Search

The JWST has ushered in a new era of exoplanet transit spectroscopy. Among the JWST instruments, the Near-Infrared Spectrograph (NIRSpec) has the most extensive set of configurations for exoplanet time-series observations. The NIRSpec Prism and G395H grating represent two extremes in NIRSpec instrument modes, with the Prism spanning a wider spectral range (0.6–5.3 µm) at lower resolution (R ∼ 100) compared to G395H (2.87–5.14 µm; R ∼ 2700). In this work, we develop a new data reduction framework, JexoPipe, to conduct a homogeneous assessment of the two NIRSpec modes for exoplanet spectroscopy. We use observations of the hot Saturn WASP-39 b obtained as part of the JWST Transiting Exoplanet Early Release Science programme to assess the spectral quality and stability between the two instrument modes at different epochs. We explore the noise sources, effect of saturation, and offsets in transmission spectra between the different instrument modes and also between the two G395H NRS detectors. We find an inter-detector offset in G395H of ∼40–50 ppm, consistent with recent studies. We find evidence for correlated noise in the Prism white light curve. We find the G395H spectrum to be of higher precision compared to the Prism spectrum at the same resolution. We also compare the JexoPipe spectra with those reported from other pipelines. Our work underscores the need for robust assessment of instrument performance and identification of optimal practices for JWST data reduction and analyses. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise operators as more general cases. Also, several types of quantum (stochastic) gradients are formulated as continuous linear operators which are related to the quantum white noise derivatives and reflecting the interactions with the external noises. Finally, we formulate further systematical study of anticipating quantum stochastic integrals. [ABSTRACT FROM AUTHOR]

This paper studies the zero-viscosity limit for the Navier-Stokes equations with rotation, an additive white noise and nonslip boundary condition in dimension three. By establishing the well-posedness of the limit problems and constructing approximate solutions, we obtain the convergence in the mean square for the Oseen type equation with nonlinear source term, and the convergence in probability of the martingale solution of the stochastic Navier-Stokes equations with rotation. [ABSTRACT FROM AUTHOR]

The quaternion cubature Kalman filter (QCKF) algorithm has emerged as a prominent nonlinear filter algorithm and has found extensive applications in the field of GNSS/SINS integrated attitude determination and positioning system (GNSS/SINS-IADPS) data processing for unmanned aerial vehicles (UAV). However, on one hand, the QCKF algorithm is predicated on the assumption that the random model of filter algorithm, which follows a white Gaussian noise distribution. The noise in actual GNSS/SINS-IADPS is not the white Gaussian noise but rather a ubiquitous non-Gaussian noise. On the other hand, the use of quaternions as state variables is bound by normalization constraints. When applied directly in nonlinear non-Gaussian system without considering normalization constraints, the QCKF algorithm may result in a mismatch phenomenon in the filtering random model, potentially resulting in a decline in estimation accuracy. To address this issue, we propose a novel Gaussian sum quaternion constrained cubature Kalman filter (GSQCCKF) algorithm. This algorithm refines the random model of the QCKF by approximating non-Gaussian noise with a Gaussian mixture model. Meanwhile, to account for quaternion normalization in attitude determination, a two-step projection method is employed to constrain the quaternion, which consequently enhances the filtering estimation accuracy. Simulation and experimental analyses demonstrate that the proposed GSQCCKF algorithm significantly improves accuracy and adaptability in GNSS/SINS-IADPS data processing under non-Gaussian noise conditions for Unmanned Aerial Vehicles (UAVs). [ABSTRACT FROM AUTHOR]

Aim Methods Results Conclusions This study aims to investigate the effects of the white noise, swaddling and white noise + swaddling methods on pain and physiological parameters associated with orogastric tube insertion procedure.This was a randomized controlled trial. A total of 132 preterm infants were randomly assigned to four groups as white noise group (n = 33), swaddling group (n = 33), white noise + swaddling group (n = 33) and control group (n = 33). Interventions were initiated 5 min before the orogastric tube insertion procedure and continued during and up to 5 min after the procedure.White noise intervention alone did not have a significant effect on reducing pain associated with orogastric tube insertion (p > 0.05). Compared with the control group, the preterm infants in the swaddling group experienced 0.587 times less pain, and those in the white noise + swaddling group experienced 0.473 times less pain.Findings indicate the swaddling and the combination of white noise + swaddling may be a useful intervention in reducing the invasive pain experienced by preterm infants during and after orogastric tube insertion and in improving the physiological parameters associated with pain. [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]

Chaos is prevalent in both nature and science, appearing in data, time series and complex systems. Chaotic systems exhibit numerous uncertainties, akin to noise, which challenge researchers to distinguish or analyze potential underlying patterns or even identify the type of system involved. However, determining the kind of chaotic system is essential, as it enables prediction, synchronization, control, treatment and application. This study employs machine learning to classify chaotic data through a simulation involving three types of research data: Lorenz data, Lorenz combined with Gaussian white noise, Gaussian white noise and pink noise, utilizing six distinct algorithms. The most effective testing results are achieved using Mobilenet, with a classification accuracy of 97.38% and a loss of 0.2680 across these six data types. [ABSTRACT FROM AUTHOR]

The series tuned inerter dampers (STID) with distributed inerters are proposed in this paper to suppress seismic response for ground motion excited structures with broadband characteristics. In order to reveal the mechanism of the STID for vibration mitigation, the dimensionless displacement objective function of a single degree of freedom structure equipped with an STID under random Gaussian white noise base excitations is thereupon derived. Based on the principle of the reasonable distribution of inertance, the analytical optimal design parameters of STID are obtained under constraint for total inerter-mass ratio. The vibration mitigation performance of the STID is evaluated and further compared with the tuned inerter damper (TID), tuned mass damper (TMD) and typical series dampers using same mass ratio or inerter-mass ratio when structure is subjected to harmonic and random excitation. Results demonstrate that the performance of structural vibration control and broadband characteristics of STID outperform both the TMD and TID. On the condition of same inerter-mass ratio, the deformation enhancement of damping element can be further increased compared with TID because of dual-tuning effect of series inerters. The higher vibration control performance of STID is realized by using very small nominal damping ratio compared with the TMD and TID. Meanwhile, there exist two grounded inerters in STID compared to other series dampers, and both two subsystems are not affected by base random acceleration excitation which also brings STID a wider VSB and better seismic response mitigation effect. Substantially, due to STID is a type of dual-grounded inerter-based device, for force and base acceleration excited main system, the optimal expressions are identical. Hence, STID can adapt to more complex practical engineering and random and diverse excitations. Hence, the STID can be deemed to be a broadband, high effectiveness and high-performance inerter system. Meanwhile, considering low damping, lightweight and flexible install of STID, it is easier for implementation in practical engineering. [ABSTRACT FROM AUTHOR]

The response of a nonlinear system excited by multi-frequency signals and Poisson white noise contains abundant dynamic behaviours. The study on system response has certain practical values. Utilising optimal dynamics response has unique advantages in weak feature identification under strong background noise. In this work, we study the optimal dynamics response in the bistable system excited by multi-frequency signals and Poisson white noise. The effects of noise parameters on system response and feature identification are discussed and analysed. Also, a signal identification method for unknown multi-frequency signals based on the optimal resonance response of the nonlinear system is proposed and applied to the compound fault diagnosis of rolling bearings, which utilises the difference between stochastic resonance and coherence resonance to determine characteristic components of the signals. The proposed method effectively identifies the characteristic components of the original excitation and avoids misjudgment caused by strong noise, which is effectively verified via simulation analysis and experiments. [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]

The core of electrostatic tomography (EST) is to solve the inverse problem, but the EST independent measurement data are much smaller than the value that needs to be reconstructed, resulting in a more serious inverse problem. This paper presents an improved ResNet-34 network (P-ResNet), which consists of an input layer, a residual feature extraction layer, and an output layer. The number of residual blocks is 3, 4, 4, and 3. After the second convolution in the main path of each residual block, a ReLU activation function is added to enhance the nonlinear expression ability of the network, and the generalization ability of the model is improved by introducing the L2 regularization loss function. A total of 15 930 sets of samples were simulated for the simulation test. After 200 rounds of iteration, the reconstruction results show that the network achieves high accuracy in EST image reconstruction tasks. In addition, the model is tested under different degrees of Gaussian white noise to verify its anti-noise ability. Compared with the traditional algorithms, the image correlation coefficients of this proposed model network are higher. In addition, this paper designs a small sensor to obtain the induced charge values through the principle of electrostatic induction. The reconstructed results obtained from the experimental data are consistent with the simulation results, which verifies the effectiveness and generalization ability of the proposed model. [ABSTRACT FROM AUTHOR]

Lévy noise is a paradigmatic noise used to describe out-of-equilibrium systems. Typically, properties of Lévy noise driven systems are very different from their Gaussian white noise driven counterparts. In particular, under action of Lévy noise, stationary states in single-well, super-harmonic, potentials are no longer unimodal. Typically, they are bimodal; however, for fine-tuned potentials, the number of modes can be further increased. The multimodality arises as a consequence of the competition between long displacements induced by the non-equilibrium stochastic driving and action of the deterministic force. Here, we explore robustness of bimodality in the quartic potential under action of the Lévy noise. We explore various scenarios of bounding long jumps and assess their ability to weaken and destroy multimodality. In general, we demonstrate that despite its robustness it is possible to destroy the bimodality, however it requires drastic reduction in the length of noise-induced jumps. [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]

This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model's solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus. [ABSTRACT FROM AUTHOR]

In this article, we consider 3D stochastic primitive equations (PEs) driven by affine-linear multiplicative white noise, with random initial condition. Our main objective is to obtain the global well-posedness of the stochastic equations under the sufficient Malliavin regularity of the initial condition. Apart from the conventional strategy, we adopt the dynamical system approach and techniques from Malliavin calculus to attack the global well-posedness problem for the PEs. [ABSTRACT FROM AUTHOR]

In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition: \begin{equation*} \left (\partial ^{\beta }_t+\dfrac {\nu }{2}\left (-\Delta \right)^{\alpha / 2}\right) u(t, x) = \: I_{t}^{\gamma }\left [\lambda u(t, x) \dot {W}(t, x)\right ] \quad t>0,\: x\in \mathbb {R}^d, \end{equation*} with constants \lambda \ne 0 and \nu >0, where \partial ^{\beta }_t is the Caputo fractional derivative of order \beta \in (0,2], I_{t}^{\gamma } refers to the Riemann-Liouville integral of order \gamma \ge 0, and \left (-\Delta \right)^{\alpha /2} is the standard fractional/power of Laplacian with \alpha >0. We concentrate on the scenario where the noise \dot {W} is the space-time white noise. The existence and uniqueness of solution in the Itô-Skorohod sense is obtained under Dalang's condition. We obtain explicit formulas for both the second moment and the second moment Lyapunov exponent. We derive the p-th moment upper bounds and find the matching lower bounds. Our results solve a large class of conjectures regarding the order of the p-th moment Lyapunov exponents. In particular, by letting \beta = 2, \alpha = 2, \gamma = 0, and d = 1, we confirm the following standing conjecture for the stochastic wave equation: \begin{align*} \frac {1}{t}\log \mathbb {E}[|u(t,x)|^p ] \asymp p^{3/2}, \quad \text {for p\ge 2 as t\to \infty.} \end{align*} The method for the lower bounds is inspired by a recent work of Hu and Wang, where the authors focus on the space-time colored Gaussian noise case. [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]

In this paper, we study the stochastic Fokas–Lenells equation with multiplicative white noise in the Itô sense. For this purpose, we will use the Jacobi elliptic expansion function method. The nonlinear partial differential equation is transformed into ordinary differential equations through the symmetry reduction technique. New optical solutions are constructed as dark, combined hyperbolic, periodic, bright, and rational solutions. Depending on the parameters, these optical solutions exhibit varying periods of qualitative characteristics. Furthermore, the effects of time on the solutions of the nonlinear stochastic Fokas–Lenells equation are examined. In addition, graphical representations of a few solutions are included to supplement our analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new electrocardiogram (ECG) denoising technique based on the application of a 1D double-density complex discrete wavelet transform (DWT) denoising method in the stationary bionic wavelet transform (SBWT) domain. SBWT was introduced in our previous work for speech enhancement. The first step in this proposed ECG denoising technique consists of applying the SBWT to the noisy ECG signal to obtain two noisy wavelet coefficients wtb1 and wtb2. The coefficients wtb1 and wtb2 are, respectively, the details and approximation coefficients. To estimate the level, σ , of the additive white noise corrupting the original ECG signal, we use wtb1 which is then thresholded using soft thresholding function. The noisy approximation wtb2 is denoised by using 1D double-density complex DWT denoising method. The latter requires the use of this noise level, σ. The results obtained from SNR computations show the performance of the ECG denoising technique proposed in this work. [ABSTRACT FROM AUTHOR]

Background: Neonates experience varying intensities of pain after surgery. While white noise has been used for postoperative pain relief in infants, its effects on neonates after surgery need further exploration. Purpose: This study aimed to evaluate the effects of white noise on pain scores and salivary cortisol levels in surgical neonates. Methods: In this randomized controlled trial, 64 neonates scheduled for surgery were recruited and assigned by block randomization into 2 groups. The intervention group listened to white noise at 50 dB, while the control group listened to white noise at 0 dB, for 30 minutes 6 times for 48 hours postoperatively. Pain scores, measured by the COMFORTneo Scale, and salivary cortisol levels were compared. Results: Although pain scores decreased after surgery in all subjects, no statistically significant difference was observed between the 2 groups (P = .937). There was a significant difference between pre- and postintervention pain scores in the intervention group only (P = .006). Salivary cortisol levels decreased after intervention in the intervention group, but there was no significant difference between pre- and postintervention levels in the 2 groups (P = .716). Implications for Practice: Given the reduction in pain scores and salivary cortisol concentrations after white noise intervention, white noise shows potential as an adjunctive soothing measure for neonates after surgery. Implications for Research: Future studies are needed to confirm the efficacy and utility of white noise intervention in clinical settings. [ABSTRACT FROM AUTHOR]

A significant portion of individuals undergoing colonoscopy report stress and anxiety before the procedure. The efficacy of white noise as a nonpharmacological intervention on state anxiety and vital signs of individuals waiting for colonoscopy has not been investigated in previous studies. The current study aimed to analyze the effect of white noise on preprocedural anxiety and vital signs among older adults undergoing colonoscopy. A pre-test/post-test quasi-experimental study. Subjects (N = 60) were older adults in the colonoscopy unit and divided into experimental (n = 30) and control groups (n = 30). The subjects in the experimental group listened to the white noise via binaural headphones for 20 minutes, while the control group received routine pre-endoscopic care. State anxiety and vital signs were assessed before and after intervention using the State-Trait Anxiety Inventory and vital signs monitor, respectively. The data were analyzed using SPSS-25 software. No statistically significant differences were found between the two groups on demographic characteristics, state-anxiety, systolic and diastolic blood pressure, pulse rate, and respiratory rate before the intervention (P >.05). A significant difference was found between the experimental and control groups in terms of state-anxiety (P =.00) and pulse rate (P =.003) after the intervention. No significant differences were found between the two groups in terms of systolic blood pressure (P =.69), diastolic blood pressure (.59), and respiratory rate (P =.164) after the intervention. This study provides preliminary evidence supporting the use of white noise in older adults undergoing colonoscopy to reduce anxiety. The authors recommend that this intervention, as a nonpharmacological and easily administered approach, is adopted to reduce precolonoscopy anxiety. Continued investigation into the effect of white noise on vital signs is recommended. [ABSTRACT FROM AUTHOR]

In this article, an S V I R age structure model is formulated that describes the dynamics of the Hepatitis B virus (HBV), keeping in view the vaccinated population and the standard incidence rate. After the formulation of the deterministic system, the model is extended to a stochastic system, taking into account the noises in the transmission coefficient. Utilizing the well-known formula of Itô's and the Lyapunov function theory, first, demonstrate that the perturbed system has a unique global positive solution subject to positive initial conditions. Analyze the model for the extinction of HBV, and the required condition is derived. The threshold parameter for the model is calculated, and by using this quantity, it is proved that for small values of the white noises and R s < 1 , the disease will eventually go extinct at a negative exponential rate. It is also proved that for R s 0 > 1 , the weak permanence of the disease is observed. The criterion R s 0 > 1 confirms the stationary distribution of mean infected persons, suggesting that the illness will remain throughout time. To reinforce the primary analytical findings of this paper, various illustrative examples are conducted separately through numerical simulations. [ABSTRACT FROM AUTHOR]

In the presence of spatio-temporal dispersion, perturbation terms of the Hamiltonian type as well as multiplicative white noise, analytical investigation of the concatenation model having the Kerr law of nonlinearity is carried out in this work. The Cole–Hopf transformation and direct assumptions with arbitrary functions are utilized to determine several analytic solutions to the governing equation, including multi-wave, two solitary wave, breather, periodic cross kink, Peregrine-like rational, and three-wave solutions. The parameter constraints that serve as the requisite condition for the existence of these wave solutions are also identified. In order to explore and illustrate the propagation and dynamical behaviors of some solutions reported in this research, 3D graphics and their corresponding contour plots are included. Results of this paper may be useful for the experimental realization of certain nonlinear waves in optical fibers and further understanding of their propagation dynamics. [ABSTRACT FROM AUTHOR]

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

Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions. Several numerical simulations for various fractional orders and randomization intensities are illustrated. [ABSTRACT FROM AUTHOR]

In approximate query searching (AQS), the given query point ( q ¯ ′ ) can be seen as a noise ( η ¯ ) corrupted version of one of the points ( q ¯ ) in the existing database X , i.e., q ¯ ′ = q ¯ + η ¯ . Thus deciding on an appropriate distance d that would return the correct match ( q ¯ ) entails that the chosen distance should be aware of the type of distribution of the noise. In this work, we study the suitability of Minkowski-type distances in AQS when the q ¯ is afflicted by both white and coloured noises to different extent. To this end, we employ a simple similarity search based scoring algorithm proposed in François et al. (ESANN 2005, 13th European Symposium on Artificial Neural Networks, Bruges, Belgium, April 27–29, 2005, Proceedings, pp 339–344, 2005). Our study reveals an interesting interplay of the following 3D's in the quest for an appropriate distance: Dimensionality and Domain geometry of the data and the type of noise Distribution and has led us to explore this problem from a basic geometric perspective. Our main contribution herein is the proposal of a novel index called the Relative Contained Volume (RCV) that helps explain the performance of the considered distances. [ABSTRACT FROM AUTHOR]

The existence and uniqueness of the global positive solution are proved for the system of stochastic differential equations describing a two-species Lotka–Volterra mutualism model disturbed by white noise, centered and noncentered Poisson noises. For the considered system, sufficient conditions of stochastic ultimate boundedness, stochastic permanence, nonpersistence and strong persistence in the mean are obtained. [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]

Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made additionally more difficult by cortical neurons' trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian "map" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The fitted models yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple/complex nature of cells can vary in a continuous manner. We demonstrate that complex-like cells respond less reliably than simple-like cells. However, compensation for this unreliability with noise ceiling analysis reveals predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17/18 receptive fields. Author summary: Methods for recording increasingly many visual cortex neurons are advancing rapidly, demanding new approaches to characterize diverse receptive fields. We present a compact convolutional neural network model of early cortical neurons, which is uniformly applicable to simple and complex cells, and whose parameters are straightforwardly interpretable and readily estimated from responses to natural image stimuli. This novel approach introduces a single estimated model parameter to capture the simple/complex nature of a neuron's receptive field, revealing a continuum of simple vs complex-like behaviour. We show that almost all complex-like cells exhibit a lower response reliability to repeated presentations of the same stimuli, compared to more reliable responses from simple-like cells. Accounting for this "noise ceiling" brings predictive performance for complex cells proportionately closer to that for simple cells. Using this model estimation approach with natural images, we evaluate findings from previous approaches that were restricted to simple-type cells and the use of grating or white noise stimuli, revealing a diversity of Gabor-like spatial receptive field shapes, which lie along a continuum of spatial bandwidths. [ABSTRACT FROM AUTHOR]

The ambient daylight variation is coded by melanopsin photoreceptors and their luxotonic activity increases towards midday when colour temperatures are cooler, and irradiances are higher. Although melanopsin and cone photoresponses can be mediated via separate pathways, the connectivity of melanopsin cells across all levels of the retina enables them to modify cone signals. The downstream effects of melanopsin-cone interactions on human vision are however, incompletely understood. Here, we determined how the change in daytime melanopsin activation affects the human cone pathway signals in the visual cortex. A 5-primary silent-substitution method was developed to evaluate the dependence of cone-mediated signals on melanopsin activation by spectrally tuning the lights and stabilizing the rhodopsin activation under a constant cone photometric luminance. The retinal (white noise electroretinogram) and cortical responses (visual evoked potential) were simultaneously recorded with the photoreceptor-directed lights in 10 observers. By increasing the melanopsin activation, a reverse response pattern was observed with cone signals being supressed in the retina by 27% (p = 0.03) and subsequently amplified by 16% (p = 0.01) as they reach the cortex. We infer that melanopsin activity can amplify cone signals at sites distal to retinal bipolar cells to cause a decrease in the psychophysical Weber fraction for cone vision. [ABSTRACT FROM AUTHOR]

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters. [ABSTRACT FROM AUTHOR]

We present direct numerical simulations of the splashing process between two cylindrical liquid rims. This belongs to a class of impact and collision problems with a wide range of applications in science and engineering, and motivated here by splashing of breaking ocean waves. Interfacial perturbations with a truncated white noise frequency profile are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier-Stokes equation with the adaptive mesh refinement technique, within the Basilisk software environment. We first derive analytical solutions predicting the unsteady interfacial and velocity profiles of the expanding sheet forming between the two rims, and develop scaling laws for the evolution of the lamella rim under capillary deceleration. We then analyse the formation and growth of transverse ligaments ejected from the lamella rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging phenomenon, and found to agree well with the numerical results presented here. The role of the mechanism in breaking waves is discussed further and necessary next steps in the problem are identified. [ABSTRACT FROM AUTHOR]

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

In this investigation, we explore a predator-prey system characterized by generalist predators exhibiting cooperative behavior during hunting, subject to nonlinear harvesting rate. Employing a Beverton-Holt type functional response to capture the impact of additional food sources on predator growth, our numerical findings affirm the destabilizing influence of hunting cooperation, excessive predation, and supplementary food sources. Conversely, the system demonstrates stabilization in response to increased prey species growth. We unveil the occurrence of both forward and backward bifurcations in the system due to the predator growth attributed to additional food sources, contingent on the degree of hunting cooperation. To broaden the scope, we extend our proposed model to its stochastic counterpart, introducing environmental white noises. Our numerical results anticipate that higher intensities of white noises lead to fluctuations of greater amplitude, while smaller intensities exhibit a more modest impact. Additionally, we elucidate the dynamics of prey and predator populations through histogram plots. The theoretical and numerical insights derived from this study provide a deeper understanding of the intricate dynamics within predator-prey systems of ecological communities, emphasizing the significance of additional food sources for cooperative predators subject to harvesting in both constant and fluctuating environments. [ABSTRACT FROM AUTHOR]

Doppler lidar (DL) applications with a focus on turbulence measurements sometimes require measurement settings with a relatively small number of accumulated pulses per ray in order to achieve high sampling rates. Low pulse accumulation comes at the cost of the quality of DL radial velocity estimates and increases the probability of outliers, also referred to as "bad" estimates or noise. Careful filtering is therefore the first important step in a data processing chain that begins with radial velocity measurements as DL output variables and ends with turbulence variables as the target variable after applying an appropriate retrieval method. It is shown that commonly applied filtering techniques have weaknesses in distinguishing between "good" and "bad" estimates with the sensitivity needed for a turbulence retrieval. For that reason, new ways of noise filtering have been explored, taking into account that the DL background noise can differ from generally assumed white noise. It is shown that the introduction of a new coordinate frame for a graphical representation of DL radial velocities from conical scans offers a different perspective on the data when compared to the well-known velocity–azimuth display (VAD) and thus opens up new possibilities for data analysis and filtering. This new way of displaying DL radial velocities builds on the use of a phase-space perspective. Following the mathematical formalism used to explain a harmonic oscillator, the VAD's sinusoidal representation of the DL radial velocities is transformed into a circular arrangement. Using this kind of representation of DL measurements, bad estimates can be identified in two different ways: either in a direct way by singular point detection in subsets of radial velocity data grouped in circular rings or indirectly by localizing circular rings with mostly good radial velocity estimates by means of the autocorrelation function. The improved performance of the new filter techniques compared to conventional approaches is demonstrated through both a direct comparison of unfiltered with filtered datasets and a comparison of retrieved turbulence variables with independent measurements. [ABSTRACT FROM AUTHOR]

The classical Lotka–Volterra predator–prey model is globally stable and uniformly persistent. However, in real-life biosystems, the extinction of species due to stochastic effects is possible and may occur if the magnitudes of the stochastic effects are large enough. In this paper, we consider the classical Lotka–Volterra predator–prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and, thus, the precise necessary conditions for the stochastic system's persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type. Therefore, in order to establish the sufficient conditions for extinction, we found the conditions for this stabilization. The analytical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge-seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. The deterministic model undergoes thorough scrutiny to ensure the positivity and boundedness of solutions, with equilibria derived and their stability properties meticulously examined. Furthermore, we explore the potential for Hopf bifurcation within the system dynamics. In the stochastic counterpart, we prioritize discussions on the existence of a globally positive solution. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Moreover, for the stochastic system, the oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem. [ABSTRACT FROM AUTHOR]

Inhibitory control, as an essential cognitive ability, affects the development of higher cognitive functions. Rhythmic perceptual stimulation has been used to improve cognitive abilities. It is unclear, however, whether it can be used to improve inhibitory control. This study used the Go/NoGo task and the Stroop task to assess various levels of inhibitory control using rhythmic audio-visual stimuli as the stimulus mode. Sixty subjects were randomly divided into three groups to receive 6 Hz, 10 Hz, and white noise stimulation for 30 min. Two tasks were completed by each subject both before and after the stimulus. Before and after the task, closed-eye resting EEG data were collected. The results showed no differences in behavioral and EEG measures of the Go/NoGo task among the three groups. While both 6 Hz and 10 Hz audio-visual stimulation reduced the conflict effect in the Stroop task, only 6 Hz audio-visual stimulation improved the amplitude of the N2 component and decreased the conflict score. Although rhythmic audio-visual stimulation did not enhance response inhibition, it improved conflict inhibition. [ABSTRACT FROM AUTHOR]

• Children had longer latencies than adults in all listening conditions for P1 and N1. • There were fewer identifiable wave peak components in children than in adults. • /da/ was the most resistant stimulus to noise, especially in white noise. • P1, P2 and N2 amplitudes were reduced, and latencies were elongated in noise. • N1 amplitude was significantly more negative in the noise conditions than in quiet for /da/ Children are disadvantaged compared to adults when they perceive speech in a noisy environment. Noise reduces their ability to extract and understand auditory information. Auditory-Evoked Late Responses (ALRs) offer insight into how the auditory system can process information in noise. This study investigated how noise, signal-to-noise ratio (SNR), and stimulus type affect ALRs in children and adults. Fifteen participants from each group with normal hearing were studied under various conditions. The findings revealed that both groups experienced delayed latencies and reduced amplitudes in noise but that children had fewer identifiable waves than adults. Babble noise had a significant impact on both groups, limiting the analysis to one condition: the /da/ stimulus at +10 dB SNR for the P1 wave. P1 amplitude was greater in quiet for children compared to adults, with no stimulus effect. Children generally exhibited longer latencies. N1 latency was longer in noise, with larger amplitudes in white noise compared to quiet for both groups. P2 latency was shorter with the verbal stimulus in quiet, with larger amplitudes in children than adults. N2 latency was shorter in quiet, with no amplitude differences between the groups. Overall, noise prolonged latencies and reduced amplitudes. Different noise types had varying impacts, with the eight-talker babble noise causing more disruption. Children's auditory system responded similarly to adults but may be more susceptible to noise. This research emphasizes the need to understand noise's impact on children's auditory development, given their exposure to noisy environments, requiring further exploration of noise parameters in children. [ABSTRACT FROM AUTHOR]

Great changes have taken place in the speed and mode of information dissemination in the digital age. In this paper, combined Word of mouth (WOM) and Internet word of mouth (IWOM), we further propose a stochastic SI1I2AD transmission model. WOM and IWOM are two channel to influence the consumers' decisions. We investigate the existence and uniqueness of the solution to the stochastic differential equations model. Then the basic reproduction numbers are obtained, and the dynamical behaviors of the individuals are investigated. In particular, we obtain the sufficient conditions of two types of information dissemination exist alone and together, respectively. Theoretical results show that greater environmental uncertainty poses a risk to the dissemination of product information, resulting in the disappearance of the disseminating population, and that lower noise intensity favours the continued presence of the product in the market. Moreover, only when, the rate at which people from WOM to IWOM, remains low, the two modes of information diffusion could coexist. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) enable the determination of station displacements, which are essential to understanding geophysical processes and establishing terrestrial reference frames. Unfortunately, GNSS station position time series exhibit spatially and temporally correlated noise, hindering their contribution to geophysical and geodetic applications. While temporal correlations are commonly accounted for, a strategy for modeling spatial correlations is still lacking. Therefore, this study proposes a diagnosis of the spatial correlations of the white and flicker noise components of GNSS position time series, using the global Nevada Geodetic Laboratory dataset. This analysis reveals different spatial correlation patterns for white and flicker noise and the superposition of three distinct spatial correlation regimes (large-scale, short-scale and station-specific), providing insight into the noise sources. We show, in particular, that about 70% of flicker noise corresponds to large-scale variations possibly attributable to orbit modeling errors. We also evidence an increase in the spatial correlations of white noise at distances below 50 km, most pronounced in the vertical component, where 50% of the white noise appears to be driven by short-scale effects—possibly tropospheric delay mismodeling. [ABSTRACT FROM AUTHOR]

Poisson white noise is a typical non-Gaussian noise that can induce stochastic resonance to detect feature signals submerged within it. In this paper, we propose a detection method for overdamped tri-stable stochastic resonance in Poisson white noise environment. Based on the model of over-damped tri-stable stochastic resonance. To begin with, the influence of the parameters of the tri-stable system on the potential function is studied. Then, the cross-correlation coefficient Csx is used to measure Poisson white noise under different pulse arrival rates β, system structural parameters a, b, c, and noise intensity D the law of action on system resonance. Ultimately, the system is successfully applied to the fault diagnosis of bearing under variable speed conditions and the background of Poisson white noise, and the simulation and experimental results are compared with the classical bistable system. The findings suggest that the performance of the system significantly surpasses that of the classical bistable system. [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]

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]

A novel source enumeration method based on criterion of searching for the best-matched preset sparse dictionary is presented in this paper, which is applicable under the condition of both white and colored noise. In this method, different source numbers are mapped with different sparse dictionaries innovatively in advance, which are constructed by utilizing the K-SVD algorithm and the training data under the same SNR. Then, in the source enumeration stage, all the preset dictionaries are employed to sparsely encode the observed signal through the orthogonal matching pursuit (OMP) algorithm, and the best-matched one which corresponds to the correct source number leads to the least information loss after sparse encoding. Due to the difficulty of directly evaluating the information loss through each error signal which is the difference between the observed signal and the sparse reconstructed signal, the energy norm for the singular values, which is calculated after performing singular value decomposition (SVD) on error signal, is proposed to reflect the information loss indirectly. Simultaneously, the source number corresponding to the best-matched preset sparse dictionary is the final estimated result. The experimental results show the superiority of our proposed method compared to other advanced methods. [ABSTRACT FROM AUTHOR]

A differential pursuit game in a stochastic descriptor linear system is analyzed. The dynamic of the system is described by Ito's stochastic differential algebraic equation. Solutions of the equation are presented by the stochastic formula of the variation of constants in terms of the initial data and control unit. Constraints on the support functionals of two sets defined by the behaviors of the pursuer and evader are used to obtain the game completion conditions. The method of resolving functions is applied to construct pursuer's control bringing the dynamic vector of the system to the terminal set. The results are illustrated by an example of a stochastic descriptor system that describes transients in a radio engineering filter with random disturbances in the form of white noise. [ABSTRACT FROM AUTHOR]

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements. [ABSTRACT FROM AUTHOR]

In recent years, the hardware implementation of neural networks, leveraging physical coupling and analog neurons has substantially increased in relevance. Such nonlinear and complex physical networks provide significant advantages in speed and energy efficiency, but are potentially susceptible to internal noise when compared to digital emulations of such networks. In this work, we consider how additive and multiplicative Gaussian white noise on the neuronal level can affect the accuracy of the network when applied for specific tasks and including a softmax function in the readout layer. We adapt several noise reduction techniques to the essential setting of classification tasks, which represent a large fraction of neural network computing. We find that these adjusted concepts are highly effective in mitigating the detrimental impact of noise. [ABSTRACT FROM AUTHOR]