LURE: An Unsupervised Denoising Framework for Multiplicative Lognormal Noise

Turing instability suppressed and induced by multiplicative noise in Brusselator system

Optical soliton perturbation with complex ginzburg-landau equation having multiplicative white noise and nine forms of self-phase modulation structures.

Dynamical analysis of Jacobian elliptic function soliton solutions, and chaotic behavior with defective tools of the stochastic PNLSE equation with multiplicative white noise

Multiple complex construction noise signal decomposition and prediction methods: based on WOA-VMD and stacked LSTM

Clinical improvement of speech perception in noise with Automatic Sound Management 3.0.

The common reflection surface (CRS) stack is an advanced stacking technique that improves the continuity of reflectors in seismic sections by simulating reflections from curved subsurface interfaces. However, CRS results often exhibit amplitude weakening and residual noise, limiting reflector clarity. This study aims to enhance CRS seismic images by integrating pre-stack and post-stack filtering techniques to reduce coherent, multiple, and random noise while preserving reflector amplitude. Seismic data from the Nias Sea in Indonesia were processed with F-K and radon filters during the pre-stack stage. Later, K-L, F-X deconvolution, and dip scan stack filters were applied during post-stack filtering. The F-K filter reduces coherent and multiple noise effectively. The radon filter helps in shallow multiple attenuation. Post-stack filtering also enhances reflector continuity and amplitude stability. Obvious reflector pattern changes, especially in those depths over 2400ms, display weak reflectors in this final CRS seismic section. Quantitative evaluation indicates that the SNR increased from 14.2 dB to 23.8 dB. Moreover, the NRMSE decreased from 0.162 to 0.094, while the CC increased from 0.73 to 0.89. Therefore, these results confirm that the processing on the combined pre- and post-stack enhances the clarity of the reflectors and the coherence of their amplitude. A cost-effective and efficient way of improving CRS seismic imaging, especially in complex offshore geological environments such as the Nias basin, is presented by the

Estimating selection from genetic time-series data is fundamental to understanding evolutionary dynamics. Accurate selection inference is confounded by multiple noise sources, including limited sampling of populations and genetic drift. To characterize how these uncertainties collectively affect estimator performance, we analyze a mathematically tractable selection coefficient estimator derived under the marginal path likelihood (MPL) framework. We identify a parameter, the integrated mutant allele variance, as a key quantity determining estimator precision. Our analysis reveals that variance integration mitigates sampling and genetic drift errors at different rates, with drift typically becoming the dominant source of error in longer trajectories. The increased robustness of MPL-based estimation to sampling is surprising, since MPL is derived from a model that neglects this effect. Our findings offer insights into how incorporating temporal information reduces multiple sources of noise when estimating selection coefficients.

This paper is about the retrieval of gap dromions in presence of multiplicative white noise. The self-phase modulation structure is with cubic-quintic-septic-nonic structure. Two integration approaches retrieve the dromions and domain walls with the usage of the enhanced direct algebraic approach and the addendum to Kudryashov’s scheme. The solutions are subsequently classified.

ABSTRACT In this paper, a concatenation model with nonlinear Kerr's law is studied in detail with the presence of spatio‐temporal dispersion, Hamiltonian disturbance terms, and multiplicative white noise. The trial equation method is applied to give an integral factor equation of high order nonlinear amplitude equation, and bifurcation theory is employed to analyze the Hamiltonian and topological properties to the reduced system. Then, the stochastic single traveling wave solutions to the equation are obtained in terms of soliton solutions, singular solutions, and Jacobian elliptic function periodic solutions by the complete discrimination system for polynomial method. Among those, there exist new solutions. Furthermore, the averaging values of the solutions under Brownian motion are given, and it is found that there is a delay factor so that the white noise affects not only the phase factors but also the amplitudes of the solutions. Additionally, the chaotic behaviors of the model are also discovered by taking the external perturbed terms into consideration.

In this paper, a reinforcement learning-based model-free event-triggered control algorithm is proposed for discrete-time stochastic systems. A model-based event-triggered control algorithm is first presented to reduce communication frequency. To eliminate the need for prior knowledge of the system dynamics, a model-free reinforcement learning-based event-triggered control algorithm is then developed. This model-free algorithm uses online data to learn the parameters of the event-triggered mechanism and to update the controller accordingly. It is shown that the estimation error of the kernel matrix is bounded with sufficient collected data, and that the stability of the closed-loop system under the model-free event-triggered mechanism can be guaranteed. A numerical simulation is provided to demonstrate the effectiveness of the algorithm.

Effects of Multiplicative Noise on the Hartree-type Schrödinger Equation

There are many exotic thermodynamic processes that are hard to study in nature. Here, we synthesize a structured environment to explore the extremes of thermodynamics. We present an engine running at extreme temperatures of above ten Megakelvin. Our underdamped engine is realised by electrically levitating and controlling a charged microparticle in vacuum. Giant fluctuations are observed in the engine's heat exchange with the environment, while its efficiency shows stochastic events where more work is performed by the engine than heat consumed. Moreover, the nonuniformity of the synthetic environment leads to the particle experiencing position dependent diffusion, a critical phenomenon in microscale biological processes. We theoretically account for the effects of multiplicative noise and find excellent agreement with the observed behavior.

In this work, we study the stochastic Burgers-Huxley equation driven by multiplicative Gaussian noise, focussing on global solvability and the asymptotic behaviour of its solutions. We establish the existence of a global strong solution by exploiting the local monotonicity of the linear and nonlinear operators, together with a stochastic version of the localized Minty-Browder technique. We further investigate the zero-reaction limit of the stochastic Burgers-Huxley equation, connecting it to both the Burgers and Huxley equations. For the case of additive Gaussian noise, we derive exponential estimates for the probability that solutions exit a ball of radius R by time T and analyse these estimates in the framework of a Freidlin-Wentzell type large deviations principle. Finally, leveraging the exponential stability of solutions, we prove the existence of a unique ergodic and strongly mixing invariant measure for the stochastic Burgers-Huxley equation with additive Gaussian noise.

Abstract To support the development of the data processing pipeline and the scientific performance assessment for the Cool Planet Imaging Coronagraph (CPI-C) on the China Space Station Telescope (CSST), we have developed the end-to-end instrument simulation program, CPISM. This paper details the core modules of CPISM that simulate the CPI-C instrument, focusing on the simulation of the high-contrast imaging optical system and the visible-band science camera. We modeled key optical components, such as the transmission apodizing filter, the wavefront corrector, and the focal plane mask using the HCIPy package. A $10^{−8}$ contrast dark hole region, consistent with design specifications, was simulated using the Electric Field Conjugation (EFC) optimization method, and broadband observation effects were considered. For the science camera, which is an electron multiplying charge-coupled device (EMCCD), we established a detailed model encompassing photon collection, charge transfer, electron multiplication (EM), and readout processes, based on test data. This model simulates complex instrumental features including dark current, charge transfer efficiency, clock-induced charge, multiplication noise factor, and various readout effects like striping and drift. We also proposed and validated an improved statistical model for the EM process to enhance simulation efficiency. CPISM can generate simulated images containing rich instrumental details, closely similar to the expected real observational data, thus laying the foundation for the development and verification of CPI-C data processing algorithms and preparations for future scientific research.

We review some basic results on existence and uniqueness of the invariant measure for the two-dimensional stochastic Navier-Stokes equations. A large part of the literature concerns the additive noise case; after revising these models, we consider our recent result [Ferrario and Zanella, Discrete Contin. Dyn. Syst. 44(1), 2024] with a multiplicative noise.

Introduction Ischemic stroke remains a leading cause of disability and mortality, making a rapid and reliable diagnosis essential. Dynamic Susceptibility Contrast Magnetic Resonance Imaging (DSC-MRI) is widely used to assess cerebral perfusion, yet its diagnostic accuracy strongly depends on the computational model applied. This study investigates how model selection influences the reliability of CBV-based ischemic stroke detection under varying noise conditions and tissue types. Methods Simulated tissue signal curves were generated from clinical reference data and modified to reflect ischemic alterations across multiple noise levels. Cerebral Blood Volume (CBV) was estimated using two established approaches: the modified gamma variate function and a compartmental (triple-exponential) model. Diagnostic performance was evaluated by comparing the accuracy and robustness of CBV estimation. Results The compartmental model consistently outperformed the gamma variate function, providing more accurate and stable CBV estimates, particularly under high-noise conditions. In contrast, the gamma variate function demonstrated reduced robustness and greater sensitivity to noise. Discussion These findings underscore the importance of computational model selection in DSC-MRI analysis. The performance of the compartmental model suggests its potential for integration into clinical workflows, particularly in acute stroke care, where reliability under challenging conditions is crucial. However, this study has several limitations. Most importantly, the analysis was based on simulated tissue signal curves derived from clinical reference data rather than on in vivo measurements, which may not fully capture the complexity of real patient physiology. Conclusion Computational modeling influences the diagnostic value of DSC-MRI in ischemic stroke assessment. The compartmental model offers greater robustness and accuracy, supporting its use in diagnostic systems.

Rolling bearings are essential components of rotating machinery, and their operational conditions directly affect the safety and stability of the equipment. However, in complex industrial environments, fault signals are often non-stationary, weak, and susceptible to noise interference, which significantly degrades the performance of traditional feature-extraction and classification methods. To address these challenges, this study proposes an adaptive fault diagnosis method that integrates variational mode decomposition (VMD) with deep learning (DL). First, an improved grey wolf optimizer (IGWO) with an adaptive adjustment factor was employed to optimize the key parameters of VMD, thereby enhancing the quality of signal decomposition and fault feature extraction. Then, a new WPEK index was constructed, which combined weighted-permutation entropy and kurtosis. The WPEK and correlation coefficient were used to select information-rich intrinsic mode functions (IMFs) for signal reconstruction, effectively suppressing redundant components and noise. Finally, a ConvTransNet model, incorporating convolutional neural networks and transformers, was designed to extract and fuse local and global features for accurate fault classification. Experimental results demonstrate that the proposed GVMD-ConvTransNet method achieves superior diagnostic performance and robustness across multiple datasets and noise conditions, offering a reliable solution for practical industrial fault diagnosis applications.

Spatial Quadratic Variation for Stochastic Heat Equations Driven by Multiplicative Noise with Piecewise Constant Coefficients

Event-Based Nonfragile Extended State Estimation for Uncertain Networked Systems With Multiplicative Noise