White Noise Research Articles

Stochastic fractional diffusion equations with Gaussian noise rough in space

Stochastic fractional diffusion equations with Gaussian noise rough in space

Asymptotically autonomous robustness of random attractors for the stochastic wave lattice equations with random viscosity

In this paper, we focus on the asymptotic behavior of solutions to the non-autonomous stochastic wave lattice systems with random viscosity and multiplicative white noise. Under proper conditions, we first prove the existence and uniqueness of the pullback random attractors and then show their backward compactness in a weighted space. Finally, we establish the asymptotically autonomous robustness of pullback random attractors when the nonlinearity is bounded and the time-dependent forcing term converges to the time-independent counterpart.

Reconstruction of excitation waves from mechanical deformation using physics-informed neural networks

Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One promising path is to measure the mechanical contraction via echocardiography and utilize this as an indirect way of measuring the original activation pattern. To solve this demanding inversion task, we make use of physics-informed neural networks, an upcoming methodology to solve forward and inverse physical problems governed by partial differential equations. In this study, synthetic data sets were created, consisting of 2D excitation waves coupled to an isotropic and linearly deforming elastic medium. We show that for both focal and spiral patterns, the underlying excitation waves can be reconstructed accurately. We test the robustness of the method against Gaussian noise, reduced spatial resolution and projected tri-planar data. In situations where the data quality is heavily reduced, we show how to improve the reconstruction by additional regularization on the wave speed. Our findings suggest that physics-informed neural networks hold the potential to solve sparse and noisy bio-mechanical inversion problems and may offer a pathway to non-invasive assessment of certain cardiac arrhythmias.

Random flutter analysis of a novel binary airfoil with fractional order viscoelastic constitutive relationship

The fractional order model emerges naturally when the integer order model fails to meet practical requirements and finds extensive applications in engineering practice. However, there is still limited research on the random flutter of fractional order viscoelastic binary airfoils. This study aims to explore the random flutter of such airfoils under the influence of Gaussian white noise excitation by utilizing the pth moment Lyapunov exponent. Firstly, a two-degree-of-freedom fractional order stochastic dynamic equation is established for the viscoelastic binary airfoil through the introduction of fractional order damping. The singular perturbation method is then employed to derive the pth moment Lyapunov exponent of the system. An approximate analytical solution of the pth moment Lyapunov exponent is obtained through Fourier series expansion, which exhibits good agreement with numerical results obtained from Monte Carlo simulations. Subsequently, a comprehensive analysis is conducted to examine the impacts of fractional order, airflow velocity, noise intensity, and key structural parameters on the stochastic flutter of the fractional order viscoelastic binary airfoil. The findings indicate that compared with the typical binary airfoil model, the flutter speed of the fractional-order viscoelastic binary airfoil is significantly increased, the stability of the system is highly sensitive to the natural frequency of the system, and the fractional-order factor has a positive effect on the stochastic stability of the binary airfoil before the critical value. The above research results can guide the design optimization of the fractional-order viscoelastic airfoil.

Weak noise approximation for the Kolmogorov forward equation for a leaky integrate-and-fire neuron subject to stochastic stimulation

We develop a weak noise approximation for the Kolmogorov forward equation governing the dynamics of a leaky integrate-and-fire neuron subject to white noise. Although being very simple, our approximation provides accurate results as far the magnitude of noise-induced fluctuations Δ remains much smaller than the distance A between the mean potential (center of mass) and the excitation threshold. The error for the firing rate is <3% if A/Δ>3 for the stationary stimuli and if A/Δ>5 for time-varying stimuli.

Fuzzy adaptive cruise control with model predictive control responding to dynamic traffic conditions for automated driving

Traditional Adaptive Cruise Control (ACC) systems often struggle to dynamically adapt to rapidly changing traffic conditions, resulting in suboptimal performance. Additionally, with fuel consumption emerging as a critical consideration alongside safety, there is a pressing need for more advanced solutions. This paper presents a novel approach to address these challenges by integrating Fuzzy ACC with Model Predictive Control, denoted as FACMPC. This integration aims to enhance both the longitudinal safety of AVs and fuel efficiency by considering real-time traffic conditions. The FACMPC system utilizes fuzzy logic inside the MPC, adaptively generates controller's weighting factors, allowing the system to adapt instantly to varying traffic environments and driving circumstances. The findings show that this adaptation improves the balance between driving safety, efficiency, and comfort. Additionally, three interruption scenarios, Alpha, Beta and Gama, are examined. In Alpha, the study evaluates the sensitivity of the FACMPC to disturbances by applying band-limited white noise to the lead vehicle velocity. In Beta, the AV experiences a loss of the lead vehicle velocity signal for a defined period, prompting safety considerations and assumptions. The Gama scenario includes a sensitivity analysis to account for variations and uncertainties in parameters by considering a range of ±5% around the nominal values for four key parameters: road slope, wind speed, wind direction, and rolling resistance. The findings indicate that the proposed controller's mean fuel consumption is 8.110, only a 3.21% increase over the nominal, compared to a 7.03% increase for the conventional ACC, demonstrating greater robustness against uncertainties.

Open-loop quantum control of small-size networks for high-order cumulants and cross-correlations sensing

Quantum control techniques are one of the most efficient tools for attaining high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit affected by pure dephasing classical correlated 1/f-noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants. The error is separated in contributions of Gaussian and non-Gaussian noise, with the corresponding generalized filter functions calculated up to the fourth order. By exploiting the properties of selected pulse sequences, we show that it is possible to extract the second-order statistics (spectrum and cross-spectrum) and to highlight non-Gaussian features contained in the fourth-order cumulant. We discuss the applicability of these results to state-of-the-art small networks based on solid-state platforms.

Uncertainty quantification via localized gradients for deep learning-based medical image assessments

Objective. Deep learning models that aid in medical image assessment tasks must be both accurate and reliable to be deployed within clinical settings. While deep learning models have been shown to be highly accurate across a variety of tasks, measures that indicate the reliability of these models are less established. Increasingly, uncertainty quantification (UQ) methods are being introduced to inform users on the reliability of model outputs. However, most existing methods cannot be augmented to previously validated models because they are not post hoc, and they change a model’s output. In this work, we overcome these limitations by introducing a novel post hoc UQ method, termed Local Gradients UQ, and demonstrate its utility for deep learning-based metastatic disease delineation. Approach. This method leverages a trained model’s localized gradient space to assess sensitivities to trained model parameters. We compared the Local Gradients UQ method to non-gradient measures defined using model probability outputs. The performance of each uncertainty measure was assessed in four clinically relevant experiments: (1) response to artificially degraded image quality, (2) comparison between matched high- and low-quality clinical images, (3) false positive (FP) filtering, and (4) correspondence with physician-rated disease likelihood. Main results. (1) Response to artificially degraded image quality was enhanced by the Local Gradients UQ method, where the median percent difference between matching lesions in non-degraded and most degraded images was consistently higher for the Local Gradients uncertainty measure than the non-gradient uncertainty measures (e.g. 62.35% vs. 2.16% for additive Gaussian noise). (2) The Local Gradients UQ measure responded better to high- and low-quality clinical images (p < 0.05 vs p > 0.1 for both non-gradient uncertainty measures). (3) FP filtering performance was enhanced by the Local Gradients UQ method when compared to the non-gradient methods, increasing the area under the receiver operating characteristic curve (ROC AUC) by 20.1% and decreasing the false positive rate by 26%. (4) The Local Gradients UQ method also showed more favorable correspondence with physician-rated likelihood for malignant lesions by increasing ROC AUC for correspondence with physician-rated disease likelihood by 16.2%. Significance. In summary, this work introduces and validates a novel gradient-based UQ method for deep learning-based medical image assessments to enhance user trust when using deployed clinical models.

A Multi-Agent Reinforcement Learning-Based Task-Offloading Strategy in a Blockchain-Enabled Edge Computing Network

In recent years, many mobile edge computing network solutions have enhanced data privacy and security and built a trusted network mechanism by introducing blockchain technology. However, this also complicates the task-offloading problem of blockchain-enabled mobile edge computing, and traditional evolutionary learning and single-agent reinforcement learning algorithms are difficult to solve effectively. In this paper, we propose a blockchain-enabled mobile edge computing task-offloading strategy based on multi-agent reinforcement learning. First, we innovatively propose a blockchain-enabled mobile edge computing task-offloading model by comprehensively considering optimization objectives such as task execution energy consumption, processing delay, user privacy metrics, and blockchain incentive rewards. Then, we propose a deep reinforcement learning algorithm based on multiple agents sharing a global memory pool using the actor–critic architecture, which enables each agent to acquire the experience of another agent during the training process to enhance the collaborative capability among agents and overall performance. In addition, we adopt attenuatable Gaussian noise into the action space selection process in the actor network to avoid falling into the local optimum. Finally, experiments show that this scheme’s comprehensive cost calculation performance is enhanced by more than 10% compared with other multi-agent reinforcement learning algorithms. In addition, Gaussian random noise-based action space selection and a global memory pool improve the performance by 38.36% and 43.59%, respectively.

Correction to: Nonlinear random vibration of damaged cable systems under Gaussian white noise excitations

Correction to: Nonlinear random vibration of damaged cable systems under Gaussian white noise excitations

Structure-aware diffusion for low-dose CT imaging

Reducing the radiation dose leads to the x-ray computed tomography (CT) images suffering from heavy noise and artifacts, which inevitably interferes with the subsequent clinic diagnostic and analysis. Leading works have explored diffusion models for low-dose CT imaging to avoid the structure degeneration and blurring effects of previous deep denoising models. However, most of them always begin their generative processes with Gaussian noise, which has little or no structure priors of the clean data distribution, thereby leading to long-time inference and unpleasant reconstruction quality. To alleviate these problems, this paper presents a Structure-Aware Diffusion model (SAD), an end-to-end self-guided learning framework for high-fidelity CT image reconstruction. First, SAD builds a nonlinear diffusion bridge between clean and degraded data distributions, which could directly learn the implicit physical degradation prior from observed measurements. Second, SAD integrates the prompt learning mechanism and implicit neural representation into the diffusion process, where rich and diverse structure representations extracted by degraded inputs are exploited as prompts, which provides global and local structure priors, to guide CT image reconstruction. Finally, we devise an efficient self-guided diffusion architecture using an iterative updated strategy, which further refines structural prompts during each generative step to drive finer image reconstruction. Extensive experiments on AAPM-Mayo and LoDoPaB-CT datasets demonstrate that our SAD could achieve superior performance in terms of noise removal, structure preservation, and blind-dose generalization, with few generative steps, even one step only.

Using the Haken-Strobl-Reineker Model to Determine the Temperature Dependence of the Diffusion Coefficient.

Stochastic quantum Liouville equations (SQLE) are widely used to model energy and charge dynamics in molecular systems. The Haken-Strobl-Reineker (HSR) SQLE is a particular paradigm in which the dynamical noise that destroys quantum coherences arises from a white noise (i.e., constant-frequency) spectrum. A system subject to the HSR SQLE thus evolves to its "high-temperature" limit, whereby all the eigenstates are equally populated. This result would seem to imply that the predictions of the HSR model, e.g., the temperature dependence of the diffusion coefficient, have no validity for temperatures lower than the particle bandwidth. The purpose of this paper is to show that this assumption is incorrect for translationally invariant systems. In particular, provided that the diffusion coefficient is determined via the mean-squared-displacement, considerations about detailed-balance are irrelevant. Consequently, the high-temperature prediction for the temperature dependence of the diffusion coefficient may be extrapolated to lower temperatures, provided that the bath remains classical. Thus, for diagonal dynamical disorder the long-time diffusion coefficient, D∞(T) = c1/T, while for both diagonal and off-diagonal disorder, D∞(T) = c1/T + c2T, where c2 ≪ c1. An appendix discusses an alternative interpretation from the HSR model of the "quantum to classical" dynamics transition, whereby the dynamics is described as stochastically punctuated coherent motion.

A Low-Computational Burden Closed-Form Approximated Expression for MSE Applicable for PTP with gfGn Environment

The Precision Time Protocol (PTP) plays a pivotal role in achieving precise frequency and time synchronization in computer networks. However, network delays and jitter in real systems introduce uncertainties that can compromise synchronization accuracy. Three clock skew estimators designed for the PTP scenario were obtained in our earlier work, complemented by closed-form approximations for the Mean Squared Error (MSE) under the generalized fractional Gaussian noise (gfGn) model, incorporating the Hurst exponent parameter (H) and the a parameter. These expressions offer crucial insights for network designers, aiding in the strategic selection and implementation of clock skew estimators. However, substantial computational resources are required to fit each expression to the gfGn model parameters (H and a) from the MSE perspective requirement. This paper introduces new closed-form estimates that approximate the MSE tailored to match gfGn scenarios that have a lower computational burden compared to the literature-known expressions and that are easily adaptable from the computational burden point of view to different pairs of H and a parameters. Thus, the system requires less substantial computational resources and might be more cost-effective.

Head and neck tumor segmentation from [18F]F-FDG PET/CT images based on 3D diffusion model

Objective. Head and neck (H&N) cancers are among the most prevalent types of cancer worldwide, and [18F]F-FDG PET/CT is widely used for H&N cancer management. Recently, the diffusion model has demonstrated remarkable performance in various image-generation tasks. In this work, we proposed a 3D diffusion model to accurately perform H&N tumor segmentation from 3D PET and CT volumes. Approach. The 3D diffusion model was developed considering the 3D nature of PET and CT images acquired. During the reverse process, the model utilized a 3D UNet structure and took the concatenation of 3D PET, CT, and Gaussian noise volumes as the network input to generate the tumor mask. Experiments based on the HECKTOR challenge dataset were conducted to evaluate the effectiveness of the proposed diffusion model. Several state-of-the-art techniques based on U-Net and Transformer structures were adopted as the reference methods. Benefits of employing both PET and CT as the network input, as well as further extending the diffusion model from 2D to 3D, were investigated based on various quantitative metrics and qualitative results. Main results. Results showed that the proposed 3D diffusion model could generate more accurate segmentation results compared with other methods (mean Dice of 0.739 compared to less than 0.726 for other methods). Compared to the diffusion model in 2D form, the proposed 3D model yielded superior results (mean Dice of 0.739 compared to 0.669). Our experiments also highlighted the advantage of utilizing dual-modality PET and CT data over only single-modality data for H&N tumor segmentation (with mean Dice less than 0.570). Significance. This work demonstrated the effectiveness of the proposed 3D diffusion model in generating more accurate H&N tumor segmentation masks compared to the other reference methods.

Enhancing collective entanglement witnesses through correlation with state purity

This research analyzes the adverse impact of white noise on collective quantum measurements and argues that such noise poses a significant obstacle for the otherwise straightforward deployment of collective measurements in quantum communications. Our findings then suggests addressing this issue by correlating outcomes of these measurements with quantum state purity. To test the concept, a support vector machine is employed to boost the performance of several collective entanglement witnesses by incorporating state purity into the classification task of distinguishing entangled states from separable ones. Furthermore, the application of machine learning allows to optimize specificity of entanglement detection given a target value of sensitivity. A response operating characteristic curve is reconstructed based on this optimization and the area under curve calculated to assess the efficacy of the proposed model. Finally, we test the presented approach on an experimental dataset of Werner states.

Seismic data denoising using the 3D curvelet transform method

One of the major difficulties in processing and interpreting seismic data is the contamination of seismic signals by noise from numerous sources. Conventional denoising methods are mostly used for processing 2D seismic data, but noise also exists in the 3D data space, resulting in poor results using conventional denoising methods. Consequently, here, for seismic data denoising, a multiscale and multidirectional 3D curvelet transform was adopted. Our study combined the core principle of the 3D curvelet approach with the threshold iteration method to denoise simulated and actual seismic data with varying signal-to-noise ratios, and the results were quantitatively compared with the processing outcomes of existing denoising methods. The effectiveness of our method is illustrated using both genuine 2D and 3D post-stack seismic data, and synthetic 2D sections with added white and colored noise. Finally, we demonstrate how to prepare the data for frequency-domain full-waveform inversion using curvelet denoising. Despite the complexity of the procedure used to create the training samples, testing results using synthetic and real seismic data demonstrate that this method has mastered the capacity to suppress Gaussian and super-Gaussian noise from various training samples.

CLT for NESS of a reaction-diffusion model

AbstractWe study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions $$d \le 3$$ d ≤ 3 we show a central limit theorem for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.

Estimation of wind dynamic load linear transfer matrix using proper orthogonal decomposition method and genetic algorithm

ABSTRACT Due to the advantages of Laplace domain in both time and frequency domains, the dynamic analysis and control tools in engineering software like MATLAB and Python have been designed based on it. Dynamic analysis of structures requires determination of the overall transfer matrix, which is obtained by multiplying the structure's transfer matrix (TM) with the load TM. With the input vector of unit intensity white-noise processes and the overall TM, the structural responses can be obtained. Furthermore, having the load TM is crucial for implementation of active control systems. In this article, the TM of along-wind loads was estimated for a tall building using the proper orthogonal decomposition (POD) method and the genetic algorithm (GA). To evaluate the effectiveness of the proposed approach, an example of a tall building was provided. The wind load cross-power spectral matrix (XPSD) was decomposed using POD technique, followed by the truncation of higher loading modes. Subsequently, the loading TM was derived by estimating the target non-linear functions with linear transfer functions through GA technique. Then, the responses of the structure were computed using the loading TM. The results demonstrated the efficacy of the proposed method in acquiring the loading TM and predicting wind-induced responses.

Brain wave modulation and EEG power changes during auditory beats stimulation

BackgroundAuditory 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 (ITd). ObjectiveThis study investigated neural oscillatory responses induced by ITd in comparison with formerly well-established ABS protocols, such as gamma-binaural beats (BB) and white noise (WN). MethodsWe recorded the electroencephalographic brain activity in 28 participants during 4 min of BB, ITd, and WN presentation. ResultsData demonstrated that while both BB and WN enhanced oscillatory power on the EEG gamma band, consistently with the expected brain entrainment effect, ITd 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 ITd window compared to BB (p < 0.05). Findings also revealed that ITd elicited acute changes in the alpha band of EEG oscillations, through a progressive decrease in power over time, which is distinctly different from the pattern observed while listening BB and WN. Such dual alpha-gamma effects underline the promising and unique potential of ITd to modulate neural oscillations which selectively differ from BB and WN. ConclusionThis study contributes to the evolution of ABS research, highlighting the promise of ITd for cognitive enhancement and clinical applications.

Mimicking classical noise in ion channels by quantum decoherence

The mechanism of selectivity in ion channels is still an open question in biology. Recent studies suggest that the selectivity filter may exhibit quantum coherence, which could help explain how ions are selected and conducted. However, environmental noise causes decoherence and loss of quantum effects. It is hoped that the effect of classical noise on ion channels can be modeled using the framework provided by quantum decoherence theory. In this paper, the behavior of the ion channel system was simulated using two models: the Spin–Boson model and the stochastic Hamiltonian model under classical noise. Additionally, using a different approach, the system’s evolution was modeled as a two-level Spin–Boson model with tunneling, interacting with a bath of harmonic oscillators, based on decoherence theory. We investigated under what conditions the decoherence model approaches and deviates from the noise model. Specifically, we examined Gaussian noise and Ornstein-Uhlenbeck noise in our model. Gaussian noise shows a very good agreement with the decoherence model. By examining the results, it was found that the Spin–Boson model at a high hopping rate of potassium ions can simulate the behavior of the system in the classical noise approach for Gaussian noise.