White Noise Research Articles

Homoclinic Bifurcations and Chaotic Dynamics in a Bistable Vibro-Impact SD Oscillator Subject to Gaussian White Noise

This paper studies the effect of Gaussian white noise on homoclinic bifurcations and chaotic dynamics of a bistable, vibro-impact Smooth-and-Discontinuous (SD) oscillator. First, the SD oscillator is reproduced and generalized by installing a slider on a fixed rod, so the slider is connected by a pair of linear springs initially pre-compressed in the vertical direction to achieve bistable vibration characteristics, and two screw nuts are installed on the rod as two adjustable bilateral rigid constraints to generate the vibro-impact. A discontinuous dynamical equation with a map defined on switching boundaries to represent velocity loss during each collision is derived to describe the vibration pattern of the bistable, vibro-impact SD oscillator through studying the persistence of the unique, unperturbed, nonsmooth, homoclinic structure. Second, the general framework of random Melnikov process for a class of bistable, vibro-impact systems contaminated with Gaussian white noise is derived and employed through the corresponding Melnikov function to obtain the necessary parameter thresholds for homoclinic tangency and possible chaos of the bistable, vibro-impact SD oscillator. Third, the effectiveness of a semi-analytical prediction by the Melnikov function is verified using the largest Lyapunov exponent, bifurcation series, and 0–1 test. Finally, the sensitivity to the initial values of chaos is verified by the fractal attractor basins, and the influence of the Gaussian white noise on periodic and chaotic structures is studied through Poincaré mapping to show the rich dynamical geometric structures.

Enhancing Speaker Recognition Models with Noise-Resilient Feature Optimization Strategies

This paper delves into an in-depth exploration of speaker recognition methodologies, with a primary focus on three pivotal approaches: feature-level fusion, dimension reduction employing principal component analysis (PCA) and independent component analysis (ICA), and feature optimization through a genetic algorithm (GA) and the marine predator algorithm (MPA). This study conducts comprehensive experiments across diverse speech datasets characterized by varying noise levels and speaker counts. Impressively, the research yields exceptional results across different datasets and classifiers. For instance, on the TIMIT babble noise dataset (120 speakers), feature fusion achieves a remarkable speaker identification accuracy of 92.7%, while various feature optimization techniques combined with K nearest neighbor (KNN) and linear discriminant (LD) classifiers result in a speaker verification equal error rate (SV EER) of 0.7%. Notably, this study achieves a speaker identification accuracy of 93.5% and SV EER of 0.13% on the TIMIT babble noise dataset (630 speakers) using a KNN classifier with feature optimization. On the TIMIT white noise dataset (120 and 630 speakers), speaker identification accuracies of 93.3% and 83.5%, along with SV EER values of 0.58% and 0.13%, respectively, were attained utilizing PCA dimension reduction and feature optimization techniques (PCA-MPA) with KNN classifiers. Furthermore, on the voxceleb1 dataset, PCA-MPA feature optimization with KNN classifiers achieves a speaker identification accuracy of 95.2% and an SV EER of 1.8%. These findings underscore the significant enhancement in computational speed and speaker recognition performance facilitated by feature optimization strategies.

Performance analysis of the FSO communication system with random jamming over a composite Málaga turbulence fading channel

The performance analysis of a free space optical (FSO) communication system in the presence of random jamming is presented over a Málaga (M) distributed channel model with pointing errors and atmospheric attenuation. Firstly, the probability density function expressions of the transmission channel, signal-to-jamming ratio, and signal-to-noise ratio are derived. Then, considering the probability of the jammer and Gaussian white noise, the closed-form expressions for the ergodic channel capacity, outage probability, and average bit error rate are derived. Moreover, asymptotic expressions for the aforementioned performance metrics are also derived to ascertain the diversity gain of the system. Extensive Monte Carlo simulations are performed to demonstrate the credibility of this theoretical analysis. Results indicate that the adverse impact of random jamming is higher than that of Gaussian noise for the FSO communication system. Besides, this observation highlights the pulsating nature of the jamming effect, showcasing that within high signal-to-jamming ratio regions, a low probability jammer exerts the most significant impact on the FSO system.

Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

Enhancing genome-wide populus trait prediction through deep convolutional neural networks.

As a promising model, genome-based plant breeding has greatly promoted the improvement of agronomic traits. Traditional methods typically adopt linear regression models with clear assumptions, neither obtaining the linkage between phenotype and genotype nor providing good ideas for modification. Nonlinear models are well characterized in capturing complex nonadditive effects, filling this gap under traditional methods. Taking populus as the research object, this paper constructs a deep learning method, DCNGP, which can effectively predict the traits including 65 phenotypes. The method was trained on three datasets, and compared with other four classic models-Bayesian ridge regression (BRR), Elastic Net, support vector regression, and dualCNN. The results show that DCNGP has five typical advantages in performance: strong prediction ability on multiple experimental datasets; the incorporation of batch normalization layers and Early-Stopping technology enhancing the generalization capabilities and prediction stability on test data; learning potent features from the data and thus circumventing the tedious steps of manual production; the introduction of a Gaussian Noise layer enhancing predictive capabilities in the case of inherent uncertainties or perturbations; fewer hyperparameters aiding to reduce tuning time across datasets and improve auto-search efficiency. In this way, DCNGP shows powerful predictive ability from genotype to phenotype, which provide an important theoretical reference for building more robust populus breeding programs.

Quantum state engineering by steering in the presence of errors

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit. Published by the American Physical Society 2024

Fault Diagnosis of Wind Turbine Gearbox Using Vibration Scatter Plot and Visual Geometric Group Network

This study aims to develop a fault detection system designed specifically for wind turbine gearboxes. It proposes a hybrid fault diagnosis algorithm that combines scatter plot analysis with the visual geometric group (VGG) technique to identify various fault types, including gear rust, chipping, wear, and aging. To capture vibration signals, a three-axis vibration sensor was integrated with a NI-9234 DAQ card. Digital signal processing techniques were employed to actively filter out noise from the captured signals. Gaussian white noise was incorporated into the training data to enhance the noise resistance of the network model, which was then utilized for scatter plot generation. The VGG technique was subsequently applied to identify faults. The testing data were collected at two different speeds, with 1500 samples taken at each speed, totaling 3000 samples. For both training and testing, 400 samples of each fault type were employed for training, while 200 samples were allocated for testing. The test results demonstrated an overall identification accuracy of 97.7% for both the no-fault gearbox and the four-fault states, underscoring the effectiveness of the proposed methodology.

GNBoost-Based Ensemble Machine Learning for Predicting Tribological Properties of Liquid-Crystal Lubricants.

The intricate development of liquid-crystal lubricants necessitates the timely and accurate prediction of their tribological performance in different environments and an assessment of the importance of relevant parameters. In this study, a classification model using Gaussian noise extreme gradient boosting (GNBoost) to predict tribological performance is proposed. Three additives, polysorbate-85, polysorbate-80, and graphene oxide, were selected to fabricate liquid-crystal lubricants. The coefficients of friction of these lubricants were tested in the rotational mode using a universal mechanical tester. A model was designed to predict the coefficient of friction through data augmentation of the initial data. The model parameters were optimized using particle swarm optimization techniques. This study provides an effective example for lubricant performance evaluation and formulation optimization.

ОДНОВИМІРНА ЗГОРТКОВА МОДЕЛЬ НЕЙРОННОЇ МЕРЕЖІ ДЛЯ ОБРОБЛЕННЯ СИГНАЛІВ З АМПЛІТУДНОЮ МОДУЛЯЦІЄЮ БАГАТЬОХ СКЛАДОВИХ

The processing of radio signals using artificial neural networks (ANNs) has great potential for research, which can be explained by the adaptability of ANNs to various transmission conditions and the ability to detect abstract patterns of changes in signal parameters. The article reviews the works of other authors devoted to different ways of using ANNs for processing radio signals. Taking into account the information in the reviewed works, the research task was formed, which consists in developing an optimized ANN model for radio signal processing. Signals with amplitude modulation of many components (AMMC) were chosen to form training samples for ANN. The choice of modulation type is justified by greater energy efficiency compared to other widely used digital modulation types, such as quadrature amplitude modulation. Mathematic basis of AMMC signal generation is described. The process of finding the coordinates of three component 8-AMMC signal constellation is explained, the formation of signals in the time plane based on the found coordinates is explained as well as their discretization and the addition of white noise. An iterative algorithm for generating initial data for ANN based on the described ratios is proposed. The general structure of one-dimensional convolutional neural network is considered. Functions of individual neurons, connections between them, the formation of layers and the convolution operation are described mathematically. On the basis of the previously given ratios, a final display of the network was formed. Specific dimensions and activation functions for layers are selected. The use of convolutional layers is justified by time invariance. Based on the reviewed mathematical models, selected activation functions and dimensions, a neural model was formed. The process of validating the effectiveness of the formed neural model is described, which is based on comparing the symbolic error probabilities of the proposed and reference models at different signal-to-noise ratios. The validation results are presented. The advantages of the obtained model over the previously proposed purely recurrent model and the AMMC reference receiver are explained.

Traffic Noise Impacts Glucocorticoid Response, Activity, and Growth in Two Species of Tadpoles.

There is a large body of evidence linking increased noise to negative health effects for animals. Anthropogenic noise induces behavioral and physiological reactions across a range of taxa and increased traffic noise affects glucocorticoid (GC) hormones associated with the stress response in amphibians. GCs help to maintain homeostasis while balancing energetic tradeoffs between reproduction, growth, and activity. Stressors during early development can impact fitness at later life stages. We measured growth, activity, and GCs in response to high levels of traffic noise in two tadpole species that differ in life-history: Acris crepitans and Rana berlandieri. We predicted earlier exposures to traffic noise will slow development and alter behavior and GC concentrations differently than later exposures. Subjects were initially either exposed to natural levels of traffic noise for 8 days (early exposure) or a white noise control (later exposure), then the treatment was switched. Activity was measured via focal sampling and tadpoles were categorized as active if movement was detected. Tadpoles exposed to white noise initially maintained mass and activity throughout the experiment and early exposure to traffic noise had a greater impact on mass, activity, and GCs. Tadpoles exposed to traffic noise initially lost mass, with A. crepitans regaining mass but not R. berlandieri. When exposed earlier to traffic noise, R. berlandieri increased movement when shifted to the white noise treatment while A. crepitans did not significantly change activity. A. creptians had higher corticosterone release rates compared to R. berlandieri, and in both species, release rates were higher for tadpoles exposed to noise earlier. The longer-lived R. berlandieri allocated more of their energetic resources into activity while the shorter-lived A. crepitans allocated energy towards growth. R. berlandieri and A. crepitans utilized different coping strategies to contend with early exposure to traffic noise, potentially due to differences in life histories. Our findings suggest that these tadpoles employ different coping mechanisms to modulate stress responses in noise-polluted environments, and these mechanisms could influence their fitness later in life. Further study is needed to understand the impact in more sensitive tadpole species.

A Machine-Learning-Assisted Classification Algorithm for the Detection of Archaeological Proxies (Cropmarks) Based on Reflectance Signatures

The detection of subsurface archaeological remains using a range of remote sensing methods poses several challenges. Recent studies regarding the detection of archaeological proxies like those of cropmarks highlight the complexity of the phenomenon. In this work, we present three different methods, and associated indices, for identifying stressed reflectance signatures indicating buried archaeological remains, based on a dataset of measured ground spectroradiometric reflectance. Several spectral profiles between the visible and near-infrared parts of the spectrum were taken in a controlled environment in Cyprus during 2011–2012 and are re-used in this study. The first two (spectral) methods are based on a suitable analysis of the spectral signatures in (1) the visible part of the spectrum, in particular in the neighborhood of 570 nm, and (2) the red edge part of the spectrum, in the neighborhood of 730 nm. Machine learning (decision trees) allows for the deduction of suitable wavelengths to focus on in order to formulate the proposed indices and the associated classification criteria (decision boundaries) that can enhance the detection probability of stressed vegetation. Noise in the signal is taken into account by simulating reflectance signatures perturbed by white noise. Applying decision tree classification on the ensemble of simulations and basic statistical analysis, we refine the formulation of the indices and criteria for the noisy signatures. The success rate of the proposed methods is over 90%. The third method rests on the estimation of vegetation/canopy reflectance parameters through inversion of the physical-based PROSAIL reflectance model and the associated classification through machine learning methods. The obtained results provide further insights into the formation of stress vegetation that occurred due to the presence of shallow buried archaeological remains, which are well aligned with physical-based models and existing empirical knowledge. To the best of the authors’ knowledge, this is the first study demonstrating the usefulness of radiative transfer models such as PROSAIL for understanding the formation of cropmarks. Similar studies can support future research directions towards the development of regional remote sensing methods and algorithms if systematic observations are adequately dispersed in space and time.

Wick multiplication and its relationship with integration and stochastic differentiation on spaces of nonregular test functions in the Lévy white noise analysis

We deal with spaces of nonregular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our goal is to study properties of a natural multiplication $-$ a Wick multiplication on these spaces, and to describe the relationship of this multiplication with integration and stochastic differentiation. More exactly, we establish that the Wick product of nonregular test functions is a nonregular test function; show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of a generalized stochastic integral; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the generalized stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise; and prove that the operator of stochastic differentiation of first order on the spaces of nonregular test functions satisfies the Leibnitz rule with respect to the Wick multiplication.

Weak signal detection method based on nonlinear differential equations

With the rapid development of computer network technology, it is often necessary to collect weak signals to collect favorable information. The development of signal detection technology is ongoing; however, various issues arise during the detection process. These issues include low efficiency and a high signal noise threshold. However, many problems will be encountered in the process of detection. In order to solve these problems, the nonlinear chaos theory is introduced to detect signals, and the simulation experiments of weak pulse signals and weak partial discharge signals are carried out respectively. The experimental results showed that the detection effect was remarkable in the quasi periodic state, and it had a good detection effect for weak pulse signals. At a signal-to-noise ratio of -25 dB, double coupling system, two-way ring coupling system, and single ring coupling system displayed detection success rates exceeding 98%. Meanwhile, the detection success rate of the strong coupling system was only 12%. Even at a noise signal ratio as low as -40 dB, the dual coupling system still maintained a detection success rate above 80%. The simulation results of partial discharge signal detection showed that there was a high fluctuation only at 2 ms, and the rest was basically stable at about 0 V, indicating that the system had a strong suppression effect on Gaussian white noise. When comparing the simulation results of the detection of the new chaotic system and the double coupling system, it was found that the new chaotic system has a superior impact in detecting weakly attenuated partial discharge signals. Through analysis of the system’s dynamic behavior, the research confirms its rich dynamic characteristics and sheds light on the reasons for phase state mutation and missed detection. The noise system is utilized for comparing the performance of various systems, with the goal of enhancing the system’s detection capability.

Amplification in parametrically-driven resonators near instability based on Floquet theory and Green’s functions

Abstract Here we use Floquet theory to calculate the response of
parametrically-driven time-periodic systems near the onset of parametric
instability to an added external ac signal or white noise.
We provide new estimates, based on the Green's function method,
for the response of the system in the frequency domain.
Furthermore, we present novel expressions for the power and
noise spectral densities.
We validate our theoretical results by comparing our predictions for the
specific cases of a single degree of freedom parametric amplifier and of the
parametric amplifier coupled to a harmonic resonator with the
numerical integration results and with analytical approximate results obtained via
the averaging method up to second order.

Decision Analysis of Cold Chain Supply Chain Based on a Stochastic Evolution Model

Accelerating the development of cold chain logistics for agricultural products is not only an objective requirement for the development of agricultural product circulation but also a necessary demand to promote rural revitalization and upgrade agricultural consumption. Addressing the evolutionary problems of cold chain transportation in uncertain environments, this study considers the actual stochastic disturbances in the cold chain supply chain system, introducing Gaussian white noise to reflect the random perturbations experienced during the evolution of the cold chain. A three-party stochastic evolutionary game model is established involving farmers, logistics enterprises, and government regulatory authorities. Based on this model, numerical simulation analysis is conducted to explore the effects of different factors such as the intensity of random disturbances and the loss transfer coefficient on the fluctuation of strategic choices of the entities and the convergence speed to a stable state during evolution. Finally, combining the results of numerical simulation, relevant policies and recommendations are proposed to provide insights and guidance for the development of cold chain logistics in agricultural products.

Optically synchronized unidirectional optical amplifier-based coherent optical fiber links.

We report on the realization of a unidirectional transmission-based bidirectional erbium-doped fiber amplifier (UTB-EDFA) for the coherent optical fiber links. By applying an optical phase-locked loop (OPLL) between the two unidirectional EDFA (Ui-EDFA) paths, the annoying uncorrelated phase noise between the two paths can be largely suppressed. Promisingly, we can independently optimize the gains of the UTB-EDFAs for bidirectional transmissions, resulting in higher net gain acquired compared with the conventional single-path bidirectional EDFA (SPBA)-based ones. We demonstrate that the fractional frequency instability of the UTB-EDFA-based scheme can be decreased by 26.3% over the most asymmetrical 100 km two-way optical frequency comparison (TWC) system compared with the SPBA-based ones and, more importantly, can acquire higher net gain for unevenly distributed sub-links over ultra-long fiber links, such as 1000 km, by independently optimizing the gains. This technique paves the way for the applications of large-scale fiber networks.

Hyperspectral Image Mixed Noise Removal via Double Factor Total Variation Nonlocal Low-Rank Tensor Regularization

A hyperspectral image (HSI) is often corrupted by various types of noise during image acquisition, e.g., Gaussian noise, impulse noise, stripes, deadlines, and more. Thus, as a preprocessing step, HSI denoising plays a vital role in many subsequent tasks. Recently, a variety of mixed noise removal approaches have been developed for HSI, and the methods based on spatial–spectral double factor and total variation (DFTV) regularization have achieved comparable performance. Additionally, the nonlocal low-rank tensor model (NLR) is often employed to characterize spatial nonlocal self-similarity (NSS). Generally, fully exploring prior knowledge can improve the denoising performance, but it significantly increases the computational cost when the NSS prior is employed. To solve this problem, this article proposes a novel DFTV-based NLR regularization (DFTVNLR) model for HSI mixed noise removal. The proposed model employs low-rank tensor factorization (LRTF) to characterize the spectral global low-rankness (LR), introduces 2-D and 1-D TV constraints on double-factor to characterize the spatial and spectral local smoothness (LS), respectively. Meanwhile, the NLR is applied to the spatial factor to characterize the NSS. Then, we developed an algorithm based on proximal alternating minimization (PAM) to solve the proposed model effectively. Particularly, we effectively controlled the computational cost from two aspects, namely taking small-sized double factor as regularization object and putting the time-consuming NLR model before the main loop with fewer iterations to solve it independently. Finally, considerable experiments on simulated and real noisy HSI substantiate that the proposed method is superior to the related state-of-the-art methods in balancing the denoising effect and speed.

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

Temporal approximation of stochastic evolution equations with irregular nonlinearities

In this paper, we prove convergence for contractive time discretisation schemes for semi-linear stochastic evolution equations with irregular Lipschitz nonlinearities, initial values, and additive or multiplicative Gaussian noise on 2-smooth Banach spaces X. The leading operator A is assumed to generate a strongly continuous semigroup S on X, and the focus is on non-parabolic problems. The main result concerns convergence of the uniform strong errorEk∞:=(Esupj∈{0,…,Nk}‖U(tj)-Uj‖Xp)1/p→0(k→0),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ extrm{E}_{k}^{\\infty } {:}{=}\\Big (\\mathbb {E}\\sup _{j\\in \\{0, \\ldots , N_k\\}} \\Vert U(t_j) - U^j\\Vert _X^p\\Big )^{1/p} \\rightarrow 0\\quad (k \\rightarrow 0), \\end{aligned}$$\\end{document}where p∈[2,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \\in [2,\\infty )$$\\end{document}, U is the mild solution, Uj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U^j$$\\end{document} is obtained from a time discretisation scheme, k is the step size, and Nk=T/k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_k = T/k$$\\end{document} for final time T>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T>0$$\\end{document}. This generalises previous results to a larger class of admissible nonlinearities and noise, as well as rough initial data from the Hilbert space case to more general spaces. We present a proof based on a regularisation argument. Within this scope, we extend previous quantified convergence results for more regular nonlinearity and noise from Hilbert to 2-smooth Banach spaces. The uniform strong error cannot be estimated in terms of the simpler pointwise strong errorEk:=(supj∈{0,…,Nk}E‖U(tj)-Uj‖Xp)1/p,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ extrm{E}_k {:}{=}\\bigg (\\sup _{j\\in \\{0,\\ldots ,N_k\\}}\\mathbb {E}\\Vert U(t_j) - U^{j}\\Vert _X^p\\bigg )^{1/p}, \\end{aligned}$$\\end{document}which most of the existing literature is concerned with. Our results are illustrated for a variant of the Schrödinger equation, for which previous convergence results were not applicable.

C-Phycocyanin Attenuates Noise-Induced Cochlear Synaptopathy via the Inhibition of Oxidative Stress and Intercellular Adhesion Molecule-1 in the Cochlea

The synapses between inner hair cells (IHCs) and spiral ganglion neurons (SGNs) are the most vulnerable structures in the noise-exposed cochlea. Cochlear synaptopathy results from the disruption of these synapses following noise exposure and is considered the main cause of poor speech understanding in noisy environments, even when audiogram results are normal. Cochlear synaptopathy leads to the degeneration of SGNs if damaged IHC-SGN synapses are not promptly recovered. Oxidative stress plays a central role in the pathogenesis of cochlear synaptopathy. C-Phycocyanin (C-PC) has antioxidant and anti-inflammatory activities and is widely utilized in the food and drug industry. However, the effect of the C-PC on noise-induced cochlear damage is unknown. We first investigated the therapeutic effect of C-PC on noise-induced cochlear synaptopathy. In vitro experiments revealed that C-PC reduced the H2O2-induced generation of reactive oxygen species in HEI-OC1 auditory cells. H2O2-induced cytotoxicity in HEI-OC1 cells was reduced with C-PC treatment. After white noise exposure for 3 h at a sound pressure of 118 dB, the guinea pigs intratympanically administered 5 μg/mL C-PC exhibited greater wave I amplitudes in the auditory brainstem response, more IHC synaptic ribbons and more IHC-SGN synapses according to microscopic analysis than the saline-treated guinea pigs. Furthermore, the group treated with C-PC had less intense 4-hydroxynonenal and intercellular adhesion molecule-1 staining in the cochlea compared with the saline group. Our results suggest that C-PC improves cochlear synaptopathy by inhibiting noise-induced oxidative stress and the inflammatory response in the cochlea.