White Noise Research Articles

Quantum continuity equations and quantum evolution systems for white noise operators

Quantum continuity equations and quantum evolution systems for white noise operators

Variation in responses to conspecific and heterospecific advertisement vocalizations in sympatric grasshopper mice (Onychomys).

Advertisement vocalizations that function in mate acquisition and resource defense within species may also mediate behavioral interactions among species. While olfactory signals play an important role in mate choice and territoriality in rodents, less is known about the function of acoustic signals in influencing interspecific interactions. In this study, we used playback experiments in the laboratory to assess the function of long-distance vocalizations within and among three sympatric species of grasshopper mice. We found that, within each species, individuals of both sexes varied widely in spontaneous vocal behavior and response to playback. The largest species (Onychomys leucogaster) was most responsive to conspecifics, but smaller O. arenicola and O. torridus exhibited no clear pattern in their vocal behavior and were even responsive to the white noise controls. Our results indicate that grasshopper mice are broadly responsive to a range of sounds that resemble calls and that long-distance vocalizations function primarily as signals that facilitate localization for subsequent close-distance assessment by both sexes in various social contexts. Variation in vocal responses among species may depend on competitive dominance, degree of interaction, acoustic similarity, or behavioral changes resulting from captivity. Replicating playback experiments in the field will help validate whether the observed variation in the laboratory reflects ecologically relevant patterns in nature.

Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

We construct a positivity-preserving Lie–Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of semilinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate 1/4 in time and rate 1/2 in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity.

Compressed intracellular motility via non-uniform temporal sampling in dynamic optical coherence tomography.

Optical coherence tomography has great utility for capturing dynamic processes, but such applications are particularly data-intensive. Samples such as biological tissues exhibit temporal features at varying time scales, which makes data reduction challenging. We propose a method for capturing short- and long-term correlations of a sample in a compressed way using non-uniform temporal sampling to reduce scan time and memory overhead. The proposed method separates the relative contributions of white noise, fluctuating features, and stationary features. The method is demonstrated on mammary epithelial cell spheroids in three-dimensional culture for capturing intracellular motility without loss of signal integrity. Results show that the spatial patterns of motility are preserved and that hypothesis tests of spheroids treated with blebbistatin, a motor protein inhibitor, are unchanged with up to eightfold compression. The ability to measure short- and long-term correlations compressively will enable new applications in (3+1)D imaging and high-throughput screening.

Outcome measures of brainwave entrainment using delta wave stimulation in individuals with tinnitus having normal hearing sensitivity.

The current study aimed to evaluate the efficacy of delta frequency binaural beats stimulation in treatment of individuals with tinnitus having normal hearing sensitivity. Twenty-four individuals who reported bothersome tinnitus in the presence of clinically normal hearing were grouped into two (I and II). The group was provided with delta frequency binaural beats and II was provided with white noise stimulation (both of 20min duration) for 30days. Post 30days, the re-assessment of tinnitus handicap, depression, anxiety, and quality of life parameters were performed and compared with that of pre-treatment scores. A considerable reduction of tinnitus handicap scores, depression and anxiety levels were observed for both the groups, except for the quality-of-life parameters. However, few of the participants showed limited or negligible improvement post-treatment. On comparison of reduction of scores observed across the groups, there was a higher reduction of scores observed for group I when compared to group II. The current study was an initial attempt to study the efficacy of binaural beats in treatment of individuals with tinnitus having normal hearing. Apart from a few individuals, the delta wave stimulation acted as a helpful tool in improving tinnitus borne distress symptoms in such patients with normal hearing.The results of the present study put forward the scope of adapting binaural beats stimulation for the treatment of individuals presenting with tinnitus having normal hearing sensitivity. This technique could be adopted into clinical practice after extensive research involving an extended treatment duration on a larger population.

Modulation of Thermodynamic Properties of Doped GaAs Quantum Dot under the Influence of Noise

In the present enquiry, an in‐depth analysis of internal energy, entropy, heat capacity, and Helmholtz free energy of GaAs quantum dot (QD) which contains Gaussian impurity as dopant and falls under the influence of applied Gaussian white noise (GWHN) is performed. GWHN takes additive and multiplicative routes for its entrance to the doped QD. In this study, highly delicate and complex interplay between temperature, presence/absence of GWHN, mode of incorporation of GWHN, and the particular physical parameters concerned is unveiled. The said interplay, in effect, designs the features of the thermal properties. The enquiry uncovers competitive behavior between thermal disorder and spatial disorder that also affects the said thermodynamic properties.

A Statistical Model of Hazard Rate Change Caused by a Random Shock

In the framework of statistical reliability analysis, we propose a model describing the change of reliability of a technical component after certain event, as for instance a shock, or the failure and maintenance. Two kinds of failure rate changes are considered, namely a shift of virtual age of analyzed component and the acceleration of its subjective time. The objective is to estimate both the baseline lifetime probability distribution and the magnitude of these changes. The estimation procedure is based on the maximum likelihood method, both parametric and nonparametric distributions of lifetime are considered. Further, a graphical method of the goodness-of-fit test is proposed. The method is then checked on artificial examples, finally a real data problem is solved.

The Effect of Listening to White Noise and Heart Sound on Pain During Sternum Dressing in Newborn

The research was conducted to determine the effect of listening to white noise and heart sounds during the sternum dressing process on the pain felt by newborns who had congenital heart surgery. The research sample consisted of 48 newborns who underwent cardiac surgery in a training and research hospital in Istanbul and met the sample selection criteria. Newborn Pain Scale (NIPS) was used to assess pain. It was seen that there was a statistically significant difference in terms of physiological parameter values evaluated between the groups during the sternum dressing procedure (p

Distributed Consensus Multi-Distribution Filter for Heavy-Tailed Noise

Distributed state estimation is one of the critical technologies in the field of target tracking, where the process noise and measurement noise may have a heavy-tailed distribution. Traditionally, heavy-tailed distributions like the student-t distribution are employed, but our observation reveals that Gaussian noise predominates in many instances, with occasional outliers. This sporadic reliance on heavy-tailed distributions can degrade performances or necessitate frequent parameter adjustments. To overcome this, we introduce a novel distributed consensus multi-distribution state estimation method that combines Gaussian and student-t filters. Our approach establishes a system model using both Gaussian and student-t distributions. We derive a multi-distribution filter for a single sensor, assigning probabilities to Gaussian and student-t noise models. Parallel estimation under both distributions, utilizing Gaussian and student-t filters, allows us to calculate the likelihood of each distribution. The fusion of these results yields a mixed-state estimation and corresponding error matrix. Recognizing the increasing degrees of freedom in the student-t distribution over time, we provide an effective approximation. An information consensus strategy for multi-distribution filters is introduced, achieving global estimation through consensus on fused local filter results via interaction with neighboring nodes. This methodology is extended to the distributed case, and the recursive process of the distributed multi-distribution consensus state estimation method is presented. Simulation results demonstrate that the estimation accuracy of the proposed algorithm improved by at least 20% compared to that of the traditional algorithm in scenarios involving both Gaussian and heavy-tailed distributions.

Nonstationary response statistics of structures with hysteretic damping to evolutionary stochastic excitation

The damping of a structure has often been modeled as linear hysteretic damping (LHD), so its corresponding equation of motion (EOM) is an integro-differential equation that involves the Hilbert transform of response displacement. As a result, the system is non-causal in nature, and it is challenging to compute its nonstationary response statistics under evolutionary stochastic excitation. This article develops an efficient solution method to obtain closed-form solutions for various nonstationary response statistics, including the evolutionary power spectrum (EPS), correlation function and mean square values. The novel solution method utilizes the concept of causalization time to introduce a “causalized” impulse response function (IRF), by which causal response statistics are computed based on a pole-residue approach. This approach requires obtaining a pole-residue form of the transfer function (TF) from the frequency response function (FRF) of the system, which is readily obtained from the EOM. Subsequently, the desired response statistics are obtained by shifting the causal response statistics back to the original time. To obtain the pole-residue form of the TF, two steps are necessary: (1) taking the inverse Fourier transform of the FRF of the oscillator to obtain a discrete IRF and (2) using the Prony-SS method to decompose this discrete IRF to obtain the pole residues associated with the TF. The correctness of the proposed method is numerically verified by Monte Carlo simulations through examples of hysteretic damping and mixed viscous-hysteretic damping oscillators that are subjected to white noise, modulated white noise and modulated Kanai–Tajimi model random excitations.

The Reliability and Availability Analysis of a Single-Unit System under the Influence of Random Shocks and the Variation in Demand from Production with Erlang Distribution

This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure with probability p. The system may also fail completely for various reasons other than shocks. The unit is serviced by a technician if it is affected by a shock. However, the system may fail during operation for various other reasons, such as a programming error, human error, operational continuity and stress, and weather conditions. A single technician immediately repairs or maintains the failed unit. The system is in an operational state when there is demand or in an idle state when there is no demand. The distributions of all times in this system follow a negative exponential, while the time to repair follows a two-stage Erlang distribution. The expressions for the reliability metrics are obtained as functions of time using the Laplace transform and the supplementary variables technique. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, the efficiency of the system is illustrated using numerical examples.

FDM: Document image seen-through removal via Fuzzy Diffusion Models

While scanning or shooting a document, factors like ink density and paper transparency may cause the content from the reverse side to become visible through the paper, resulting in a digital image with a ‘seen-through’ phenomenon, which will affect practical applications. In addition, document images can be affected by random factors during the imaging process, such as differences in the performance of camera equipment and variations in the physical properties of the document itself. These random factors increase the noise of the document image and may cause the seen-through phenomena to become more complex and diverse. To tackle this issue, we propose the Fuzzy Diffusion Model (FDM), which combines fuzzy logic with diffusion models. It effectively models complex seen-through effects and handles uncertainties in document images. Specifically, we gradually degrade the original image with mean-reverting stochastic differential equation(SDE) to transform it into seen-through mean state with fixed Gaussian noise version. Following this, fuzzy operations are introduced into the noise network. Which helps the model better learn noise and data distributions by reasoning about the affiliation relationship of each pixel point through fuzzy logic. Eventually, in the reverse process, the low-quality image is gradually restored by simulating the corresponding reverse-time SDE. Extensive quantitative and qualitative experiments conducted on various datasets demonstrate that the proposed method significantly removes the seen-through effects and achieves good results under several metrics. The proposed FDM effectively solves the seen-through effects of document images and obtains better visual quality.

Detection of Straw Coverage under Conservation Tillage Based on an Improved Mask Regional Convolutional Neural Network (Mask R-CNN)

Conservation tillage, a crucial method for protecting soil fertility, depends heavily on maintaining adequate straw coverage. The current method of straw coverage detection relies primarily on manual measurement, which is both time-consuming and laborious. This paper introduces a novel straw coverage detection approach based on an improved mask regional convolutional neural network (Mask R-CNN) algorithm. Several images of wheat straw-covered fields were taken, and the dataset was augmented using techniques like image inversion, contrast enhancement, Gaussian noise addition, and translation after cropping the original images. These fields use a crop rotation cycle of wheat and corn. Subsequently, the straw images were annotated using the Labelme annotation tool to obtain the available straw instance segmentation dataset. The Mask R-CNN algorithm was improved by refining the mask generation network structure through a multi-feature fusion strategy, which interweaves features from both the encoder and the mask generation network, enhancing the model’s ability to capture detailed and shape information of the straw. Lastly, using the mask information output by the improved Mask R-CNN algorithm, the straw coverage was calculated by counting the proportion of pixels within each segmented region. In the results, compared to the original Mask R-CNN algorithm, our improved Mask R-CNN algorithm achieved an average improvement of 7.8% in segmentation accuracy, indicating that the improved Mask R-CNN algorithm offers superior segmentation performance. Thus, the new algorithm can achieve straw coverage detection with higher accuracy and can provide a reference for other agricultural applications.

Stochastic hyperplane-based ranks and their use in multivariate portmanteau tests

The article proposes and justifies an optimal rank-based portmanteau test of multivariate elliptical strict white noise against multivariate serial dependence. It is based on new stochastic hyperplane-based ranks that are simpler and easier to compute than other usable hyperplane-based competitors and still share with them many good properties such as their distribution-free nature, affine invariance, efficiency, robustness and weak moment assumptions. The finite-sample performance of the portmanteau test is illustrated empirically in a small Monte Carlo simulation study.

Approximate averaged derivative moments and stochastic response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises

Stochastic response prediction is one of the principal topics in diverse branches of engineering, such as aerospace engineering, mechanical engineering, and vehicle engineering. However, the challenge of addressing high-dimensional partial differential equations or evaluating high-dimensional domain integrals in determining averaged derivative moments has limited the research. This study proposes a method to predict the stochastic response of high-degree-of-freedom (DOF) quasi-non-integrable Hamiltonian systems under Poisson white noises. The original finite DOF system is reduced to a one-dimensional one governing the Hamiltonian by applying the stochastic averaging method, and the associated reduced generalized Fokker–Planck–Kolmogorov (GFPK) equation is derived. Then, the two-step generalized elliptical coordinate transformation is extended to evaluate averaged derivative moments that are the key to obtaining the stationary probability density function (SPDF) for probabilistic information prediction. Moreover, the perturbation method is introduced to address the high-order GFPK equation. Finally, an 8-DOF strongly nonlinear system under purely additive Poisson white noises is given as an example to highlight the accuracy of the proposed method. Results from the proposed method show good agreement with those from Monte Carlo simulations, which indicates that the proposed method can be applied to assess the response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises. In addition, if the potential energy of an arbitrary finite n-DOF system is the same form as that in Appendix B, pertinent high-dimensional domain integrals are converted into explicit expressions when n is even.

Promising Young Women and the White Noise of Patriarchy

Abstract Noticing that, in The Second Sex, Simone de Beauvoir deftly describes patriarchy as a male sensorium encompassing vision, smell, touch, taste, and sound, this article focuses on the way feminist directors utilize sound in film and television. Three examples—Chantal Akerman’s 1968 Blow Up My Town, Emerald Fennell’s 2020 Promising Young Woman, and Michaela Coel’s 2020 I May Destroy You—show how feminist media showcases the white noise of patriarchy to reorient the ears of its audience to hear the way feminists do.

Chatter and Surface Waviness Analysis in Oerlikon Face Hobbing of Spiral Bevel Gears

A vectorized analytical model for the cutting dynamics in the spiral bevel gear face hobbing process has been developed, which is based on machine tool kinematics and vibration vectorization. The structural modal parameters of the cutter head spindle system are obtained through experimental modal analysis with hammer impact testing. The analytical model is utilized to simulate the generation of simulated vibration acceleration signals during spiral bevel gear hobbing. A wavelet threshold denoising method is applied to process the simulated vibration signals of the spiral bevel gear face hobbing with added white noise. Signal processing methods, including short-time Fourier transform are employed for time-domain analysis, frequency-domain analysis, and time–frequency-domain analysis of measured signals and simulated signals, thereby extracting the corresponding statistical features. In addition to the results of the experimental modal analysis, the causes of chatter in spiral bevel gear hobbing are discussed in detail, revealing that the main factor is cutter head vibration in the Y direction of the Hunan ZDCY CNC EQUIPMENT YKA2260 machine tool used in this research. The error in the time-domain characteristic parameters between simulated signals and measured vibration acceleration signals is within 15%, with a difference of 3.5% in spectral peak values. The predicted tooth surface morphology from simulation matches the actual morphology on the workpiece, comprehensively validating the reliability of the cutting dynamics model for the spiral bevel gear face hobbing process. Another conclusion drawn from numerical simulation experiments is that the amount of tooth surface waviness of the spiral bevel gears is the ratio of tool chatter frequency to cutting fundamental frequency.

CDTFAFN: A novel coarse-to-fine dual-scale time-frequency attention fusion network for machinery vibro-acoustic fault diagnosis

When the machinery device operates abnormally, it is not sufficient for fault detection only via extracting fault features from a single sensor due to the latent fault information may be scattered across multiple sensors. Multi-sensory fusion techniques with deep learning framework have attracted increasing attention from researchers due to the exploiting and integration of fault information between multiple sensors. Nevertheless, there are two remaining shortcomings in most existing multi-sensory fusion technologies. (1) Most existing fusion methods merely concentrate on conducting multi-sensory information fusion from time-domain or frequency-domain to achieve fault diagnosis, which are often unsatisfactory in the face of strong noise environments. (2) The collaborative fusion between several vibration sensors is generally considered in the past works, whereas the complementary information fusion between multi-sensory vibro-acoustic heterogeneous data are rarely studied. To address these deficiencies, this paper proposes a novel coarse-to-fine dual-scale time-frequency attention fusion network (CDTFAFN) for machinery fault diagnosis, which not only adequately considers the complementary information fusion of vibro-acoustic signal, but also has robust feature learning capabilities in a noisy scenario. Firstly, the signal-to-image encoding unit (SIEU) containing the improved constant-Q non-stationary Gabor transform (ICQ-NSGT) is introduced to convert the collected raw vibro-acoustic heterogeneous signal into time-frequency representation (TFR) and achieve the coarse-grained feature fusion. Secondly, the time-frequency attention feature fusion unit (TFA-FFU) is designed to concurrently learn the fine-grained features at two scales from the low-level fused features which are meaningful for fault diagnosis. Finally, the coarse-to-fine features are sequentially concatenated and fed into softmax classifier to preferably promote the network learning performance and automatically implement fault classification. The performance of the proposed approach is validated against those state-of-the-art results on two groups of multi-sensory vibro-acoustic data in different experimental platforms. Experiment results show that the proposed method with the diagnosis accuracy of 99 % above outperforms other several representative fusion technologies (i.e., 2MNet, MFF-GBFD, MSCNN-BiLSTM, MFAN-VAF, 1D-CNN-VAF, MI-CNN-TFT and TFFN-VAF) in the raw noise-free addition scenario. Moreover, the average testing accuracy of the proposed method can still reach 97 % above in the noisy scenarios with Gaussian white noises, which shows its competitive superiority and strong robustness against noises in machinery fault diagnosis. According to the five ensemble macro-average performance evaluation metrics (i.e., accuracy, precision, sensitivity, specificity and F1-score) and the receiver operator characteristic (ROC) analysis, our findings also emphasize the superiority of applying our method for machinery fault diagnosis under the colored noises compared with other fusion technologies (i.e., 2MNet, MFF-GBFD, MSCNN-BiLSTM, MFAN-VAF, 1D-CNN-VAF, MI-CNN-TFT and TFFN-VAF) reported in this paper.

Performance Evaluation of Fractal Wavelet Packet Transform on Wireless Communication Systems

The performance of the phase shift keying (PSK) modulation technique over additive white Gaussian noise (AWGN) and multipath propagation channels generally becomes worse for higher-order modes. Therefore, a new modulation technique should be provided in order to have a system that is capable of transmitting data with higher efficiency while maintaining better performance at the same time. This paper presents the development of a fractal wavelet packet transform incorporated within the M-ary PSK system, namely M-ary PSK orthogonal wavelet division multiplexing (OWDM), which is proposed to obtain high performance of modulation in terms of spectrum efficiency and bandwidth resources intended for wireless communication systems. To demonstrate performance improvement over a Rayleigh frequency selective fading channel and in the presence of AWGN noise, the proposed system was evaluated and compared to the basic modulation system and M-ary PSK employing orthogonal frequency division multiplexing (OFDM). The performance results show that M-ary PSK OWDM had better performance in comparison with M-ary PSK OFDM and the conventional system. By utilizing 16 subcarriers, QPSK OWDM achieved bit error rate performance improvement from 1.5 × 10-3 to 1 × 10-4 for Eb/N0 of 20 dB with efficient bandwidth.

Random attractors for three-dimensional stochastic globally modified Navier–Stokes equations driven by additive noise on unbounded domains

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