perceptual consistency. Here, we propose the term "selective consistency" to describe this input-dependent consistency and hypothesize that it will be acquired in a self-organizing manner by plasticity within the neural system. To test this, we investigated whether a reservoir-based plastic model could acquire selective consistency to repeated stimuli. We used white noise sequences randomly generated in each trial and referenced white noise sequences presented multiple times. The results showed that the plastic network was capable of acquiring selective consistency rapidly, with as little as five exposures to stimuli, even for white noise. The acquisition of selective consistency could occur independently of performance optimization, as the network's time-series prediction accuracy for referenced stimuli did not improve with repeated exposure and optimization. Furthermore, the network could only achieve selective consistency when in the region between order and chaos. These findings suggest that the neural system can acquire selective consistency in a self-organizing manner and that this may serve as a mechanism for certain types of learning. Author summary: This study explores how the brain can achieve stable information processing despite its inherent variability. Here we introduced the concept of "selective consistency"—the brain's ability to enhance response consistency to stimuli experienced multiple times—and investigated how it is achieved in an unsupervised and self-organizing manner. Using a reservoir-based neural network model with Hebbian plasticity, we tested how it acquires selective consistency by exposing it to repeated white noise stimuli multiple times. Remarkably, our results demonstrate that the neural network can acquire this consistency quickly, with just five exposures to the stimuli. Additionally, the plastic neural network only achieved selective consistency when operating near the edge of chaos—a critical state maintaining a delicate balance between order and chaos. These findings suggest that a brain near criticality can self-organize its structure with plasticity to improve perceptual consistency without explicit supervision. This study underscores the potential for neural plasticity to drive selective consistency and suggests that such mechanisms may be fundamental to how the brain develops to achieve consistent information processing from experiences. [ABSTRACT FROM AUTHOR]

The fault diagnosis of rolling bearings is faced with the problem of a lack of fault data. Currently, fault diagnosis based on traditional convolutional neural networks decreases the diagnosis rate. In this paper, the developed adaptive residual shrinkage network model is combined with transfer learning to solve the above problems. The model is trained on the Case Western Reserve dataset, and then the trained model is migrated to a small-sample dataset with a scaled-down sample size and the Jiangnan University bearing dataset to conduct the experiments. The experimental results show that the proposed method can efficiently learn from small-sample datasets, improving the accuracy of the fault diagnosis of bearings under variable loads and variable speeds. The adaptive parameter-rectified linear unit is utilized to adapt the nonlinear transformation. When rolling bearings are in operation, noise production is inevitable. In this paper, soft thresholding and an attention mechanism are added to the model, which can effectively process vibration signals with strong noise. In this paper, the real noise is simulated by adding Gaussian white noise in migration task experiments on small-sample datasets. The experimental results show that the algorithm has noise resistance. [ABSTRACT FROM AUTHOR]

Analysis of tracheal breathing sounds (TBS) is a significant area of study in medical diagnostics and monitoring for respiratory diseases and obstructive sleep apnea (OSA). Recorded at the suprasternal notch, TBS can provide detailed insights into the respiratory system's functioning and health. This method has been particularly useful for non-invasive assessments and is used in various clinical settings, such as OSA, asthma, respiratory infectious diseases, lung function, and detection during either wakefulness or sleep. One of the challenges and limitations of TBS recording is the background noise, including speech sound, movement, and even non-tracheal breathing sounds propagating in the air. The breathing sounds captured from the nose or mouth can interfere with the tracheal breathing sounds, making it difficult to isolate the sounds necessary for accurate diagnostics. In this study, two surface microphones are proposed to accurately record TBS acquired solely from the trachea. The frequency response of each microphone is compared with a reference microphone. Additionally, this study evaluates the tracheal and lung breathing sounds of six participants recorded using the proposed microphones versus a commercial omnidirectional microphone, both in environments with and without background white noise. The proposed microphones demonstrated reduced susceptibility to background noise particularly in the frequency ranges (1800–2199) Hz and (2200–2599) Hz with maximum deviation of 2 dB and 2.1 dB, respectively, compared to 9 dB observed in the commercial microphone. The findings of this study have potential implications for improving the accuracy and reliability of respiratory diagnostics in clinical practice. [ABSTRACT FROM AUTHOR]

Accurately classifying the intra-pulse modulations of radar emitter signals is important for radar systems and can provide necessary information for relevant military command strategy and decision making. As strong additional white Gaussian noise (AWGN) leads to a lower signal-to-noise ratio (SNR) of received signals, which results in a poor classification accuracy on the classification models based on deep neural networks (DNNs), in this paper, we propose an effective denoising method based on a denoising diffusion probabilistic model (DDPM) for increasing the quality of signals. Trained with denoised signals, classification models can classify samples denoised by our method with better accuracy. The experiments based on three DNN classification models using different modal input, with undenoised data, data denoised by the convolutional denoising auto-encoder (CDAE), and our method's denoised data, are conducted with three different conditions. The extensive experimental results indicate that our proposed method could denoise samples with lower values of the SNR, and that it is more effective for increasing the accuracy of DNN classification models for radar emitter signal intra-pulse modulations, where the average accuracy is increased from around 3 to 22 percentage points based on three different conditions. [ABSTRACT FROM AUTHOR]

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a generalized spectral density function to account for pairwise dependence at all lags and construct a Cramér–von Mises-type test statistic. New theoretical arguments are developed to establish the asymptotic behaviour of the test statistic. A wild bootstrap is also introduced to obtain the critical values of the nonpivotal limiting null distribution. Extensive numerical simulations and two real data applications on cumulative intraday returns and human mortality data are conducted to illustrate the effectiveness and versatility of our proposed test. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the three-dimensional globally modified Navier–Stokes equations driven by additive white noise on some unbounded domains 풪. By using the Ornstein–Uhlenbeck process, we transfer the original equation to a random dynamical system, and then we prove the existence of pullback attractors for the random dynamical system equations under suitable conditions. Due to the unboundedness of the domains, we get the asymptotic compactness of the solutions by Ball's idea of energy equations. The periodicity of the attractors is also proved when the deterministic non-autonomous external terms are periodic in time. [ABSTRACT FROM AUTHOR]

In this study, we focus on the stochastic pure-cubic optical solitons of the nonlinear Schrödinger equation, characterized by a parabolic law of nonlinearity. The nonlinear Schrödinger equation models are crucial for simulating pulse propagation in optical fibers especially ultrashort pulses. To obtain optical soliton solutions, we employ the effective and well-known the new Kudryashov and the generalized Kudryashov methods. Through these methods, we successfully derive dark, bright, and singular optical soliton solutions. Our findings are illustrated with 2D and 3D graphics for clarity. A significant aspect of our study is the inclusion of stochasticity in the model. We specifically examine the impact of white noise on the solutions. This effect is detailed in the results section, with corresponding graphs. Throughout our research, we did not encounter any restrictive factors that hindered access to the results. Ultimately, considering the growing number of studies on optical fibers, our work stands out by being the first to obtain optical solutions for this specific model and by investigating the influence of stochastic theories on wave behavior. [ABSTRACT FROM AUTHOR]

The fractional differential equation L^\beta u = f posed on a compact metric graph is considered, where \beta >0 and L = \kappa ^2 - \nabla (a\nabla) is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients \kappa,a. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L^{-\beta }. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L_2(\Gamma \times \Gamma)-error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for {L = \kappa ^2 - \Delta, \kappa >0} are performed to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn–Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in L^1(\mathbb {R}) of the numerical solution. Our results partially answer positively to the open problem posed by J. Cui and J. Hong [J. Differential Equations 269 (2020), pp. 10143–10180] on computing the density of the exact solution numerically. [ABSTRACT FROM AUTHOR]

This study introduces a new method for precise acoustic drone localization and tracking via the noise generated by the drone. Drone noises include harmonic frequency components which are related to the rotational speed of the propeller and the number of blades. This study integrates utilization of the frequency components around harmonics into Steered Response Power - Phase Transform (SRP-PHAT). First, a custom discrete Fourier transform (namely DFT-Harmonics) is defined which concentrates only on the vicinities of harmonics to capture the frequency components possibly related to the drone sound. Then, DFT-Harmonics is integrated into SRP-PHAT, which is named SRP-Harmonics. The benefits of SRP-Harmonics are explained and illustrated via SRP maps and videos. Experiments with real microphone array data show that SRP-Harmonics is precise in localizing and tracking a drone, while the ordinary SRP-PHAT can not be reasonably successful. Moreover, SRP-Harmonics after Kaiser window can maintain its performance even when significant level of artificial white noise or natural wind noise exists in the data. [ABSTRACT FROM AUTHOR]

The study was conducted to determine the effects of white noise during nasal continuous positive airway pressure (CPAP) application on the newborn's pain and stress levels, physiological parameters, and crying durations. The study used a randomized, controlled experimental design. The study was completed with 80 newborns (40 in the intervention group and 40 in the control group). The Newborn Descriptive Data Form, ALPS Newborn Pain and Stress Assessment Scale, and Follow-up Form were used to collect the study data. Routine nasal CPAP application was performed to newborns in the control group. White noise was played to newborns in the intervention group before, during, and after the nasal CPAP application. The study was approved by an ethics committee. It was found that the newborn's pain and stress levels of the intervention group were lower than the control group before, during, and after the nasal CPAP application (p < 0.05). Before nasal CPAP application, the intervention group's SpO2 average was lower than that of the control group (p < 0.01). During nasal CPAP application, the intervention group's heart rate, SpO2, and crying duration averages were found to be lower than the control group (p < 0.05). After nasal CPAP application, the intervention group's crying duration average was lower than the control group (p < 0.01). It was found that white noise before, during, and after the nasal CPAP application reduced newborns' pain and stress levels. It is recommended that white noise be used as an easily applicable, economical, safe, and non-pharmacological method to reduce the pain and stress caused by nasal CPAP application in newborns. Clinical trials registration : The study was registered at Clinical-Trials.gov (NCT05440669). • White noise is used to manage pain and reduce physiological stress. • White noise before, during, and after the nasal CPAP application reduced the pain and stress levels in newborns. • It is recommended the use of white noise as an easily applicable, economical, and safe. [ABSTRACT FROM AUTHOR]

Damage identification, both in terms of size and location, in bridges is important for timely maintenance and to avoid any catastrophic failure. An earlier experimental study showed that damage in a steel box girder orthotropic plate can be successfully detected using the measured vibration acceleration data. In this study, the wavelet packet decomposition (WPD) method is used to analyze the measured vibration acceleration responses and then the estimation of the permutation entropy (PE) on the re-constructed signals. A damage index is then defined based on the permutation entropy difference (PED) between the damaged and the healthy conditions to detect the location and size of the damage. The method is further validated through the finite element (FE) model of a steel box girder and the computed vibration acceleration responses when subjected to the sinusoidal excitations at different frequencies. In addition, the robustness of the methodology under different white noise interference conditions is also verified. The results show that the proposed methodology can effectively identify the location of human-made damage and accurately estimate the degree of damage under different frequencies of sinusoidal excitation. The method has shown a strong anti-noise property. [ABSTRACT FROM AUTHOR]

In this paper, we study the Wong-Zakai approximations of stochastic evolution equations driven by a multiplicative white noise and their related dynamical behavior, where the Wong-Zakai approximations are given by a stationary process via the Wiener shift. Firstly, we show that the solutions of these stochastic evolution equations can be approximated almost surely with a polynomial rate. Next, we explore the Wong-Zakai approximations on the center manifolds of these stochastic evolution equations under an exponential trichotomy condition. Finally, we prove that these approximate center manifolds converge almost surely, with a polynomial rate. [ABSTRACT FROM AUTHOR]

Given the rapid prevalence and advancement of patent commercialization, tacit knowledge sharing during this process is increasingly being scrutinized. To explore the factors affecting tacit knowledge sharing in patent commercialization, this paper constructed a tripartite stochastic evolutionary game model to analyze the complex game interaction between inventors, enterprises, and patent intermediaries. Due to uncertainty in the external environment, Gaussian white noise was introduced into replicator dynamic equations, and numerical simulation was used to describe the tripartite dynamic evolution. The results showed the following: (1) inventors and enterprises with similar levels of relevant capabilities are more likely to achieve better results in sharing tacit knowledge. (2) The implementation of an effective market reputation evaluation system has the potential to enhance implicit knowledge sharing in the realm of patent commercialization. (3) The percentage of payments of the two‐stage payment contract will affect the behavior of inventors and enterprises. (4) The stability of the equilibrium solution is closely tied to the intensity of Gaussian white noise, which can lead to deviations from the original trajectory of equilibrium strategies. Greater external uncertainty makes tacit knowledge sharing more challenging. This study will provide constructive suggestions for promoting tacit knowledge sharing among participants in patent commercialization. [ABSTRACT FROM AUTHOR]

Classrooms are often noisy environments, which can result in unfavorable learning conditions for students. However, research has insufficiently addressed how noisy classrooms affect autistic students. This preliminary study examined differences in, and the impact of, background noise on reading performance for elementary-aged autistic and non-autistic (NA) children (N = 49). Autistic (n = 13) and NA children (n = 36) between the ages of 6 and 13 years participated in the current study. We employed a repeated measures design where each participant read four, grade-appropriate reading curriculum-based measurement (CBM) passages and subsequently completed comprehension (i.e., retell and recall) tasks in the presence of four different listening conditions (i.e., experimental condition): (1) quiet, (2) a single talker, (3) classroom noise, and (4) white noise. Using multi-level modeling (MLM), we found that listening condition differentially impacted reading fluency for all children. Children's reading fluency was more negatively impacted by the single talker in comparison to white noise and quiet. The performance of all children to retell story components (a measure of reading comprehension) was moderated by age with older children recalling more story components in the presence of white noise. Recalling story components correctly was not impacted by listening condition or disability. Regardless of disability, environments that include a single talker were not optimal for children's reading fluency skills. Moreover, preferred environments for children's reading comprehension skills—specifically the retelling of key story components—depend on student age, with background white noise being ideal for older children. Notably, no differences in how background noise impacts reading performance were found between autistic and NA children. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment. The model incorporates both white noise and telegraph noise, the latter being described by Markov process. The existence of a unique global positive solution for the stochastic chemostat model is established. Subsequently, by using the ergodic theory of Markov process and utilizing techniques of stochastic analysis, the critical value differentiating between persistence in mean and extinction for the microorganism species is explored. Moreover, the existence of a unique stationary distribution is proved by using stochastic Lyapunov analysis. Finally, numerical simulations are introduced to support the obtained results. [ABSTRACT FROM AUTHOR]

• Enhanced normalized EEG power was observed during ITd than during both WN and BB. • ITd modulated neural oscillation compared in alpha and beta frequency bands. • Changes in brain activity induced by ITd persist for minutes after stimulation. Auditory beats stimulation (ABS) has received increased attention for its potential to modulate neural oscillations through a phenomenon described as brain entrainment (i.e synchronization of brain's electrocortical activity to external stimuli at a specific frequency). Recently, a new form of ABS has emerged, inspired by isochronic tones stimulation (IT d). This study investigated neural oscillatory responses induced by IT d in comparison with formerly well-established ABS protocols, such as gamma-binaural beats (BB) and white noise (WN). We recorded the electroencephalographic brain activity in 28 participants during 4 min of BB, IT d , and WN presentation. Data demonstrated that while both BB and WN enhanced oscillatory power on the EEG gamma band, consistently with the expected brain entrainment effect, IT d yielded greater changes in EEG power (p < 0.001). This was confirmed by time-based analysis, which showed a progressive increase in normalized EEG power within the IT d window compared to BB (p < 0.05). Findings also revealed that IT d elicited acute changes in the alpha band of EEG oscillations, through a progressive decrease in power over time, which was distinctly different from the pattern observed while listening BB and WN. Such dual alpha-gamma effects underline the promising and unique potential of IT d to modulate neural oscillations which selectively differ from BB and WN. This study contributes to the evolution of ABS research, highlighting the promise of IT d for cognitive enhancement and clinical applications. [ABSTRACT FROM AUTHOR]

This research rigorously investigates a stochastic Susceptible-Infectious-Susceptible (SIS) epidemic model incorporating a generalized nonlinear incidence rate. The study further expands the model scope by introducing white and Lévy noise components. Including jumps and noises enhances the likelihood of disease extinction within the population. Initially, we utilized a comprehensive mathematical analysis to establish the global stability of the equilibrium state devoid of the disease. Our findings demonstrate that the system maintains stability even in the presence of the disease. This serves as a fundamental insight into the dynamics of disease transmission. Moreover, we define a collection of adequate criteria that contribute to the continuous presence of the ailment, thereby guaranteeing its non-complete eradication. By identifying the critical factors that contribute to the sustained presence of the disease, we enhance our understanding of the long-term behavior of the epidemic. To validate our theoretical findings, we conduct numerical simulations. These simulations effectively demonstrate the accuracy and reliability of the presented results. By comparing the simulated data with our analytical predictions, we can confidently confirm the validity of our model and its applicability in practical scenarios. [ABSTRACT FROM AUTHOR]

The Dean–Kawasaki (DK) equation is a stochastic partial differential equation (SPDE) for the global density ρ=N−1∑j=1Nδ(x−Xj(t)) of a gas of N over-damped Brownian particles, where Xj(t) is the position of the j th particle. In the thermodynamic limit N→∞ with weak pairwise interactions, the expectation ⟨ρ⟩ with respect to the white noise processes converges in distribution to the solution of a McKean–Vlasov (MV) equation. In this article, we use an encounter-based approach to derive a generalized DK equation for an interacting Brownian gas on the half-line with a partially absorbing boundary at x=0. Each particle is independently absorbed when its local time Lj(t) at x=0 exceeds a random threshold ℓ^j. The global density is now summed over the set of particles that have not yet been absorbed, and expectations are taken with respect to the Gaussian noise and the random thresholds ℓ^j. Assuming the DK equation has a well-defined mean-field limit, we derive the corresponding MV equation on the half-line. We illustrate the theory by (i) analysing stationary solutions for a Curie–Weiss (quadratic) interaction potential and a totally reflecting boundary; and (ii) calculating the effective rate of particle loss in the weak absorption limit. Extensions to finite intervals and partially absorbing traps are also considered. [ABSTRACT FROM AUTHOR]

The detrimental effects of high‐intensity noise on the auditory system and emotional status, including the induction of anxiety, are well documented. Preclinical as well as epidemiological and clinical studies have solidly established differential responses between males and females to various stressful stimuli, including high‐intensity white noise (HIWN). However, whether chronic exposure to noise affects cognitive functions and whether this effect is sex dependent has not been adequately addressed. In this study, we used two cognitive test paradigms, such as the Morris water maze (MWM) and the multi‐branch maze (MBM), to test the effect of chronic HIWN on indices of spatial learning and memory in both male and female Wistar rats. Our findings indicate that daily (1 h) exposure to 100 dB of noise for 30 consecutive days induces different task‐dependent responses in male versus female rats. For example, in the acquisition phase of MWM, female rats exposed to noise outperformed their male counterparts at twice the speed. Similarly, in the MBM test, noise‐exposed female rats outperformed the male rats in reaching the nest box. It is clear from these studies that noise impairs cognitive functions twice as negatively in male rats as in female rats. Thus, sex‐related differences in spatial learning and memory in response to HIWN must be taken into consideration when investigating the neurobiological components and/or treatment modalities. [ABSTRACT FROM AUTHOR]

AbstractObjectiveDesignStudy sampleResultsConclusionsWe have shown that the acoustic change complex (ACC) can be elicited by changing the horizontal sound location in young individuals. In this study, we aimed to evaluate the application of ACC within the elderly and its relationship with behavioural results.The minimum audible angle (MAA), as well as onset cortical auditory evoked potentials (onset-CAEPs) and ACC elicited by the stimuli of location-change white noise (±45 to ±2 degrees) were recorded. Latencies and amplitudes were analysed using repeated-measures ANOVA. Pearson correlation analysis was conducted to examine the relationship between ACC and MAA.Ten older adults with normal hearing (NH) and twenty with presbycusis.The ACC was effectively elicited with angular variations in elderly participants. The onset-CAEP N1 latency, ACC N1’-P2’ amplitude, and N1’ latency were all associated with the angle shifts, with the N1’ latency being the most predictive factor for angle discrimination. The consistency between MAA and ACC made them complementary for the clinical evaluation of sound localisation.The utilisation of ACC, evoked by location-change sounds, presented a promising clinical objective measure for evaluating sound localisation abilities in the elderly. [ABSTRACT FROM AUTHOR]

We propose single-species population models with the psychological effects and time delay in a toxicant environment in this study, of which the concentrations of toxicant nonlinearly affect the density of adults, linearly affect the density of juveniles. The models, consisting of a system of stochastic differential equations, govern the dynamics of juveniles and adults, as well as the concentrations of toxicant in the environment and organisms. First of all, the existence and uniqueness of the global solution to the models are derived, the sufficient conditions of the extinction and the time that the densities of adults and juveniles approach zero are investigated. Further, the sufficient conditions for the weak persistence in the mean are obtained around the pollution-free equilibrium point, and the stochastic permanence of adults and juveniles occurs around the pollution equilibrium points under moderate conditions. As a consequence, the corresponding numerical simulations reveal that higher psychological effects and less time delay create larger densities of juveniles and adults in the sense of weak persistence and stochastic permanence, and that less fluctuations of white noises and less psychological effects produce the earlier extinction time for adults and juveniles. [ABSTRACT FROM AUTHOR]

A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R 0 s > 1 , then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R 0 s > 1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and φ < 0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler–Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R 0 s . Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Hepatitis C model characterized by acute and chronic infections, treatment as a health-protective measure for the chronically infected is proposed, and its effect on the population is further highlighted. The model is perturbed by white noise and we incorporate Lévy jumps as means to depict abrupt fluctuations. We demonstrate the solution’s existence and uniqueness and deduce adequate criteria for the disease’s extinction and persistence. The importance of treatment as a protective strategy is manifested in its ability to eradicate or mitigate the propagation of the disease. We present numerical simulations to demonstrate the theoretical findings we have obtained. [ABSTRACT FROM AUTHOR]

We consider a system of stochastic differential equations, which is established by introducing white noises into a periodic and ratio-dependent food-chain system of three-species. We investigate the asymptotic behaviors for such a system, and obtain the sufficient conditions for its extinction and persistence with the help of Itô’s formula. We discuss the existence of a nontrivial positive periodic solution based on Has’minskii theory of periodic solution. Further, we study a ratio-dependent food-chain system of three-species including not only white noise but also telephone noise. For such a model, we give the sufficient conditions to guarantee the existence of a unique ergodic stationary distribution. [ABSTRACT FROM AUTHOR]

Noise is usually regarded as adversarial to extracting effective dynamics from time series, such that conventional approaches usually aim at learning dynamics by mitigating the noisy effect. However, noise can have a functional role in driving transitions between stable states underlying many stochastic dynamics. We find that leveraging a machine learning model, reservoir computing, can learn noise-induced transitions. We propose a concise training protocol with a focus on a pivotal hyperparameter controlling the time scale. The approach is widely applicable, including a bistable system with white noise or colored noise, where it generates accurate statistics of transition time for white noise and specific transition time for colored noise. Instead, the conventional approaches such as SINDy and the recurrent neural network do not faithfully capture stochastic transitions even for the case of white noise. The present approach is also aware of asymmetry of the bistable potential, rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns statistics of transition time between folded states, enabling us to characterize transition dynamics from a small dataset. The results portend the exploration of extending the prevailing approaches in learning dynamics from noisy time series. In many natural and engineered systems, noise adds challenges for extracting effective dynamics from time series, at the same time it may have a constructive role of driving transitions between stable states. The authors propose a framework based on reservoir computing for learning noise-induced transitions from data. [ABSTRACT FROM AUTHOR]

Public interest in the potential benefits of white, pink, and brown noise for attention-deficit/hyperactivity disorder (ADHD) has recently mushroomed. White noise contains all frequencies of noise and sounds like static; pink or brown noise has more power in the lower frequencies and may sound, respectively, like rain or a waterfall. This meta-analysis evaluated effects on laboratory tasks in individuals with ADHD or elevated ADHD symptoms. Eligible studies reported on participants with diagnosis of ADHD or elevated symptoms of ADHD who were assessed in a randomized trial using laboratory tasks intended to measure aspects of attention or academic work involving attention or executive function while exposed to white, pink, and brown noise and compared with a low/no noise condition. Two authors independently reviewed and screened studies for eligibility. A random-effects meta-analysis was conducted with preplanned moderator analyses of age, diagnostic status, and task type. Publication bias was evaluated. The GRADE tool was used to assess certainty of the evidence. Sensitivity analyses were conducted to evaluate robustness. Studies of children and college-age young adults with ADHD or ADHD symptoms (k = 13, N = 335) yielded a small but statistically significant benefit of white and pink noise on task performance (g = 0.249, 95% CI [0.135, 0.363], p <.0001). No studies of brown noise were identified. Heterogeneity was minimal, and moderators were nonsignificant; results survived sensitivity tests, and no publication bias was identified. In non-ADHD comparison groups (k = 11, N = 335), white and pink noise had a negative effect (g = −0.212, 95% CI [−0.355, −0.069], p =.0036). White and pink noise provide a small benefit on laboratory attention tasks for individuals with ADHD or high ADHD symptoms, but not for non-ADHD individuals. This article addresses theoretical implications, cautions, risks, and limitations. Public interest in the potential benefits of white, pink, and brown noise exposure for enhancing task performance for individuals with attention-deficit/hyperactivity disorder (ADHD) has increased substantially. This systematic review and meta-analysis included 13 studies with 335 participants and found that white/pink noise improved cognitive performance for children and young adults with ADHD or significant ADHD symptoms. In contrast, white/pink noise impaired cognitive performance for individuals without ADHD. Positive effects of noise were small, but these results point to a possible low-cost, low-risk intervention that may benefit youth with ADHD. Additional studies are needed to confirm effects and identify safe and appropriate decibel levels. The potential detrimental effects for individuals without ADHD also requires further study. White Noise for ADHD: A Systematic Review And Meta-analysis; https://www.crd.york.ac.uk/prospero; CRD42023393992. [ABSTRACT FROM AUTHOR]

In the present investigation, the Shannon entropy‐based magnetocaloric effect (MCE) of GaAs quantum dot (QD) is explored under the simultaneous influence of anharmonicity and Gaussian white noise (GWHN). The symmetry of the anharmonic potential (AHP), the manner of incorporation of GWHN, and the QD confinement interplay with great intricacy to tailor the MCE. AHP of odd (even) symmetry reduces (increases) the confinement of the system relative to the anharmonicity‐free system. Generally, the MCE profiles behave in diverse manner under additive white noise and multiplicative white noise and often show deviation from the noise‐free condition. It is also found that additive (multiplicative) noise lowers (raises) the magnitude of MCE in comparison with the noise‐free values. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labbé (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity. [ABSTRACT FROM AUTHOR]

In order to solve the problems of poor automaticity and difficult identification and elimination of spurious modes by covariance-driven stochastic subspace method, a new modal parameter identification method is proposed. Firstly, the covariance - driven stochastic subspace method is used to identify the modal parameters of the system. Secondly, according to the soft and hard criteria, the spurious modes are preliminarily eliminated and the 3D stabilization diagram is drawn. Then, the density-based spatial clustering algorithm with noise (DBSCAN) is improved, the sensitive parameter ε is automatically determined, and the candidate modes are clustered and analyzed. For each cluster of modalities, the modal quality assessment criterion (MQAC) is calculated, and a screening standard is formulated to determine the true modes of the system. Finally, the proposed method is used to verify the modal parameter identification of truss structure, Guangzhou Tower and Z24 bridge examples, The results indicate that this method can achieve autonomous modal analysis of typical engineering structures and effectively eliminate false modes caused by non - white noise excitation and measurement noise. [ABSTRACT FROM AUTHOR]

In biological neural networks, it has been well recognized that a healthy brain exhibits 1 / f noise patterns. However, in artificial neural networks that are increasingly matching or even out-performing human cognition, this phenomenon has yet to be established. In this work, we found that similar to that of their biological counterparts, 1 / f noise exists in artificial neural networks when trained on time series classification tasks. Additionally, we found that the activations of the neurons are the closest to 1 / f noise when the neurons are highly utilized. Conversely, if the network is too large and many neurons are underutilized, the neuron activations deviate from 1 / f noise patterns toward that of white noise. [ABSTRACT FROM AUTHOR]

Purpose: To describe the clinical, audiological, and psychometric features observed in patients with chronic tinnitus and rare variants in the ANK2 gene. Methods: We report a case series of 12 patients with chronic tinnitus and heterozygous variants in the ANK2 gene. Tinnitus phenotyping included audiological (standard and high-frequency audiometry, Auditory Brainstem Responses (ABR) and Auditory Middle Latency Responses (AMLR)), psychoacoustic and psychometric assessment by a Visual Analog Scale (VAS) for tinnitus annoyance, the Tinnitus Handicap Inventory (THI), the test on Hypersensitivity to Sound (THS-GÜF), the Patient Health Questionnaire (PHQ-9), the Hospital Anxiety and Depression Scale (HADS) and the Montreal Cognitive Assessment (MoCA). Results: All patients reported a persistent, unilateral noise-type tinnitus, mainly described as white noise or narrowband noise. Seven patients (58%) were considered to have extreme phenotype (THI score > 76), and all patients reported some degree of hyperacusis (THS-GÜF score > 18 in 75% of patients). Seven patients scored MoCA < 26, regardless of the age reported, suggesting a mild cognitive disorder. ABR showed no significant differences in latencies and amplitudes between ears with or without tinnitus. Similarly, the latencies of Pa, Pb waves, and NaPa complex in the AMLR did not differ based on the presence of tinnitus. However, there were statistical differences in the amplitudes of Pa waves in AMLR, with significantly greater amplitudes observed in ears with tinnitus. Conclusion: Patients with ANK2 variants and severe tinnitus exhibit an endophenotype featuring hyperacusis, persistent noise-like tinnitus, high-frequency hearing loss, and decreased amplitudes in AMLR. However, anxiety, depression, and cognitive symptoms vary among individuals. [ABSTRACT FROM AUTHOR]

In this article, we study the autocorrelation function (ACF), which is a crucial element in time series analysis. We compare the distribution of the ACF, both from a theoretical and empirical point of view. We focus on white noise processes (WN), i.e., uncorrelated, centered, and identically distributed variables, whose ACFs are supposed to be asymptotically independent and converge towards the same normal distribution. But, the study of the sum of the sample ACF contradicts this property. Thus, our findings reveal a deviation of the sample ACF from normality beyond a specific lag. Note that this phenomenon is observed for white noise of varying lengths, and evenforn the residuals of an ARMA( p , q ) model. This discovery challenges traditional assumptions of normality in time series modeling. Indeed, when modeling a time series, the crucial step is to validate the estimated model by checking that the associated residuals form white noise. In this study, we show that the widely used portmanteau tests are not completely accurate. Box–Pierce appears to be too conservative, whereas Ljung–Box is too liberal. We suggest an alternative method based on the ACF for establishing the reliability of the portmanteau test and the validity of the estimated model. We illustrate our methodology using money stock data in the USA. [ABSTRACT FROM AUTHOR]

This paper addresses the state estimation problem for a class of two‐dimensional shift‐varying systems with time‐correlated multiplicative measurement noises and additive noises. The time‐correlated multiplicative noises can be described as a linear system model corrupted by white noise. The main objective of this paper is to propose a recursive iterative coupled new‐type estimators and design the estimated gain reasonably to guarantee the minimum error covariance at each step. First, two new‐type coupling estimators are designed by introducing a new term. The unbiasedness of the two estimators are guaranteed by resorting to the mathematical inductive approach. Subsequently, an effective estimation is proposed given initial conditions. Moreover, the boundedness performance is investigated of the error covariance, and an upper bound is given based on the spectral norm. Finally, two numerical example are presented as an example to show the effectiveness of the estimation algorithm. [ABSTRACT FROM AUTHOR]

Chorusing animals constantly face the challenge of overcoming background noises. To minimize the masking of their own calls by conspecific or heterospecific calls, plasticity in call timing serves as an alternative tactic for chorusing animals. We examined how male rhacophorid treefrogs, Zhangixalus prasinatus , adjust their call timing in response to various noisy environments. When exposed to periodic white noise disturbances with brief silent intervals, the frogs accurately avoided overlapping with the noise and delivered their calls in the silent gaps. Moreover, they delivered long calls earlier than short calls during the silent periods to accommodate the longer duration within a brief silent gap. When exposed to noises of varying frequencies, the frogs specifically avoided medium-frequency noise, which closely matched their own call frequency. This phenomenon was also observed in experiments testing the aggregating behaviour of male frogs; they ceased to aggregate towards conspecific calls when interfered with by medium-frequency noise, whereas high-frequency and low-frequency noise interferences did not elicit the same behaviour. Compared to high-quality males, frogs with low SM i (scaled mass index) exhibited greater plasticity in call timing, indicating a condition-dependent tactic for energy allocation. Such behavioural plasticity in call timing was reflected in natural soundscape recordings. Our recordings revealed that, as a result of these adaptive strategies, males tended to avoid overlapping their calls with background noises in their natural habitats. Our research provides evidence that call plasticity is an effective strategy for chorusing animals to respond to noise at both individual and population levels. Furthermore, our study suggests that plasticity in call timing is a complex decision-making behaviour involving the consideration of noise properties and an individual's body condition. • Medium frequency interferes with frog calls and stops their aggregation behaviour. • Male treefrogs skillfully avoid noise interruption by adjusting call timing. • Low-quality frogs' calls are more plastic, revealing a condition-dependent tactic. • Call-timing plasticity effectively counters noise for individuals and populations. [ABSTRACT FROM AUTHOR]

High sensitivity and low noise of superconducting quantum interference devices make them ideal for reading the minute changes in resistance of a transition-edge sensor, which occurs when it absorbs energy or power. A series of first-order gradient, cross-coupling octagonal SQUIDs specifically tailored for use in TES were developed and fabricated for the advantage of lower parasitic capacitance compared with the overlap-coupling ones. It is obtained that a lower screening parameter and increased shunt resistance per junction lead to a higher flux-to-voltage transfer coefficient. This enhancement significantly boosts detection sensitivity and effectively minimizes noise contributions from electronics operating at room temperature. The low-temperature measurement results of the sample with an input coil of 3.5 turns indicate that a small device current white noise of 4.8 pA/√Hz, a device flux white noise of 1.1 μΦ0/√Hz, and an optimal flux-to-voltage transfer coefficient of 338.2 μV/Φ0 are achieved. The bandwidth of a SQUID current sensor with a smaller inductance of the input coil and a larger shunt resistance exceeds 10 MHz. SQUID current sensors, featuring octagonal structures with the first-order gradient cross-coupling, exhibit low flux noise, low current noise, and a high flux-to-voltage transfer coefficient, which can satisfy the requirements of TES applications. [ABSTRACT FROM AUTHOR]

A method is proposed for analyzing the tremor of the earth's surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is divided into 15 clusters. The Huang Empirical Mode Decomposition (EMD) is applied to the time series of the principal components from the clusters, with subsequent calculation of instantaneous amplitudes using the Hilbert transform. To ensure the stability of estimates of the waveforms of the EMD decomposition, 1000 independent additive realizations of white noise of limited amplitude were averaged before the Hilbert transform. Using a parametric model of the intensities of point processes, we analyze the connections between the instants of sequences of times of the largest local maxima of instantaneous amplitudes, averaged over the number of clusters and the times of earthquakes in the vicinity of Japan with minimum magnitude thresholds of 5.5 for the time interval 2012–2023. It is shown that the sequence of the largest local maxima of instantaneous amplitudes significantly more often precedes the moments of time of earthquakes (roughly speaking, has an "influence") than the reverse "influence" of earthquakes on the maxima of amplitudes. [ABSTRACT FROM AUTHOR]

The presence of noise and artifacts often has a significant impact on electrocardiogram (ECG) data. Signal corruptions of this nature impact the precise interpretation of ECG signals, necessitating the removal of noise and artifacts during the preprocessing stage. The present paper provides a thorough pre-processing phase that removes motion distortions and noise before identifying and recovering entirely distorted ECG signal segments. The initial technique, referred to as the WLNH method, is created by employing Wavelet multiresolution analysis (MRA), the Lilliefors test, NLM, and a high pass filter. The second approach involves replacing the wavelet MRA decomposition with the variational mode decomposition (VMD), while keeping all other steps from the previous approach. The abbreviation VLWNH is used to represent this approach. The two proposed methods distinguish themselves from existing methods by initially employing the Lilliefors test to determine if a component exhibits white Gaussian noise characteristics, and subsequently use the High Pass Filter to remove any motion irregularities. The simulation results demonstrate the effectiveness of the proposed strategies, especially in addressing white Gaussian noise and baseline wander (BW) noise. [ABSTRACT FROM AUTHOR]

Strong earthquake disasters can cause noticeable damage correlations among regional buildings with similar mechanical properties, termed structure‐to‐structure seismic damage correlation, which has a pronounced impact on the regional seismic risk assessment and therefore needs to be properly quantified. This study first introduces a time‐domain analytical and equivalent frequency‐domain analysis based on random vibration theory for calculating structure‐to‐structure seismic damage correlation coefficients. Subsequently, by employing the spatially consistent white noise excitation and the spatially varying white noise excitation with the Luco–Wong coherence function, the structural filtering effect and the ground motion spatial correlation effect are progressively incorporated, and an analytical interstructural damage correlation model incorporating structural dynamic properties and spatial distance is derived. Comparations with Monte Carlo simulations and existing empirical models demonstrate that the proposed analytical model possesses a clear physical basis and high reliability. Finally, a case study was conducted on a district having 29,461 buildings in Shanghai, China to illustrate the influence of interstructural damage correlation on the regional seismic risk. Results show that disregarding the interstructural seismic damage correlation can lead to underestimation of overall loss uncertainty. [ABSTRACT FROM AUTHOR]

Synthetic ground motions (GMs) play a fundamental role in both deterministic and probabilistic seismic engineering assessments. This paper shows that the family of filtered and modulated white noise stochastic GM models overlooks a key parameter—the high‐pass filter's corner frequency, fc$f_c$. In the simulated motions, this causes significant distortions in the long‐period range of the linear‐response spectra and in the linear‐response spectral correlations. To address this, we incorporate fc$f_c$ as an explicitly fitted parameter in a site‐based stochastic model. We optimize fc$f_c$ by individually matching the long‐period linear‐response spectrum (i.e., Sa(T)$Sa(T)$ for T≥1s$T \ge 1\,{\rm {s}}$) of synthetic GMs with that of each recorded GM. We show that by fitting fc$f_c$ the resulting stochastically simulated GMs can precisely capture the spectral amplitudes, variability (i.e., variances of log(Sa(T))$\log (Sa(T))$), and the correlation structure (i.e., correlation of log(Sa(T))$\log (Sa(T))$ between distinct periods T1$T_1$ and T2$T_2$) of recorded GMs. To quantify the impact of fc$f_c$, a sensitivity analysis is conducted through linear regression. This regression relates the logarithmic linear‐response spectrum (log(Sa(T))$\log (Sa(T))$) to 7 GM parameters, including the optimized fc$f_c$. The results indicate that the variance of fc$f_c$ observed in natural GMs, along with its correlation with the other GM parameters, accounts for 26% of the spectral variability in long periods. Neglecting either the fc$f_c$ variance or fc$f_c$ correlation typically results in an important overestimation of the linear‐response spectral correlation. [ABSTRACT FROM AUTHOR]

This paper primarily focused on analyzing a stochastic SVIR epidemic model that incorporates Levy noises. The population may be divided into four distinct compartments: vulnerable class (S), vaccinated individuals (V), infected individuals (I), and recovered individuals (R). To achieve this, we chose existing and unique techniques as the most feasible solution. In the nexus, the stochastic model was theoretically analyzed using a suitable Lyapunov function. This analysis broadly covered the existence and uniqueness of the non-negative solution, as well as the dynamic properties related to both the disease-free equilibrium and the endemic equilibrium. In order to eradicate diseases, a stochastic threshold value denoted as "R0" was used to determine if they may be eradicated. If R0 < 1; it means that the illnesses have the potential to become extinct. Moreover, we provided numerical performance results of the proposed model using the artificial neural networks technique combined with the Bayesian regularization method. We firmly believe that this study will establish a solid theoretical foundation for comprehending the spread of an epidemic, the implementation of effective control strategies, and addressing real-world issues across various academic disciplines. [ABSTRACT FROM AUTHOR]