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In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive athermal motion with a time-dependent anomalous exponent α. In such viscoelastic feedback, the active particle always exhibits superdiffusion with α = 3/2 at times shorter than the self-propulsion time (τA). At times greater than τA, the subdiffusive motion emerges with α bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to α = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein–Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe∗) and crossover times (τ∗ and τ†) above which active viscoelastic dynamics emerge on timescales of τ∗≲ t ≲ τ†. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments. [ABSTRACT FROM AUTHOR]

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively. The exact quantum propagator thereby becomes an expectation of the stochastic one in which the amplitude results from the potential with a fluctuating position: The particle moves with a constant velocity, subjected to a complex Brownian motion. We demonstrate that the stochastic Schrödinger equation can be feasibly used to derive the quantum propagators for the linear potential and the harmonic oscillator system. Novel semiclassical and other approximations may be developed from the new representation of quantum mechanics. [ABSTRACT FROM AUTHOR]

We consider the problem of analyzing spin-flip qubit gate operation in the presence of Random Telegraph Noise (RTN). Our compressive approach is the following. By using the Feynman disentangling operators method, we calculate the spin-flip probability of qubit driven by different kinds of composite pulses, e.g., Constant pulse (C-pulse), Quantum Well pulse (QW-pulse), and Barrier Potential pulse (BP-pulse) in the presence of RTN. When composite pulses and RTN act in the x-direction and z-direction respectively, we calculate the optimal time to achieve perfect spin-flip probability of qubit. We report that the highest fidelity of spin-flip qubit can be achieved by using C-pulse, followed by BP-pulse and QW-pulse. For a more general case, we have tested several pulse sequences for achieving high fidelity quantum gates, where we use the pulses acting in different directions. From the calculations, we find that high fidelity of qubit gate operation in the presence of RTN is achieved when QW-pulse, BP-pulse, and C-pulse act in the x-direction, y-direction, and z-direction, respectively. We extend our investigations for multiple QW and BP pulses while choosing the C-pulse amplitude constant in the presence of RTN. The results of calculation show that 98.5 % fidelity can be achieved throughout the course of RTN that may be beneficial for quantum error correction. [ABSTRACT FROM AUTHOR]

In a lot of engineering applications, one has to recover the temperature of a heat body having a surface that cannot be measured directly. This raises an inverse problem of determining the temperature on the surface of a body using interior measurements, which is called the sideways problem. Many papers investigated the problem (with or without fractional derivatives) by using the Cauchy data u(x0,t),ux(x0,t)$$ u\left({x}_0,t\right),{u}_x\left({x}_0,t\right) $$ measured at one interior point x=x0∈(0,L)$$ x={x}_0\in \left(0,L\right) $$ or using an interior data u(x0,t)$$ u\left({x}_0,t\right) $$ and the assumption limx→∞u(x,t)=0$$ {\lim}_{x\to \infty }u\left(x,t\right)=0 $$. However, the flux ux(x0,t)$$ {u}_x\left({x}_0,t\right) $$ is not easy to measure, and the temperature assumption at infinity is inappropriate for a bounded body. Hence, in the present paper, we consider a fractional sideways problem, in which the interior measurements at two interior point, namely, x=1$$ x=1 $$ and x=2$$ x=2 $$, are given by continuous data with deterministic noises and by discrete data contaminated with random noises. We show that the problem is severely ill‐posed and further constructs an a posteriori optimal truncation regularization method for the deterministic data, and we also construct a nonparametric regularization for the discrete random data. Numerical examples show that the proposed method works well. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by an adversary, and both this phenomenon and the uncertainty in the observations are modelled by two sets of Bernoulli random variables. Under the assumption that the evolution model generating the signal to be estimated is unknown and only the mean and covariance functions of the processes involved in the observation equation are available, recursive algorithms based on linear approximations of the real observations are proposed for the least-squares filtering and fixed-point smoothing problems. Finally, the feasibility and effectiveness of the developed estimation algorithms are verified by a numerical simulation example, where the impact of uncertain observation and deception attack probabilities on estimation accuracy is evaluated. [ABSTRACT FROM AUTHOR]

In this article, we study consensus robustness and performance problems for continuous‐time multi‐agent systems. We consider first‐order unstable agents coordinated by an output feedback protocol over a network subject to an unknown, uncertain constant delay. Our objectives are twofold. First, we seek to determine the largest range of delay permissible so that the agents may achieve robustly consensus despite variation of the delay length, herein referred to as the delay consensus margin. Second, we attempt to determine consensus error performance quantified under an ℋ2$$ {\mathscr{H}}_2 $$ norm criterion, which measures the disruptive effect of random nodal noises on consensus. We consider both undirected and directed graphs. For undirected graphs, we obtain analytical results for the delay consensus margin and the consensus error performance, while for directed graphs, we develop computational results and analytical bounds. The results provide conceptual insights and exhibit how the agents' unstable pole, nonminimum phase zero, as well as the network topology and network delay may limit fundamentally the consensus robustness and performance of first‐order agents. [ABSTRACT FROM AUTHOR]

With the widespread application of digital images, image processing technology plays an important role in fields such as computer vision and image analysis. Based on the orthogonal matching pursuit algorithm, an image processing method is proposed. In the process, sparse representation and reconstruction algorithm are used for image compressed sensing to complete image sampling operation. Afterwards, the theory of overcomplete sparse representation is introduced to optimize sparse representation, and an overcomplete dictionary is used to remove Gaussian noise, achieving the goal of image processing. The experimental results indicate that the research method do not show significant deficiencies in signal reconstruction when testing reconstructed signals under sparsity of 8; When testing the calculation time, the calculation time of the research method is about 0.212 s when the sparsity is 5 in the Lenna; In the error test, the mean square difference of the research method in the Lenna is stable at about 14.6; When conducting application analysis, the variance eigenvalues of the research method remained below 9.4. This indicates that the research method has good performance and can effectively process images, providing new technical support for image processing. [ABSTRACT FROM AUTHOR]

• The FPK equation of ABH energy harvester is established. • The dimension reduction method is used to converted the high dimension FPK equation. • The Lax-Friedrichs scheme is used and its stability condition is also given. The ABH effect shows potential application in vibration energy harvesting due to its wave localization property. In this study, the stochastic response of output voltage of ABH energy harvester has been investigated under Gaussian white noise excitation. The high dimensional Fokker–Planck–Kolmogorov equation of this piezoelectric coupling systems is given by using Gaussian Expansion method and dimension reduction method is used to convert it to one-dimensional first-order partial differential equation. Finally, the Lax-Friedrichs scheme is developed to solve the partial differential equation to obtain the probability density of output voltage. The results between calculated probability distribution and that of Monte Carlo simulation shows good accuracy of propose method. Finally, a comprehensive parametric analysis has been performed on this stochastic system and some conclusions are given. [ABSTRACT FROM AUTHOR]

Seismic full-waveform inversion (FWI) or waveform inversion (WI) has gained extensive attention as a cutting-edge imaging method, which is expected to reveal the high-resolution images of complex geological structures. In this paper, we regard each 1-D signal in the inversion system as a 1-D probability distribution, then use the Jensen–Shannon divergence from information theory to measure the discrepancy between the predicted and observed signals, and finally implement a novel 2-D multiparameter shallow-seismic WI (MSWI). Essentially, the novel approach achieves an implicit weighting along the time-axis for each 1-D adjoint source defined by the classical WI (CWI), thus enhancing the extra illumination for a deeper medium compared with the CWI. By evaluating the inversion results of the two-layer model and fault model, the reconstruction accuracy for S -wave velocity and density of the new method is increased by about 30 and 20 per cent compared with that of the CWI under the same conditions, respectively. The reconstruction performance for P -wave velocity of these two methods is almost equal. In addition, the new 2-D MSWI is also resilient to white Gaussian noise in the data. Numerically, the inversion system has almost the strongest sensitivities to the S -wave velocity and density, performing the poorest sensitivity to the P -wave velocity. Finally, we test the novel method with a detection case for a power tunnel. [ABSTRACT FROM AUTHOR]

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the ℓ 2 plus ℓ 0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the ℓ 2 fidelity is adopted to suppress Gaussian noise, while the ℓ 0 -norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted ℓ 1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal. [ABSTRACT FROM AUTHOR]

In order to reveal the coupling parametric vibration characteristics of stay cables under combined excitation, considering the effects of cable geometric nonlinearity, inclination and the cooperative vibration of adjacent cables and bridge deck beams, a single-beam–double-cable coupled parametric vibration model excited by Gaussian white noise and deterministic harmonic excitation is established, and the coupled motion equations are derived. The Milstein–Platen method is used to directly obtain the coupled random vibration time history of the single-beam–double-cable structure, and an iterative method is proposed to counter the influence of the parametric diffusion coefficient on the numerical format. By comparing with the finite element method and the Monte Carlo numerical simulation method, the accuracy of the Milstein–Platen method in solving the vibration time history of cable–beam coupling parameters under combined excitation is first verified. Then the random displacement, power spectral density and probability density variation of the cable and beam under the combined excitation of different intensities are analyzed from the angle of random orbit. The results show that under the joint action of deterministic harmonics and random excitation, the time–domain, frequency, and probability characteristics of the single-beam–double-cable coupling system are greatly affected by the Gaussian white noise excitation proportion coefficient, and the degree of influence is different. In addition, compared with the single cable model, the vibration analysis results of the coupling model considering multiple stay cables are more reasonable. [ABSTRACT FROM AUTHOR]

In this paper, a novel hyperspectral denoising method is proposed, aiming at restoring clean images from images disturbed by complex noise. Previous denoising methods have mostly focused on exploring the spatial and spectral correlations of hyperspectral data. The performances of these methods are often limited by the effective information of the neighboring bands of the image patches in the spectral dimension, as the neighboring bands often suffer from similar noise interference. On the contrary, this study designed a cross-band non-local attention module with the aim of finding the optimal similar band for the input band. To avoid being limited to neighboring bands, this study also set up a memory library that can remember the detailed information of each input band during denoising training, fully learning the spectral information of the data. In addition, we use dense connected module to extract multi-scale spatial information from images separately. The proposed network is validated on both synthetic and real data. Compared with other recent hyperspectral denoising methods, the proposed method not only demonstrates good performance but also achieves better generalization. [ABSTRACT FROM AUTHOR]

• Analyzed the stochastic resonance and stochastic P-bifurcation of an axially moving shape-memory alloy laminate. • A change in the volume fraction of the SMA shifted the formant of the SNR (signal-to-noise ratio) curve up and down. • Variation in axial velocity, temperature, and stochastic intensity induced stochastic P-bifurcation. This paper investigates the transverse vibration of an axially moving shape-memory alloy (SMA) fiber hybrid laminations under the combined action of transverse harmonic excitation and stochastic disturbance. Considering the shape memory alloy (SMA) fiber volume fraction random field, the kinetic energy and strain potential energy of SMA laminates are solved, and the axial motion equation of SMA laminates is derived according to Hamilton principle, a non-dimensional differential equation of the transverse vibration of the axially moving SMA laminated plates is obtained by adopting the Galerkin integral method. Considering the volume-fraction stochastic field, the stochastic natural vibration of a SMA laminate is analyzed. Considering the stochastic resonance of the SMA laminate under the action of Gaussian white noise and harmonic excitation, the effects of geometric parameters, physical parameters of materials, and temperature on the stochastic resonance behavior of the SMA laminate is analyzed. Finally, the effect of the stochastic P-bifurcation phenomenon of the parameters on the steady-state response of the SMA laminate is analyzed. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of wildfires is mainly influenced by weather, fuel, and topography. Based on fundamental conservation laws involving numerous physical processes and large scales, atmospheric models require substantial computational resources. Therefore, coupling wildfire and atmospheric models is impractical for high resolutions. Instead, a static atmospheric wind field is typically input into the wildfire model, either as boundary conditions on the control surface or distributed over the control volume. Wildfire propagation models may be (i) data-driven ; (i i) theoretical ; or (i i i) mechanistic surrogates. Data-driven models are beyond the scope of this paper. Theoretical models are based on conservation laws (species, energy, mass, momentum) and are, therefore, computationally intensive; e.g. the Fire Dynamics Simulator (FDS). Mechanistic surrogate models do not closely follow fire dynamics laws, but related laws observed to make predictions more efficiently with sufficient accuracy; e.g. FARSITE, and FDS with the Level Set model (FDS-LS). Whether theoretical or mechanistic surrogate, these wildfire models may be coupled with or decoupled from wind models (e.g. Navier-Stokes equations). Only coupled models account for the effect of the fire on the wind field. In this paper, a series of simulations of wildfire propagation on grassland are performed using FDS-LS to study the impact of the fire-induced wind on the fire propagation dynamics. Results show that coupling leads to higher Rates of Spread (RoS), closer to those reported from field experiments, with increasing wind speeds and higher terrain slopes strengthening this trend. Aiming to capture the fire–wind interaction without the hefty cost of solving Navier-Stokes equations, a conceptual framework is proposed: 1) a swarm of unmanned aerial vehicles measure wind velocities at flight height; 2) the wind field is constructed with the acquired data; 3) the high-altitude wind field is mapped to near-surface, and 4) the near-surface wind field is fed into the wildfire model periodically. A series of simulations are performed using an in-house decoupled physics-based reduced-order fire propagation model (FireProM-F) enhanced by wind field "measurements". In this proof of concept, wind velocities are not measured but extracted from physics-based Large Eddy Simulations taken as ground truth. Unsurprisingly, higher measurement frequencies lead to more accurate and realistic predictions of the propagating fire front. An initial attempt is made to study the effect of wind measurement uncertainty on the model predictions by adding Gaussian noise. Preliminary results show that higher noise leads to the fire front displaying more irregular shapes and slower propagation. • Higher wildfire model prediction accuracy normally achieved by coupling it with wind model such as Navier-Stokes equations. • Coupled fire-wind models often too computationally expensive for real-time use in operational contexts. • Prediction accuracy of wildfire model uncoupled from wind model enhanced by periodic inputs of updated wind field. • Wind field to be constructed from UAV swarm measurements, surrogated here to velocities obtained from full CFD simulations. • Proposed method to enhance wildfire model predictions robust to Gaussian noise added to represent measurement uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, we use two methods, an algorithm of the density-based spatial clustering of applications with noise combined with the Gaussian mixture model, and the maximum likelihood method, to study two open clusters: IC 2488 and IC 2714 with Gaia Data Release 3 data. We compare the two methods in terms of cluster star number, isochrone fitting, cluster mass, and radius. The comparison shows that the selections of cluster stars by the two methods are consistent. The parameters obtained by the two methods are very close. But there are slight differences between the two methods for faint stars in IC 2714. The maximum likelihood method selects more faint stars outside of the main-sequence stripe. We conclude that the maximum likelihood method is more likely affected by field stars. [ABSTRACT FROM AUTHOR]

Random noise attenuation is a fundamental task in seismic data processing aimed at improving the signal‐to‐noise ratio of seismic data, thereby improving the efficiency and accuracy of subsequent seismic data processing and interpretation. To this end, model‐based and data‐driven seismic data denoising methods have been widely applied, including f–x deconvolution, K‐singular value decomposition, feed‐forward denoising convolutional neural network and U‐Net (an improved fully convolutional neural network structure), which have received widespread attention for their effectiveness in attenuating random noise. However, they often struggle with low‐signal‐to‐noise ratio data and complex noise environments, leading to poor performance and leakage of effective signals. To address these issues, we propose a novel approach for random noise attenuation. This approach employs a multi‐model stacking structure, where the parameters governing this structure are optimized using a particle swarm optimizer. In the model‐based denoising method, we choose the f–x deconvolution method, whereas in the data‐driven denoising method, we choose K‐singular value decomposition for shallow learning and U‐Net for deep learning as components of the multi‐model stacking structure. The optimal parameters for the multi‐model stacking structure are obtained using a particle swarm optimizer, guided by the proposed novel hybrid fitness function incorporating weighted signal‐to‐noise ratio, structural similarity and correlation parameters. Finally, the effectiveness of the proposed method is verified with three synthetic and two real seismic datasets. The results demonstrate that the proposed method is effective in attenuating random noise and outperforms the benchmark methods in denoising both synthetic and real seismic data. [ABSTRACT FROM AUTHOR]

The prefabricated building has been widely promoted in recent years as it can effectively alleviate the conflict between economic growth and environmental resources. However, the development of the prefabricated building has fallen short of anticipated goals under the influence of the dynamic circumstances and behavioral strategies of multiple stakeholders. Understanding the relevant stakeholders' behavioral strategies and collaborative evolution mechanisms is key to promoting prefabricated buildings' orderly and efficient development. Therefore, this study combines the evolutionary game theory with system dynamics, introduces Gaussian white noise stochastic disturbance terms to model the complex characteristics of multiagent behavior toward prefabricated buildings, and establishes evolutionary game models and stochastic evolutionary game models for local governments, contractors, and consumers. Subsequently, the influences of strategy choice behavior with or without central government supervision were analyzed to study the collaborative driving mechanism of prefabricated buildings under the multiple effects of the government and market. The findings of this research underscore the necessity for government and market collaboration in championing the sustainable evolution of prefabricated buildings. While central government supervision spurs the growth of these structures, its static reward–punishment approach offers only fleeting collaborative momentum and fails to ensure market steadiness. In contrast, the improved dynamic incentive and disincentive mechanism can effectively control fluctuations in the evolutionary process, which is critical in achieving stable development and collaborative governance toward prefabricated buildings. This study contributes to the body of knowledge by broadening the horizons of evolutionary game theory applications and providing a perspective for understanding the behavioral strategies driving the development of prefabricated buildings by both government and market forces. Therefore, a series of driving mechanisms is proposed, providing theoretical guidance and practical insights to prompt the long-term development of prefabricated buildings more effectively. [ABSTRACT FROM AUTHOR]

In this paper, we study one-dimensional hyperbolic Anderson models (HAM) driven by space-time pure-jump Lévy white noise in a finite-variance setting. Motivated by recent active research on limit theorems for stochastic partial differential equations driven by Gaussian noises, we present the first study in this Lévy setting. In particular, we first establish the spatial ergodicity of the solution and then a quantitative central limit theorem (CLT) for the spatial averages of the solution to HAM in both Wasserstein distance and Kolmogorov distance, with the same rate of convergence. To achieve the first goal (i.e. spatial ergodicity), we exploit some basic properties of the solution and apply a Poincaré inequality in the Poisson setting, which requires delicate moment estimates on the Malliavin derivatives of the solution. Such moment estimates are obtained in a soft manner by observing a natural connection between the Malliavin derivatives of HAM and a HAM with Dirac delta velocity. To achieve the second goal (i.e. CLT), we need two key ingredients: (i) a univariate second-order Poincaré inequality in the Poisson setting that goes back to Last, Peccati, and Schulte (Probab. Theory Related Fields, 2016) and has been recently improved by Trauthwein (arXiv:2212.03782); (ii) aforementioned moment estimates of Malliavin derivatives up to second order. We also establish a corresponding functional CLT by (a) showing the convergence in finite-dimensional distributions and (b) verifying Kolmogorov's tightness criterion. Part (a) is made possible by a linearization trick and the univariate second-order Poincaré inequality, while part (b) follows from a standard moment estimate with an application of Rosenthal's inequality. [ABSTRACT FROM AUTHOR]

Due to the rapid advancement of GPU computing, deep learning has lately been widely used in image denoising. Most deep learning methods require noise-free images as labels, which are often difficult or impossible to obtain. Therefore, denoising network models have to be trained with a pair of noisy and low-noise images. However, the restored images still face the problem of losing detail information. In this paper, we propose a novel denoising network model based on the concept of Noise2Noise (N2N), where pairs of noisy images are utilized to train a neural network that can learn the noise distribution relationship between them. This newly-proposed model (RA-UNet) draws inspiration from the classical UNet architecture and is designed with a multi-Residual convolutional block with Attention that can adapt different scales to mine the key information of images and recover clearer images. The denoising performance of RA-UNet is comparable and better than that of the conventional CBM3D, while the proposed RA-UNet performs significantly better on both PSNR and SSIM with less 2.5 % FLOPs and less 3 % running time compared to existing deep learning-based methods, such as DnCNN and ADNet. From the perspective of visual quality, RA-UNet can restore images with higher clarity. Compared with the UNet model, our model improves the average PSNR and SSIM obtained by testing Gaussian noise ( σ = 50 ) images on four classic datasets by 2.28 dB and 0.0552, respectively. [ABSTRACT FROM AUTHOR]

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts, the problem reduces to stochastic Schrödinger equation with space–time white noise of Gaussian or Poisson or Lévy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by a stochastic nonlinear Schrödinger equation in the focusing case with space–time white noise. A treatment of stochastic transport equation, the Korteweg–De Vries equation as well as a number of other nonlinear wave equations with space–time white noise is also given. The main technique is the S-transform (we will actually use the closely related Hermite transform) which converts the stochastic partial differential equation (PDE) with space–time white noise to a deterministic PDE defined on the Hida–Kondratiev white noise distribution space. We then utilize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite-dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for path-wise solutions of this class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in the propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of PDEs, that arise in nonlinear wave propagation, have polynomial-type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises. [ABSTRACT FROM AUTHOR]

In this paper, we address the image denoising problem in presence of speckle degradation typically arising in ultra-sound images. Variational methods and Convolutional Neural Networks (CNNs) are considered well-established methods for specific noise types, such as Gaussian and Poisson noise. Nonetheless, the advances achieved by these two classes of strategies are limited when tackling the de-speckle problem. In fact, variational methods for speckle removal typically amounts to solve a non-convex functional with the related issues from the convergence viewpoint; on the other hand, the lack of large datasets of noise-free ultra-sound images has not allowed the extension of the state-of-the-art CNN denoiser methods to the case of speckle degradation. Here, we aim at combining the classical variational methods with the predictive properties of CNNs by considering a weighted total variation regularized model; the local weights are obtained as the output of a statistically inspired neural network that is trained on a small and composite dataset of natural and synthetic images. The resulting non-convex variational model, which is minimized by means of the Alternating Direction Method of Multipliers (ADMM) is proven to converge to a stationary point. Numerical tests show the effectiveness of our approach for the denoising of natural and satellite images. • An hybrid strategy for the despeckling problem combining convolutional neural networks and variational methods is proposed. • The proposed neural architecture is statistically-inspired and not requires the training on a large data-set of images. • A proof of convergence to a stationary point for the alternating direction method is given. [ABSTRACT FROM AUTHOR]

An effective extension to the particle swarm optimizer scheme has been developed to visualize and modelize robustly magnetic data acquired across vertical or dipping faults. This method can be applied to magnetic data sets that support various investigations, including mining, fault hazards assessment, and hydrocarbon exploration. The inversion algorithm is established depending on the second horizontal derivative technique and the particle swarm optimizer algorithm and was utilized for multi-source models. Herein, the inversion method is applied to three synthetic models (a dipping fault model contaminated without and with different Gaussian noises levels, a dipping fault model affected by regional anomaly, and a multi-source model) and three real datasets from India, Australia, and Egypt, respectively. The output models confirm the inversion approach's accuracy, applicability, and efficacy. Also, the results obtained from the suggested approach have been correlated with those from other methods published in the literature. [ABSTRACT FROM AUTHOR]

Distribution-to-distribution point cloud registration algorithms are fast and interpretable and perform well in unstructured environments. Unfortunately, existing strategies for predicting the solution error for these methods are overly optimistic, particularly in regions containing large or extended physical objects. In this paper, we introduce the iterative closest ellipsoidal transform (ICET), a novel three-dimensional (3D) lidar scan-matching algorithm that re-envisions the normal distributions transform (NDT) in order to provide robust accuracy prediction from first principles. Like NDT, ICET subdivides a lidar scan into voxels in order to analyze complex scenes by considering many smaller local point distributions; however, ICET assesses the voxel distribution to distinguish random noise from deterministic structure. ICET then uses a weighted least-squares formulation to incorporate this noise/structure distinction while computing a localization solution and predicting the solution-error covariance. To demonstrate the reasonableness of our accuracy predictions, we verify 3D ICET in three lidar tests involving real-world automotive data, high-fidelity simulated trajectories, and simulated corner-case scenes. For each test, ICET consistently performs scan matching with sub-centimeter accuracy. With this level of accuracy, combined with the fact that the algorithm is fully interpretable, this algorithm is well suited for safety-critical transportation applications. Code is available at https://github.com/mcdermatt/ICET. [ABSTRACT FROM AUTHOR]

In this study, to solve the low accuracy of multi-space-based sensor joint tracking in the presence of unknown noise characteristics, an adaptive multi-sensor joint tracking algorithm (AMSJTA) is proposed. First, the coordinate transformation from the target object to the optical sensors is considered, and the observation vector-based measurement model is established. Then, the measurement noise characteristics are assumed to be white Gaussian noise, and the measurement covariance matrix is set as a constant. On this premise, the traditional iterative extended Kalman filter is applied to solve this problem. However, in most actual engineering applications, the measurement noise characteristics are unknown. Thus, a forgetting factor is introduced to adaptively estimate the unknown measurement noise characteristics, and the AMSJTA is designed to improve the tracking accuracy. Furthermore, the lower bound of the proposed algorithm is theoretically proved. Finally, numerical simulations are executed to verify the effectiveness and superiority of the proposed AMSJTA. [ABSTRACT FROM AUTHOR]

Interactions between mobile robots and human operators in common areas require a high level of safety, especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection, the crossings of planned trajectories and their uncertainty based on model fluctuations, system noise and sensor noise play an outstanding role. This paper discusses the calculation of the expected areas of interactions during human–robot navigation with respect to fuzzy and noisy information. The expected crossing points of the possible trajectories are nonlinearly associated with the positions and orientations of the robots and humans. The nonlinear transformation of a noisy system input, such as the directions of the motion of humans and robots, to a system output, the expected area of intersection of their trajectories, is performed by two methods: statistical linearization and the sigma-point transformation. For both approaches, fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from the given output distribution parameters. [ABSTRACT FROM AUTHOR]

Motivated by an important geophysical application, we analyze the nonlinear dynamics of the number of earthquakes per unit time in a given Earth's surface area. At first, we consider a dynamical model of earthquakes describing their rhythmic behavior with time delays. This model comprises different earthquake scenarios divided into three types (A, B, and C) accordingly to various system dynamics. We show that the deterministic system contains stable equilibria and a limit cycle whose size drastically depends on the production rate α$$ \alpha $$ of earthquakes and their time delay effect. As this takes place, the frequency of earthquakes possesses an oscillatory behavior dependent on α$$ \alpha $$. To study the role of α$$ \alpha $$ in more detail, we have introduced a white Gaussian noise in the governing equation. First of all, we have shown that the dynamical system is stochastically excitable, that is, it excites larger‐amplitude noise‐induced fluctuations in the frequency of earthquakes. In addition, these large‐amplitude stochastic fluctuations can alternate with small‐amplitude fluctuations over time. In other words, the frequency of earthquakes can change its amplitude in an irregular manner under the influence of white noise. Another important effect is how close the current value of α$$ \alpha $$ is to its bifurcation point. The closer this value is, the less noise generates large‐amplitude fluctuations in the earthquake frequency. [ABSTRACT FROM AUTHOR]

Accurate prediction of the remaining useful life (RUL) of lithium-ion batteries is advantageous for maintaining the stability of electrical systems. In this paper, an interpretable online method which can reflect capacity regeneration is proposed to accurately estimate the RUL. Firstly, four health indicators (HIs) are extracted from the charging and discharging process for online prediction. Then, the HIs model is trained using support vector regression to obtain future features. And the capacity model of Gaussian process regression (GPR) is trained and analyzed by Shapley additive explanation (SHAP). Meanwhile, the state space for capacity prediction is constructed with the addition of Gaussian non-white noise to simulate the capacity regeneration. And the modified predicted HIs and noise are obtained by unscented Kalman filter. Finally, according to SHAP explainer, the predicted HIs acting as the baseline and the modified HIs containing information on capacity regeneration are chosen to predict RUL. In addition, the bounds of confidence intervals (CIs) are calculated separately to reflect the regenerated capacity. The experimental results demonstrate that the proposed online method can achieve high accuracy and effectively capture the capacity regeneration. The absolute error of failure RUL is below 5 and the minimum confidence interval is only 2. [ABSTRACT FROM AUTHOR]

Industrial development has made air pollution increasingly severe, and many respiratory diseases are closely related to air quality in terms of infection and transmission. In this work, we used the classic stochastic susceptible–infectious–recovered (SIR) model to reflect the spread of respiratory disease, coupled with the diffusion process of air pollutants to the infectious disease model, and we investigated the impact of various environmental noises on the process of disease transmission and air pollutant diffusion. The value of this study lies in two aspects. Mathematically, we define threshold R 1 s for extinction and threshold R 2 s for persistence of the disease in the stochastic model ( R 2 s < R 1 s ) when the parameters are constant, and we show that (i) when R 1 s is less than 1, the disease will go to stochastic extinction; (ii) when R 2 s is larger than 1, the disease will persist almost surely and the model has a unique ergodic stationary distribution; (iii) when R 1 s is larger than 1 and R 2 s is less than 1, the extinction of the disease has randomness, which is demonstrated through numerical experiments. In addition, we derive the exact expression of the probability density function of the stationary distribution by solving the corresponding Fokker–Planck equation under the condition of disease persistence and analyze the effects of random noises on stationary distribution characteristics and the disease extinction. Epidemiologically, the change of the concentration of air pollutants affects the conditions for disease extinction and persistence. The increase in the inflow of pollutants and the increase in the clearance rate have negative and positive impacts on the spread of diseases, respectively. We found that an increase in random noise intensity will increase the variance, reduce the kurtosis of distribution, which is not conducive to predicting and controlling the development status of the disease; however, large random noise intensity can also increase the probability of disease extinction and accelerates disease extinction. We further investigate the dynamic of the stochastic model, assuming that the inflow rate switches between two levels by numerical experiments. The results show that the random noise has a significant impact on disease extinction. The data fitting of the switching model shows that the model can effectively depict the relationship and changes in trends between air pollution and diseases. [ABSTRACT FROM AUTHOR]

Many practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system. [ABSTRACT FROM AUTHOR]

Magnetic resonance sounding is a geophysical method for quantitatively determining the state for groundwater storage that has gained international attention in recent years. However, the practical acquisition of magnetic resonance sounding signals, which are on the nanovolt scale, is susceptible to various types of interference, such as power-line harmonics, random noise, and spike noise. Such interference can degrade the quality of magnetic resonance sounding signals and, in severe cases, be completely drowned out by noise. This paper introduces an adaptive Gaussian filtering algorithm that is well-suited for handling intricate noise signals due to its adaptive solving characteristics and iterative sifting approach. Notably, the algorithm can process signals without relying on prior knowledge. The adaptive Gaussian filtering algorithm is applied for the envelope extraction of noisy magnetic resonance sounding signals, and the reliability and effectiveness of the method are rigorously validated. The simulation results reveal that, even under strong noise interference (with original signal-to-noise ratios ranging from −7 dB to −25 dB), the magnetic resonance sounding signal obtained after algorithmic processing is compared to the ideal signal, with 16 sets of data statistics, and the algorithm ensures an initial amplitude uncertainty within 4nV and restricts the uncertainty of the relaxation time within a 6 ms range. The signal-to-noise ratio can be boosted by up to 53 dB. The comparative assessments with classical algorithms such as empirical mode decomposition and the harmonic modeling method confirm the superior performance of the adaptive Gaussian filtering algorithm. The processing of the field data also fully proved the practical application effects of the algorithm. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields. [ABSTRACT FROM AUTHOR]

Geothermal energy exploitation in urban areas necessitates robust real-time seismic monitoring for risk mitigation. While surface-based seismic networks are valuable, they are sensitive to anthropogenic noise. This study investigates the capabilities of borehole Distributed Acoustic Sensing (DAS) for local seismic monitoring of a geothermal field located in Munich, Germany. We leverage the operator's cloud infrastructure for DAS data management and processing. We introduce a comprehensive workflow for the automated processing of DAS data, including seismic event detection, onset time picking, and event characterization. The latter includes the determination of the event hypocenter, origin time, seismic moment, and stress drop. Waveform-based parameters are obtained after the automatic conversion of the DAS strain-rate to acceleration. We present the results of a 6-month monitoring period that demonstrates the capabilities of the proposed monitoring set-up, from the management of DAS data volumes to the establishment of an event catalog. The comparison of the results with seismometer data shows that the phase and amplitude of DAS data can be reliably used for seismic processing. This emphasizes the potential of improving seismic monitoring capabilities with hybrid networks, combining surface and downhole seismometers with borehole DAS. The inherent high-density array configuration of borehole DAS proves particularly advantageous in urban and operational environments. This study stresses that realistic prior knowledge of the seismic velocity model remains essential to prevent a large number of DAS sensing points from biasing results and interpretation. This study suggests the potential for a gradual extension of the network as geothermal exploitation progresses and new wells are equipped, owing to the scalability of the described monitoring system. [ABSTRACT FROM AUTHOR]

Mode decomposition (MD) provides profound evidence to reveal the internal modal transmission mechanism. However, the indelible noise has always been the main stubborn hindrance in practical MD. In the complex superposition case with a large number of modes, the traditional MD is not capable enough to distinguish the real modal intensity and the annoying noise, sustaining an unacceptable accuracy and fluctuation. This paper proposes a radial intensity-orientated MD (RIO-MD) method with reliable noise elimination. Our approach focuses on the inherent modal radial features in Polar coordinates, getting rid of the traditional two-dimensional image processing in Cartesian ones. The RIO-MD introduces the inherent radial intensity relationship into MD for better extracting mode coefficients. Based on the expectable real radial modal intensity, the RIO-MD enables to recognize and extraction of the three kinds of stubborn noise, including interference pattern noise, device noise, and random noise. The RIO-MD works well in mode decomposition case. The values of correlation coefficients (C) between the experimental and reconstructed image are higher than 93%. The mean square error (MSE) is lower than 3 × 10−3. Both the C and MSE keep stable, with the standard deviation 30 times lower than the other widely used methods, demonstrating the high-robustness of the RIO-MD. Due to the reliable noise recognition, the RIO-MD shows great possibility in mode number expansion. [ABSTRACT FROM AUTHOR]

Seismic images are essential for understanding the subsurface geological structure and resource distribution. However, the accuracy and certainty of geological analysis using seismic images are limited by the resolution and signal-to-noise ratio. Simultaneously improving resolution and suppressing random noise with traditional methods can be quite challenging. This research proposes a new approach called SeisGAN which leverages a generative adversarial network to address the challenge at hand. Due to the lack of high-resolution noiseless and low-resolution noisy seismic data, stochastic parameter control is employed to simulate a vast range of diverse, paired seismic data for SeisGAN training. The results on the synthetic dataset demonstrate that the proposed method is effective in enhancing the resolution and suppressing the random noise in the original images. Spectrum analysis shows that the proposed method increases the bandwidth of the original data, primarily at high frequencies. Ablation experiments reveal that, under similar conditions, SeisGAN outperforms traditional convolutional neural networks. Incorporating the VGG loss in the generator loss function improves the model's ability to recover high-frequency details. The application of the technique on two publicly available field seismic datasets indicates SeisGAN's excellent generalizability, despite being trained only on synthetic seismic data. Compared with bicubic interpolation and traditional noise suppression and resolution enhancement methods, SeisGAN is capable of effectively suppressing the random noise and enhancing the dominant frequency of field seismic data, making it easier to identify adjacent thin layers and fault features, even for small-scale faults. The zoomed images are clearer and easier to interpret. Furthermore, an example of automatic machine fault identification demonstrates the significant contribution of the SeisGAN-enhanced image to accurate fault recognition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A lower bound for minimax risk is constructed for the problem of estimating an unknown pseudoperiodic function observed in Gaussian stationary noise with spectral density satisfying some version of the Muckenhoupt condition. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative electrocardiogram (ECG ) denoising technique based on stationary wavelet transform ( S W T) and wavelet/total variation (WATV). In this technique, we also use two different artificial neural networks ( ANNs ) to determine two ideal thresholds, t h r 1 and t h r 2 . The latter is used for the soft thresholding of a noisy details coefficient, c d b 2 , to obtain a denoised coefficient, c d d 2 . The threshold t h r 1 is used for the soft thresholding of a noisy details coefficient, c d b 1 , yielding a denoised coefficient, c d d 1. The coefficient c d b 1 and a noisy approximation coefficient, c a b 1 , are obtained by applying SWT to the noisy ECG signal. The coefficient c d b 2 and another noisy approximation coefficient, c a b 2 , are obtained by applying SWT to c a b 1 . In this proposed ECG denoising system, we also apply a WATV-based denoising technique to c a b 2 to obtain a denoised approximation coefficient, c a d 2 . This WATV-based denoising technique requires the estimation of the level of the noise corrupting the clean ECG signal. This noise is additive Gaussian white noise (AGWN) and its level is denoted as σ , which is estimated from c d b 1 . After that, the inverse of SWT ( S W T - 1 ) is applied to c d d 2 and c a d 2 to obtain a denoised approximation coefficient, c a d 1 . Subsequently, we apply S W T - 1 to c d d 1 and c a d 1 to finally obtain the denoised ECG signal. The performance of this proposed ECG denoising technique is proven by the results obtained after computing the signal-to-noise ratio ( SNR ), the peak SNR ( PSNR ), the mean square error ( MSE ), the mean absolute error ( MAE ) and the cross-correlation ( CC ). [ABSTRACT FROM AUTHOR]

Low-frequency vibration measurements in harsh environments are considerably challenging owing to strong background noise. In this study, a simple, high-dynamic-range, and high-precision vibration-measuring system using a frequency-modulated interferometer was proposed and validated. Harmonics with perfectly orthogonal phases were extracted directly from the interference signal, and noise with random frequencies was filtered using a synchronous detection method. The modulation index of the interferometer was controlled to remove the effect of Bessel functions; hence, a full-circle Lissajous diagram was obtained. The ratio of the two harmonics was used to determine the vibration; hence, the effects of intensity fluctuation and background noise can be neglected. The vibration measurement bandwidth was well controlled by controlling the modulation and cutoff frequencies of the bandpass filters. The best noise level of 1 nm/√Hz under harsh measuring conditions can be archived in the low-frequency range. [ABSTRACT FROM AUTHOR]

Point-scatterer detection plays a key role in medical ultrasound B-mode imaging. Speckle noise and insufficient spatial resolution are important factors affecting point-scatterer detection. To address this issue, normalized spatial autocorrelation in ultrasound B-mode imaging (NSACB) is proposed. First, the acquired data are pre-processed by adding Gaussian white noise (GWN) with a certain signal-to-Gaussian white noise ratio (SGWNR). Next, normalized spatial autocorrelation is applied to the pre-processed data, and the data are divided into several new signals with different spatial lags. Then, the new signals are performed unsigned delay multiply and sum. Finally, the NSACB beamformed data are bandpass filtered by extracting the frequency component around twice the center frequency. Simulated and in vitro experiments were designed for validation. Simulations revealed that the lateral resolution of NSACB measured by the –6-dB mainlobe width can reach as high as 11.11% of delay and sum (DAS), 25.01% of filtered delay multiply and sum (F-DMAS) and 50% of LAG-FDMAS-SCF. The sidelobe level of the NSACB can be reduced at most by 28 dB. Experimental results of simple and complex scatterer phantoms indicate the image resolution of the proposed NSACB can even reach up to 18.76% of DAS, 27.28% of F-DMAS and 14.29% of LAG-FDMAS-SCF. Compared with these methods, the proposed NSACB can reduce the sidelobe level at least by 18 dB. Although the proposed method causes loss of the ability to observe hypo-echoic structures, these results suggest future work to determine the ability to detect breast microcalcifications, kidney stones, biopsy needle tracking and other scenarios requiring scatterer detection. [ABSTRACT FROM AUTHOR]

Protein design is central to nearly all protein engineering problems, as it can enable the creation of proteins with new biological functions, such as improving the catalytic efficiency of enzymes. One key facet of protein design, fixed-backbone protein sequence design, seeks to design new sequences that will conform to a prescribed protein backbone structure. Nonetheless, existing sequence design methods present limitations, such as low sequence diversity and shortcomings in experimental validation of the designed functional proteins. These inadequacies obstruct the goal of functional protein design. To improve these limitations, we initially developed the Graphormer-based Protein Design (GPD) model. This model utilizes the Transformer on a graph-based representation of three-dimensional protein structures and incorporates Gaussian noise and a sequence random masks to node features, thereby enhancing sequence recovery and diversity. The performance of the GPD model was significantly better than that of the state-of-the-art ProteinMPNN model on multiple independent tests, especially for sequence diversity. We employed GPD to design CalB hydrolase and generated nine artificially designed CalB proteins. The results show a 1.7-fold increase in catalytic activity compared to that of the wild-type CalB and strong substrate selectivity on p -nitrophenyl acetate with different carbon chain lengths (C2–C16). Thus, the GPD method could be used for the de novo design of industrial enzymes and protein drugs. The code was released at https://github.com/decodermu/GPD. [ABSTRACT FROM AUTHOR]

Rank‐reduction‐based simultaneous random noise attenuation and three‐dimensional seismic‐data interpolation has recently become a hot topic in reflection seismology. However, the rank of traditional methods is fixed without considering the variation of signal‐to‐noise ratio on different frequency components, leading to serious residual noise and further affecting the following processing and interpretation tasks. In addition, traditional methods also heavily rely on the application of singular value decomposition technique for rank reduction, which is proven to be computationally expensive for large‐scale data. Thus, a fast‐adaptive rank‐reduction method is proposed in this study. First, the information entropy theory is introduced to adaptively select the optimal rank at various frequencies by calculating the increment of singular entropy. Second, we propose a fast Random Block Krylov algorithm and a subspace multiplexing technique to replace the singular value decomposition algorithm used in traditional methods. The proposed method can significantly improve computational efficiency and yield better seismic‐data reconstruction performance than traditional methods. Applications of the proposed approach on both synthetic and field seismic data demonstrate its superior performance over a well‐known rank‐reduction‐based method, that is the random multi‐channel singular spectrum analysis, in terms of recovered signal‐to‐noise ratio and visual view. [ABSTRACT FROM AUTHOR]

The CNN framework has gained widespread attention in texture feature analysis; however, handcrafted features still remain advantageous if computational cost needs to take precedence and in cases where textures are easily extracted with few intra-class variation. Among the handcrafted features, the local binary pattern (LBP) is extensively applied for analysing texture due to its robustness and low computational complexity. However, in local difference vector, it only utilizes the sign component, resulting in unsatisfactory classification capability. To improve classification performance, most LBP variants employ multi-feature fusion. Nevertheless, this can lead to redundant and low-discriminative sub-features and high computational complexity. To address these issues, we propose the neighbourhood feature-based local binary pattern (NF-LBP). Inspired by gradient's definition, we extract the neighbourhood feature in a local region by simply using the first-order difference and 2-norm. Next, we introduce the neighbourhood feature (NF) pattern to describe intensity changes in the neighbourhood. Finally, we combine the NF pattern with the local sign component and the centre pixel component to create the NF-LBP descriptor. This approach provides better complementary texture information to traditional local sign pattern and is less sensitive to noise. Additionally, we use an adaptive local threshold in the encoding scheme. Our experimental results of classification accuracy and F1 score on five texture databases demonstrate that our proposed NF-LBP method attains outstanding texture classification performance, outperforming existing state-of-the-art approaches. Furthermore, extensive experimental results reveal that NF-LBP is strongly robust to Gaussian noise and salt-and-pepper noise. [ABSTRACT FROM AUTHOR]

We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling. [ABSTRACT FROM AUTHOR]

This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research. [ABSTRACT FROM AUTHOR]

As devices scale closer to the atomic size, a complete understanding of the physical mechanisms involving defects in high-κ dielectrics is essential to improve the performance of electron devices and to mitigate key reliability phenomena, such as Random Telegraph Noise (RTN). In fact, crucial aspects of defects in HfO2 are still under investigation (e.g., the presence of metastable states and their properties), but it is well known that oxygen vacancies (V+s) and oxygen ions (O0s) are the most abundant defects in HfO2. In this work, we use simulations to gain insights into the RTN that emerges when a constant voltage is applied across a TiN/(4 nm)HfO2/TiN stack. Signals exhibit different RTN properties over bias and, thus, appear to originate from different traps. Yet, we demonstrate that they can be instead promoted by the same O0s which change their capture (τc) and emission (τe) time constants with the applied bias, which, in turn, changes the extent of their electrostatic interactions with the traps that assist charge transport (V+s). For a certain bias, RTN is given by the modulation of the trap-assisted current at V+s induced by trapping/detrapping events at O0s, which are, in turn, influenced by the bias itself and by trapped charge at nearby O0s. In this work, we demonstrate that accounting for the effect of trapped charge is essential to provide accurate estimation of the RTN parameters, which allow us to retrieve information about traps and to explain key mechanisms behind complex RTN signals. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem for the stochastically perturbed high-dimensional modified Euler-Poincaré system (MEP2) on the torus T d , d ≥ 1. We first establish a local well-posedness framework in the sense of Hadamard for the MEP2 driven by general nonlinear multiplicative noises. Then two kinds of global existence and uniqueness results are demonstrated: One indicates that the MEP2 perturbed by nonlocal-type random noises with proper intensity admits a unique large global strong solution; The other one infers that, if the initial data is sufficiently small, then the MEP2 perturbed by linear multiplicative noise has a unique global solution with high probability. In the case of one dimension, we find that the stochastic MEP2 will break down in finite time when the initial data meets appropriate shape condition. [ABSTRACT FROM AUTHOR]

Interacting particle or agent systems that exhibit diverse swarming behaviors are prevalent in science and engineering. Developing effective differential equation models to understand the connection between individual interaction rules and swarming is a fundamental and challenging goal. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of N particles in \mathbb {R}^d under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of the interaction function with pointwise uncertainty quantification, and the other is the inference of unknown scalar parameters in the noncollective friction forces of the system. We formulate the learning problem as a statistical inverse learning problem and introduce an operator-theoretic framework that provides a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. Given data collected from M i.i.d trajectories with independent Gaussian observational noise, we provide a finite-sample analysis, showing that our posterior mean estimator converges in a Reproducing Kernel Hilbert Space norm, at an optimal rate in M equal to the one in the classical 1-dimensional Kernel Ridge regression. As a byproduct, we show we can obtain a parametric learning rate in M for the posterior marginal variance using L^{\infty } norm and that the rate could also involve N and L (the number of observation time instances for each trajectory) depending on the condition number of the inverse problem. We provide numerical results on systems exhibiting different swarming behaviors, highlighting the effectiveness of our approach in the scarce, noisy trajectory data regime. [ABSTRACT FROM AUTHOR]

The fractional differential equation L^\beta u = f posed on a compact metric graph is considered, where \beta >0 and L = \kappa ^2 - \nabla (a\nabla) is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients \kappa,a. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L^{-\beta }. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L_2(\Gamma \times \Gamma)-error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for {L = \kappa ^2 - \Delta, \kappa >0} are performed to illustrate the results. [ABSTRACT FROM AUTHOR]