Noise Perturbations Research Articles

Initial Condition Convection-Allowing Ensembles with Large Membership for Probabilistic Prediction of Convective Hazards

Abstract Convection-allowing model (CAM) ensemble forecasts provide quantitative probabilistic guidance of convective hazards that forecasters would otherwise qualitatively assess. Various initial condition (IC) strategies can be used to generate CAM probabilistic forecasts, but it is still unclear how different configurations perform. Schwartz et al. verified five 10-member IC CAM ensembles over one month of 0000 UTC initializations with a focus on precipitation. Here, we initialize four 42-member IC CAM ensembles every 12 h over 6 weeks and verify forecasts of precipitation, column maximum reflectivity, and hourly maximum updraft helicity. The Texas Tech University real-time EnKF ensemble and three additional IC ensemble modeling systems are verified. Holding the model configuration constant, additional ICs are generated by downscaling time-lagged Global Ensemble Forecast System (GEFS) members, applying correlated random noise to Global Forecast System (GFS) analyses, and recentering EnKF perturbations about GFS analyses. We found that ensemble ICs constructed with correlated random noise and EnKF perturbations about GFS analyses both produced higher-quality precipitation forecasts than downscaled GEFS and EnKF strategies. However, downscaled GEFS and EnKF perturbations about GFS analyses frequently initialized more skillful forecasts of reflectivity than ICs with random perturbations, suggesting that flow-dependent perturbations are important for forecasting deep convection. Even with a suboptimal EnKF configuration, our findings still echo those of Schwartz et al. We extend their work by exploring 1) verification of additional convective hazards and 2) empirical scaling of IC perturbations as a computationally inexpensive method for improving CAM ensemble forecasts.

Noise response in monomolecular closed systems

AbstractOne of the primary interests in understanding biological systems is the interaction between noise and cellular regulation. Noise levels can be altered by rate constant perturbations, which may result in an imbalance of important biological functions. Although the theory of noise localization can estimate noise perturbation response, it is currently limited to open systems, where the majority of biological networks belong. However, during their lifetime, some components of biological systems participate in reactions that can be categorized under a closed system. Therefore, a counterpart theory for closed systems is desirable. In this work, steady‐state perturbations of monomolecular closed systems and ways to estimate the response of noise as (co)variances are explored. We extend the structural sensitivity analysis for analyzing noise response patterns by using additional clues derived from multinomial assumptions. We identified scenarios in which this combination might fail in noise prediction, which we call noise flip, arising from the nonlinear dependence of variance upon composition. Nevertheless, theoretical intuition and simulation show that noise flip diminishes with increasing system size. This work provides an efficient and scalable means to estimate noise responses with potential applications in model discrimination, network‐wide response scanning, and reconstruction.

Inverse design of photonic crystal filters with arbitrary correlation and size for accurate spectrum reconstruction.

Spectroscopic technique based on nanophotonic filters can recover spectral information through compressive sensing theory. The spectral information is encoded by nanophotonic response functions and decoded by computational algorithms. They are generally ultracompact, low in cost, and offer single-shot operation with spectral resolution better than 1nm. Thus, they could be ideally suited for emerging wearable and portable sensing and imaging applications. Previous work has revealed that successful spectral reconstruction relies on well-designed filter response functions with sufficient randomness and low mutual correlation, but no thorough discussion has been performed on the filter array design. Here, instead of blind selection of filter structures, inverse design algorithms are proposed to obtain a photonic crystal filter array with predefined correlation coefficients and array size. Such rational spectrometer design can perform accurate reconstruction for a complex spectrum and maintain the performance under noise perturbation. We also discuss the impact of correlation coefficient and array size on the spectrum reconstruction accuracy. Our filter design method can be extended to different filter structures and suggests a better encoding component for reconstructive spectrometer applications.

Marmoset monkeys use different avoidance strategies to cope with ambient noise during vocal behavior

Multiple strategies have evolved to compensate for masking noise, leading to changes in call features. One call adjustment is the Lombard effect, an increase in call amplitude in response to noise. Another strategy involves call production in periods where noise is absent. While mechanisms underlying vocal adjustments have been well studied, mechanisms underlying noise avoidance strategies remain largely unclear. We systematically perturbed ongoing phee calls of marmosets to investigate noise avoidance strategies. Marmosets canceled their calls after noise onset and produced longer calls after noise-phases ended. Additionally, the number of uttered syllables decreased during noise perturbation. This behavior persisted beyond the noise-phase. Using machine learning techniques, we found that a fraction of single phees were initially planned as double phees and became interrupted after the first syllable. Our findings indicate that marmosets use different noise avoidance strategies and suggest vocal flexibility at different complexity levels in the marmoset brain.

A novel zeroing neural network for dynamic sylvester equation solving and robot trajectory tracking

To solve the theoretical solution of dynamic Sylvester equation (DSE), we use a fast convergence zeroing neural network (ZNN) system to solve the time-varying problem. In this paper, a new activation function (AF) is proposed to ensure fast convergence in predefined times, as well as its robustness in the presence of external noise perturbations. The effectiveness and robustness of this zeroing neural network system is analyzed theoretically and verified by simulation results. It was further verified by the application of robotic trajectory tracking.

A large deviation principle for fluids of third grade

ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.

Posterior regularization method for phase removal of shale nano-structure imaging in space domain

X-Ray computed tomography is a non-destructive method that is used, among many applications, to study the size, shape, 3D structures and interconnections of pores in shale. We use phase retrieval methods to deal with the “edge enhancement” effect caused by phase shift. The process of phase retrieval can be described by the transport-of-intensity equation (TIE). But this is an ill-posed problem. The existing methods focus on phase retrieval in the frequency domain. To tackle the ill-posedness, we propose a new method whose main idea is to solve this problem in space domain with a regularization technique. We study a synthetic shale model and simulate the projection data. Then we apply three methods to retrieve the phase: conventional method in frequency domain, direct solving method and iterative Tikhonov regularization method in space domain. Finally, we use the standard filtered back-projection (FBP) method to present the outcome. By analyzing the results, we find advantages of the new method: more stability and fewer artifacts under noise perturbations. The study shows that relative errors of the new method are nearly 1% of that of the traditional method based on frequency domain, and hence the new method is promising for the practical data processing.

Data-driven approximation for extracting the transition dynamics of a genetic regulatory network with non-Gaussian Lévy noise

In the study of biological systems, several methods based on statistical physics or machine learning have been developed for inference or prediction in the presence of complicated nonlinear interactions and random noise perturbations. However, there have been few studies dealing with the stochastic non-Gaussian perturbation case, which is more natural and universal than Gaussian white noise. In this manuscript, for a two-dimensional biological model (the MeKS network) perturbed by non-Gaussian stable Lévy noise, we use a data-driven approach with theoretical probabilistic foundation to extract the rare transition dynamics representing gene expression. This involves theories of non-local Kramers–Moyal formulas and the non-local Fokker–Planck equation, as well as the corresponding numerical algorithms, aimed at extracting the maximum likelihood transition path. The feasibility and accuracy of the method are checked. Furthermore, several dynamical behaviors and indicators are investigated. In detail, the investigation shows a bistable transition probability state of the ComK protein concentration and bifurcations in the learned transition paths from vegetative state to competence state. Analysis of the tipping time illustrates the difficulty of the gene expression. This method will serve as an example in the study of stochastic systems with non-Gaussian perturbations from biological data, and provides some insights into the extraction of other dynamical indicators, such as the mean first exit time and the first escape probability with respect to their own biological interpretations.

Noise‐tolerate and adaptive coefficient zeroing neural network for solving dynamic matrix square root

AbstractThe solving of dynamic matrix square root (DMSR) problems is frequently encountered in many scientific and engineering fields. Although the original zeroing neural network is powerful for solving the DMSR, it cannot vanish the influence of the noise perturbations, and its constant‐coefficient design scheme cannot accelerate the convergence speed. Therefore, a noise‐tolerate and adaptive coefficient zeroing neural network (NTACZNN) is raised to enhance the robust noise immunity performance and accelerate the convergence speed simultaneously. Then, the global convergence and robustness of the proposed NTACZNN are theoretically analysed under an ideal environment and noise‐perturbed circumstances. Furthermore, some illustrative simulation examples are designed and performed in order to substantiate the efficacy and advantage of the NTACZNN for the DMSR problem solution. Compared with some existing ZNNs, the proposed NTACZNN possesses advanced performance in terms of noise tolerance, solution accuracy, and convergence rate.

An Automatic ECG Signal Quality Assessment Method Based on Resnet and Self-Attention

Electrocardiogram (ECG) signals are among the significant physiological signals that indicate the essential properties of the human body. In recent years, the measurement of ECG signals has become more portable thanks to the increasing usage of wearable health testing technology. However, the enormous amount of signal data gathered over a long period of time does impose a heavy load on medical professionals. In addition, false alarms might occur due to the potential for the detected signal to become jumbled with noise and motion perturbations. Therefore, analyzing the quality of the measured raw ECG signal automatically is a valuable task. In this paper, we propose a new single-channel ECG signal quality assessment method that combines the Resnet network structure and the principle of self-attention to extract ECG signal features using the principle of similarity between individual QRS heartbeats within a time slice of ten seconds. In addition, an improved self-attention module is introduced into the deep neural network to learn the similarity between features. Finally, the network distinguishes between acceptable and unacceptable ECG segments. The model test results indicate that the F1-score can approach 0.954, which leads to a more accurate assessment of the ECG signal quality.

Robust poleward jet shifts in idealised baroclinic-wave life-cycle experiments with noisy initial conditions

Abstract. Idealised baroclinic-wave life-cycle experiments are a widely used tool to study fundamental characteristics of mid-latitude baroclinic instability. A typical life cycle evolves from an initialised baroclinically unstable jet through an exponential growth phase of a particular unstable wave mode, followed by wave breaking during the mature phase and wave–mean flow interaction driving a jet shift during the decay phase. Many authors distinguish between life cycles with predominantly anticyclonic (LC1) and cyclonic (LC2) wave breaking, and the transition between the two flavours is typically controlled via the strength of cyclonic meridional wind shear in the initial conditions. While baroclinic wave growth has traditionally been triggered via a specified initial perturbation with fixed zonal wave number, this study extends the concept of baroclinic-wave life cycles by analysing the influence of random initial perturbations without any preferred zonal dependency on the life-cycle evolution. We find that the growth phase shows a robust LC1–LC2 distinction as a function of initialised meridional shear, while a preference for LC1-like characteristics is observed during the decay phase for all life cycles with non-monochromatic initial perturbations. In particular, the persistent cut-off cyclones that typically form for LC2 initialisations are found to eventually become unstable, with the onset of instability coming sooner for larger noise perturbations. All non-monochromatic life cycles result in a poleward jet shift in their final state, regardless of the strength of the initial shear. Consistently, anticyclonic wave breaking tends to be predominant during the mature and decay phases, even for LC2 initialisations. Equatorward jet shifts associated with cyclonic wave breaking still exist, although purely as a transient interim state. We show that wave–wave interactions resulting from the initialised random wave spectrum play an important role during all phases of the life cycle.

DPBA-WGAN: A Vector-Valued Differential Private Bilateral Alternative Scheme on WGAN for Image Generation

The large amount of sensitive personal information used in deep learning models has attracted considerable attention for privacy security. Sensitive data may be memorialized or encoded into the parameters or generation of the Wasserstein Generative Adversarial Networks (WGAN), which can be prevented by implementing privacy-preserving algorithms during the parameter training process. Meanwhile, the model is also expected to obtain effective generated results. We propose a vector-valued differential private bilateral alternative (DPBA) algorithm, a novel perturbation method for the training process. The vector-valued Gaussian (VVG) noise involving functional structure information is injected into the WGAN to generate data with privacy protection, and the model is verified to satisfy differential privacy. The bilateral alternative noise can eventually randomly perturb the gradient and generates informative feature-rich samples. The dynamic noise and vector-based perturbation approach ensures privacy strength. After extensive evaluation, our algorithm outperformed state-of-the-art techniques in terms of usability metrics for all validation datasets. The downstream classification accuracy for the generated Modified National Institute of Standards and Technology (Mnist) was 97.04%, whereas that for the Fashion Modified National Institute of Standards and Technology (Fashion-Mnist) dataset was 80.91%. Mnist improved the average accuracy of the neural network classifier by at least 16.81%, and Fashion-Mnist by at least 3.55%. In the multichannel generation tasks, the binary classification accuracy improved by at least 10.4% compared to CelebFaces Attributes (CelebA), and the accuracy of the Street View House Numbers (SVHN) was as high as 86.1%. The perturbation method proved highly resilient to gradient attack recovery under simulated gradient attacks.

Improved clustering algorithm for personal privacy and security protection of elderly consumers

With the advancement of technology, there is an increasing emphasis on the personal privacy and security of elderly consumers. This article focuses on the personal privacy and security protection of elderly consumers. Based on the K-means (KM) clustering algorithm, the optimal value was obtained using the monarch butterfly optimization (MBO) algorithm. The migration operator and adjustment operator of the MBO algorithm were enhanced using differential variation algorithm and adaptive methods to obtain a modified monarch butterfly optimization (MMBO) algorithm. Then, to ensure secure protection during clustering, differential privacy (DP) was employed to add noise perturbation to data to obtained a method called DPMMBO-KM algorithm. In experiments on the UCI dataset, it was found that the MMBO-KM algorithm had better clustering performance. Taking the Iris dataset as an example, the MMBO-KM algorithm achieved the highest accuracy of 93.21%. In the application to recommendation systems, the DPMMBO-KM algorithm achieved higher F1 values under different privacy budgets; the average was 0.06. The results demonstrate that the improved clustering algorithm designed in this article can improve clustering results while ensuring personal privacy and data security, and also perform well in recommendation systems.

Approximate properties of stochastic functional differential equations with singular perturbations

This work focuses on stochastic functional differential equations (SFDEs) with wide-band noise perturbation, which is a class of actual physical process and has wide application in the modeling of communication and signal system. Using functional derivatives together with martingale methods and weak convergence techniques, this paper examines the asymptotic properties of the underlying systems as the small parameter tends to zero. Based on the techniques, this paper also establishes the average principle for a class of SFDEs with two-time scales. As a special case, this paper also considers a class of integro-differential equations with wide-band noise perturbation and examines its approximate properties. As an example, a scalar stochastic Lotka–Volterra integro-differential system with wide-band noise perturbation is investigated.

Successive lag synchronization of nonlinear stochastic networks with arbitrary structure via pinning control

AbstractIn this article, a new nonlinear stochastic network with arbitrary structure and noise is proposed for realizing the successive lag synchronization (SLS). Both the constant and adaptive pinning control laws are designed respectively to regulate the SLS to desired chaotic states, where the network structure can be directed, weighted, time‐varying and even not strongly connected. Several sufficient conditions for guaranteeing the stochastic asymptotic stability of SLS are derived by means of the Lyapunov stability theory. First, we demonstrate that the pinned nodes can be fixed via 1‐dimensional inequalities, which explicitly provide how many nodes and which nodes should be controlled. Besides, those connections from a node with a given number to other nodes with smaller numbers will lead to the increase of pinned nodes. Second, our results indicate that, in order to make the SLS stable the coupling strength must belong to a bounded interval for both the pinning control schemes. Finally, we conclude that strong noise perturbation will lead to the increase of pinned nodes and even break the SLS. The theoretical results are validated with different numerical examples by embedding the chaotic Chua's circuit to each node.

Ergodic Stationary Distribution and Threshold Dynamics of a Stochastic Nonautonomous SIAM Epidemic Model with Media Coverage and Markov Chain

A stochastic nonautonomous SIAM (Susceptible individual–Infected individual–Aware individual–Media coverage) epidemic model with Markov chain and nonlinear noise perturbations has been constructed, which is used to research the hybrid dynamic impacts of media coverage and Lévy jumps on infectious disease transmission. The uniform upper bound and lower bound of the positive solution are studied. Based on defining suitable random Lyapunov functions, we researched the existence of a nontrival positive T-periodic solution. Sufficient conditions are derived to discuss the exponential ergodicity based on verifying a Foster–Lyapunov condition. Furthermore, the persistence in the average sense and extinction of infectious disease are investigated using stochastic analysis techniques. Finally, numerical simulations are utilized to provide evidence for the dynamical properties of the stochastic nonautonomous SIAM.

Robust monocular 3D face reconstruction under challenging viewing conditions

Despite extensive research, 3D face reconstruction from a single image remains an open research problem due to the high degree of variability in pose, occlusions and complex lighting conditions. While deep learning-based methods have achieved great success, they are usually limited to near frontal images and images that are free of occlusions. Also, the lack of diverse training data with 3D annotations considerably limits the performance of such methods. As such, existing methods fail to recover, with high fidelity, the facial details especially when dealing with images captured under extreme conditions. To address this issue, we propose an unsupervised coarse-to-fine framework for the reconstruction of 3D faces with detailed textures. Our core idea is that multiple images of the same person but captured under different viewing conditions should provide the same 3D face. We thus propose to leverage a self-augmentation learning technique to train a model that is robust to diverse variations. In addition, instead of directly employing image pixels, we use a set of discriminative features describing the identity and attributes of the face as input to the refinement module, making the model invariant to viewing conditions. This combination of self-augmentation learning with rich face-related features allows the reconstruction of plausible facial details even under challenging viewing conditions. We train the model end-to-end and in a self-supervised manner, without any 3D annotations, landmarks or identity labels, using a combination of an image-level photometric loss and a perception-level loss that is identity and attribute-aware. We evaluate the proposed approach on CelebA and AFLW2000 datasets, and demonstrate its robustness to appearance variations despite learning from unlabeled images. The qualitative comparisons indicate that our method produces detailed 3D faces even under extreme occlusions, out of plane rotations and noise perturbations where existing state-of-the-art methods often fail. We also quantitatively show that our method outperforms SOTA with more than 30.14%, 9.87% and 11.3% in terms of PSNR, SSIM and IDentity similarity, respectively.

Estimations and Control of Julia Sets of the SIS Model Perturbed by Noise.

The estimations and control of Julia sets of the SIS(susceptible-infectious-susceptible) model under noise perturbation are studied. At first, a discrete SIS model is introduced, and the effects of additive and multiplicative noises on the fractal characteristics of the SIS model are discussed. Then, estimations of the Julia sets of the SIS model under additive and multiplicative noise perturbations are given, respectively. At last, the feedback control method is used to set appropriate controllers to realize control of the Julia set, and the influence of noise on the Julia set of the SIS model is reduced. The reason why this method is effective is also explained.

A fault diagnosis method for rolling bearings based on RDDAN under multivariable working conditions

Mechanical equipment in actual motion can produce noise interference with the vibration signal of rolling bearings, which have non-constant loads and speed. These factors lead to variable and unstable vibration signals of rolling bearings; therefore, it is very difficult to accurately diagnose actual running rolling bearings. In this paper, a residual denoising dynamic adaptation network (RDDAN) is proposed, which uses the signal knowledge under known working conditions to diagnose rolling bearing faults under unknown working conditions. The method mainly consists of data preprocessing, feature extraction, and dynamic distribution adaptation. First, Gaussian noise is added at the data preprocessing stage to emulate the noise perturbation during the reality of rolling bearing operation. Secondly, a deep residual shrinkage network is used for noise reduction and feature extraction. Finally, the marginal probability distribution and conditional probability distribution under different working conditions are calculated, depending on the characteristics. The network is disciplined using the relative weight of the marginal probability distribution and the conditional probability distribution. And the fault classification results are output after multiple iterations. The method was tested on the Case Western Reserve University bearing dataset and the Machine Fault Simulator Magnum bearing dataset, respectively. In comparison with other models, the RDDAN improves the average accuracy by about 23%. The results show that the RDDAN can effectively solve the problem of inconsistent data distribution in rolling bearings under operating conditions influenced by multiple variables such as noise, load, and speed.

Stochastic delay differential equations: Analysis and simulation studies

Stochastic delay differential equations play an important role in modelling scientific and engineering systems. In this paper the partial differential equation satisfying the time evolution of the probability density function of the state variable governed by the stochastic delay differential equation (SDDE) with additive white noise and coloured noise perturbation is obtained under small time delay and small correlation time approximation using path integral formalism. This partial differential equation reduces to a Fokker–Planck equation for particular linear and non-linear SDDE. Fokker–Planck equation is then solved with reflecting boundary conditions to get the analytical solutions for Stationary Probability Density Function (SPDF). The analytical solutions for SPDF is compared with the SPDF obtained using simulation. Further the Mean First Passage Time (MFPT) of the bistable system is calculated for various values of time delay and noise strength and compared with that of the simulation. The MFPT for the time delayed system for the case of cubic potential driven by Gaussian and Levy noise as well as asymmetric bistable potential driven by a noise and periodic driving force has been investigated.