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In this work, Legendre wavelet collocation method is implemented for the numerical solution of nonlinear integral and integro‐differential equations. We approximate the solution with Legendre wavelet. The evaluations of integrals has been carried out with the help of Gaussian integration formula. The system of equations is obtained using collocation approach. The system of equations is then solved to obtain the desire solution. The method works in a direct way, which does not need any discretization, linearization, or perturbation. To check the efficiency of the scheme, we match the computed results with those available in literature. From comparison, it has been concluded that obtained results are better than those presented before and require less computational cost. [ABSTRACT FROM AUTHOR]

In recent years, the application of machine learning methods in the prediction of hydrological processes such as precipitation has been widely considered. These methods can analyze large volumes of data and detect the existing trends and patterns. Therefore, in the present study, machine learning methods, including random forests (RF), Kstar algorithm and Gaussian process regression (GPR), were used to predict the precipitation of Sindh River basin in India during period of 1901 to 2020. In the next step, three distinct input scenarios include (i) using monthly precipitation data and considering the memory of time series up to 5 months delay, (ii) adding periodic term to the first scenario inputs and (iii) decomposing the data using the Daubechies 4 wavelet function and creating hybrid wavelet-learning machine (W-ML) models, were prepared and introduced to the models. The performance of each method was evaluated using the root mean square error (RMSE), mean absolute error (MAE), Kling–Gupta efficiency score (KGE) and Willmott index (WI). The results showed that single models with the first scenario inputs (without taking into account the periodicity of the data) did not have good accuracy, but by adding the periodicity, the performance of these models was significantly improved, and the average value of KGE index for all studied stations increased from 0.466 to 0.672. It was also found that the GPR model for all stations could not have good performance and RF and Kstar models are the most appropriate methods for predicting precipitation in the Sindh River basin, respectively. With the application of the third scenario and the development of W-ML hybrid models, the accuracy of precipitation forecasting was significantly improved, especially the maximum precipitation values were estimated with higher accuracy than standalone models. [ABSTRACT FROM AUTHOR]

Let a → : = (a 1 , ... , a n) ∈ [ 1 , ∞) n , p ∈ (0 , 1) , and α:= 1/p − 1. For any x ∈ ℝn and t ∈ [0, ∞), let Φ p (x , t) : = { t 1 + (t [ x ] a → ν) 1 − p if ν α ∉ ℕ , t 1 + (t [ x ] a → ν) 1 − p [ log (e + ∣ x ∣ a →) ] p if ν α ∈ ℕ , where [ ⋅ ] a → := 1 + ∣ ⋅ ∣ a → , ∣ ⋅ ∣ a → denotes the anisotropic quasi-homogeneous norm with respect to a → , and ν:= a1 +...+ an. Let H a → p (ℝ n) , ℒ α a → (ℝ n) , and H a → Φ p (ℝ n) be, respectively, the anisotropic Hardy space, the anisotropic Campanato space, and the anisotropic Musielak-Orlicz Hardy space associated with Φp on ℝn. In this article, via first establishing the wavelet characterization of anisotropic Campanato spaces, we prove that for any f ∈ H a → p (ℝ n) and g ∈ ℒ α a → (ℝ n) , the product of f and g can be decomposed into S(f, g) + T(f, g) in the sense of tempered distributions, where S is a bilinear operator bounded from H a → p (ℝ n) × ℒ α a → (ℝ n) to L1(ℝn) and T is a bilinear operator bounded from H a → p (ℝ n) × ℒ α a → (ℝ n) to H a → Φ p (ℝ n) . Moreover, this bilinear decomposition is sharp in the dual sense that any Y ⊂ H a → Φ p (ℝ n) that fits into the above bilinear decomposition should satisfy (L 1 ( R n) + Y) ∗ = (L 1 ( R n) + H a → Φ p ( R n)) ∗ . As applications, for any non-constant b ∈ ℒ α a → (ℝ n) and any sublinear operator T satisfying some mild bounded assumptions, we find the largest subspace of H a → p (ℝ n) , denoted by H a → , b p (ℝ n) , such that the commutator [b, T] is bounded from H a → , b p (ℝ n) to L1(ℝn). In addition, when T is an anisotropic Calderón-Zygmund operator, the boundedness of [b, T] from H a → , b p (ℝ n) to L1(ℝn)(or to H a → 1 (ℝ n) ) is also presented. The key of their proofs is the wavelet characterization of function spaces under consideration. [ABSTRACT FROM AUTHOR]

Introduction: Removing motion artifacts (MAs) from functional near-infrared spectroscopy (fNIRS) signals is crucial in practical applications, but a standard procedure is not available yet. Artificial neural networks have found applications in diverse domains, such as voice and image processing, while their utility in signal processing remains limited. Method: In this work, we introduce an innovative neural network-based approach for online fNIRS signals processing, tailored to individual subjects and requiring minimal prior experimental data. Specifically, this approach employs one-dimensional convolutional neural networks with a penalty network (1DCNNwP), incorporating a moving window and an input data augmentation procedure. In the training process, the neural network is fed with simulated data derived from the balloon model for simulation validation and semi-simulated data for experimental validation, respectively. Results: Visual validation underscores 1DCNNwP's capacity to effectively suppress MAs. Quantitative analysis reveals a remarkable improvement in signal-to-noise ratio by over 11.08dB, surpassing the existing methods, including the spline-interpolation, wavelet-based, temporal derivative distribution repair with a 1s moving window, and spline Savitzky-Goaly methods. Contrast-to-noise ratio (CNR) analysis further demonstrated 1DCNNwP's ability to restore or enhance CNRs for motionless signals. In the experiments of eight subjects, our method significantly outperformed the other approaches (except offline TDDR, t < -3.82, p < 0.01). With an average signal processing time of 0.53ms per sample, 1DCNNwP exhibited strong potential for real-time fNIRS data processing. Discussion: This novel univariate approach for fNIRS signal processing presents a promising avenue that requires minimal prior experimental data and adapts seamlessly to varying experimental paradigms. [ABSTRACT FROM AUTHOR]

Smart agriculture has shifted the paradigm by integrating advanced technologies, particularly weed management. This paper introduces an innovative approach to weed control by applying a Wavelet-based Convolution Neural Network (WCNN). In the era of precision agriculture, our study explores the integration of WCNN into real-world scenarios, emphasizing its adaptability to diverse environmental conditions. Utilizing the spatial-frequency analysis features of wavelets and convolutional neural networks, the WCNN model is the most effective at finding weeds, classifying them, and managing them specifically in agricultural fields in real-time. This research contributes to the scientific discourse on smart agriculture and addresses the challenges of invasive weeds, presenting a sustainable solution for optimizing resource utilization. Our investigation includes a detailed exploration of WCNN’s adaptive learning mechanisms and dynamic adjustment to changing agricultural landscapes. The model seamlessly integrates with existing smart farming infrastructure, showcasing a substantial reduction in manual intervention and a simultaneous increase in agricultural productivity. We incorporate fog computing and resource optimization into our framework, enhancing the efficiency of onboard data processing. To evaluate the real-world efficacy of WCNN, we conducted comprehensive experiments in texture classification and image labelling using two distinct datasets: the plant seedling and soybean weed datasets. Results demonstrate the superior performance of WCNN, achieving higher accuracy in training and test scenarios with significantly fewer parameters than traditional CNNs. For the soybean weed dataset, WCNN achieved remarkable accuracy in the training (0.9970) and testing (0.9987) phases, with correspondingly low losses of 0.0109 and 0.0048. The WCNN model demonstrated high accuracy during training (0.9739) and testing (0.9902), with minimal losses of 0.0898 and 0.0239 in the plant seedling dataset. [ABSTRACT FROM AUTHOR]

Rainfall is an important phenomenon for various aspects of human life and the environment. Accurate prediction of rainfall is crucial for a wide range of sectors, including agriculture, water resources management, energy production, disaster management and many more. The ability to predict rainfall in an accurate fashion enables stakeholders to make informed decisions and take necessary actions to mitigate the impacts of natural disasters, water scarcity and other issues related to rainfall. In addition, advances in rainfall prediction technologies have the potential to contribute to sustainable water management and the preservation of water resources by providing the necessary information for decision‐makers to plan and implement effective water management strategies. Hence, it is important to continuously improve the accuracy of rainfall prediction. In this paper, the integration of the maximum overlap discrete wavelet transform (MODWT) and machine learning algorithms for daily rainfall prediction is proposed. The main objective of this study is to investigate the potential of combining MODWT with various machine‐learning algorithms to increase the accuracy of rainfall prediction and extend the forecast time horizon to 3 days. In addition, the performances of the proposed hybrid models are contrasted with the models hybridized with commonly used discrete wavelet transform (DWT) algorithms in the literature. For this, daily rainfall raw data from three rainfall observation stations located in Turkey are used. The results show that the proposed hybrid MODWT models can effectively improve the accuracy of precipitation forecasting, based on model evaluation measures such as mean square error (MSE) and Nash‐Sutcliffe coefficient of efficiency (CE). Accordingly, it can be concluded that the integration of MODWT and machine learning algorithms have the potential to revolutionize the field of daily rainfall prediction. [ABSTRACT FROM AUTHOR]

Inferences from tests for non-stationarity depend critically on whether and how breaks and/or non-linearities are specified. Recent work has shown that wavelet transformations that separate a variable's high and low frequency components can enhance the performance of unit root and stationarity tests. This note provides response surface estimates of finite sample, lag-adjusted critical values and approximate probability values for an Augmented Dickey–Fuller type wavelet test that includes a Fourier term allowing for smooth breaks in the series. Applications highlight the practical benefits. [ABSTRACT FROM AUTHOR]

Automated diagnosis and evolving CNN architectures are improving diagnostic quality in digital breast cancer histopathology images. The study predominantly focuses on classifying the histopathological images of the BreakHis breast cancer dataset into distinct categories: benign and malignant. A primary challenge in this task is the uneven class distribution and limited training samples, which introduce bias and compromise the model's non-malignant classification accuracy. The study utilizes wavelet decomposition on benign images to address class imbalance and enhance the model's ability to accurately classify breast cancer histopathological images. This technique begins by filtering the image with high-pass and low-pass filters, followed by downsampling. The process is then repeated to generate four images representing different components of the original image, enabling precise localization of essential features and denoising. The DenseNet201 convolutional network is chosen for image classification due to its efficiency and accuracy. Our proposal involves concatenating features extracted from specific blocks of the pre-trained DenseNet201 model: pool3_pool, pool4_pool, and conv5_block32_conca. The proposed framework achieves an impressive overall accuracy in classifying both benign and malignant images, maintaining high accuracy rates of 99% in both multi-scale and magnification-independent classifications. These promising results indicate the potential clinical application of this approach in diagnosing diseases. [ABSTRACT FROM AUTHOR]

This study examines the relationships among exports, economic growth, the World Uncertainty Index, and the Geopolitical Risk Index for Japan within both bivariate and multivariate frameworks. We analyze quarterly data spanning from 1994Q1 to 2022Q1. This investigation contributes to the existing literature on the export-led growth hypothesis through an innovative approach. Specifically, we employ the state-of-the-art Wavelet Local Multiple Correlation (WLMC) method introduced by Polanco-Martínez et al. (Sci. Rep. 10(1): 1-11 (2020). https://doi.org/10.1038/s41598-020-77767-8). Unlike conventional bivariate wavelet methods, the WLMC enables us to capture correlations between two/ three/four variables simultaneously. To the best of our knowledge, this study represents the first empirical analysis that evaluates the short, medium, and long-term dynamics of export-led growth in the context of uncertainty. Our research findings reveal that, in the multivariate framework, exports emerge as the dominant variable, providing support for the export-led growth hypothesis in the Japanese context. Furthermore, in the long run, we identify adverse effects of the World Uncertainty Index on economic growth. Based on our results, this paper puts forth essential policy recommendations for the Japanese government. These recommendations aim to guide the development of countercyclical policies that can stabilize both exports and economic growth amid a backdrop of uncertainty. [ABSTRACT FROM AUTHOR]

This study focused on detecting the reflections of healing and change in cortex activation in full-face transplantation and lesions patients on EEG activity. Face transplant patients have facial lesions before transplantation and, to identify pre-face transplant patients' brain activity in the absence of pre-transplant recordings, we used data obtained from pre-transplant facial lesion patients. Ten healthy, four facial lesion and three full-face transplant patients participated in this study. EEG data recorded for four different sensory stimuli (brush from the right face, right hand, left face, and left-hand regions) were analyzed using wavelet packet transform method. EEG waves were analyzed for standard bands. Our findings indicate significant change in the 2–4 Hz frequency range which may be a result of ongoing or previous cortical reorganization for face lesion and transplant patients. Alterations of the delta wave seen in patients with facial lesion and face transplant can also be explained by the intense central plasticity. Our findings show that the delta band differences might be used as a marker in the evaluation of post-transplant cortical plasticity in the future. [ABSTRACT FROM AUTHOR]

This article considers a non parametric estimation problem in a regression model with mixed noise. A wavelet estimator is proposed by using projection of wavelet coefficients estimators. Uniform almost sure convergence rate of this wavelet estimator is derived under some mild conditions. It should be pointed out that the convergence rate of the wavelet estimator coincides with the optimal strong uniform convergence rate of non parametric estimations. Finally, simulation studies illustrate the good performances of the wavelet estimator. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an op- erational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black- Scholes model. [ABSTRACT FROM AUTHOR]

Gait is regarded as a unique feature for identifying people, and gait recognition is the basis of various customized services of the IoT. Unlike traditional techniques for identifying people, the Wi-Fi-based technique is unconstrained by illumination conditions and such that it eliminates the need for dense, specialized sensors and wearable devices. Although deep learning-based sensing models are conducive to the development of Wi-Fi-based identification, the latter technique relies on a large amount of data and requires a long training time, where this limits the scope of its use for identifying people. In this study, we propose a Wi-Fi sensing model called Wave-CapNet for human identification. We use data processing to eliminate errors in the raw data so that the model can extract the characteristics in channel state information (CSI). We also design a dedicated adaptive wavelet neural network to extract representative features from Wi-Fi signals with only a few epochs of training and a small number of parameters. Experiments show that it can identify human gait with an average accuracy of 99%. Moreover, it can achieve an average accuracy of 95% by using only 10% of the data and fewer than five epochs and outperforms state-of-the-art (SOTA) methods. [ABSTRACT FROM AUTHOR]

Owing to the capital-intensive nature of the power system components and safety of lives, fast response to intolerable conditions of power system networks becomes a growing concern for experts in power system monitoring and protection. To synthesize the noise nature of the signals, the multivariate principal component analysis (MPCA) wavelet method was used to extract and simplify the fault signals. An exploit of Daubechies wavelet (db3) was made and decomposed up to level 7. To have a crack at the composite noise nature, an attempt was made on leveldependent noise size estimation which was down-sampled by two at each succeeding level of 7. The results obtained from details, approximations, and simplified signals show that by far, multi-scale principal component analysis (MPCA) is better than multi-resolution signal analysis (MRSA) wavelet for signal detection and simplification. [ABSTRACT FROM AUTHOR]

This paper investigates the volatility connectedness and dynamic time–frequency relationship between Bitcoin (BTC) and 15 major agricultural commodity markets during the COVID‐19 and 2022 Russia–Ukraine war periods. We employ the TVP‐VAR‐based extended joint connectedness method, minimum connectedness investment portfolio, and wavelet coherence (WC) method. The results indicate that the sudden outbreaks of the two crises brought about increased volatility connectedness between BTC and agricultural commodity markets. Throughout the entire sample period, BTC remained a net transmitter of volatility. Moreover, in terms of the total connectedness index (TCI), the overall volatility correlation surged rapidly after the outbreak of COVID‐19 and the 2022 Russia–Ukraine war. The portfolio results demonstrated that BTC exhibited a low correlation with the agricultural commodity markets, suggesting diversification potential. Additionally, only Feeder Cattle served as an effective hedging asset for BTC throughout all periods. The WC analysis confirmed that during the COVID‐19 period and the 2022 Russia–Ukraine war, most of the linkages were primarily concentrated at medium‐ to long‐term frequencies. Our analysis will contribute to a deeper understanding of the interconnection between these markets, enabling market participants to consider risk mitigation measures and support portfolio diversification when formulating policies and regulations involving relevant markets in the future. [ABSTRACT FROM AUTHOR]

We examine the fractal volatility and long‐range dependence of Bitcoin, Ethereum, Tether and USD Coin by employing the continuous wavelet transform, maximal overlap discrete wavelet transform and rescaled range. Our dataset consists of daily prices spanning from January 2017 through to October 2022, encapsulating pre‐ and post‐epidemic eras. Generally, our findings suggest that Tether presents the least overall volatility throughout the time‐frequency spectrum. USD Coin demonstrates ephemeral turbulence, contrary to Tether's maturity in influencing market equilibrium through token issuance and trade responses. In the post‐epidemic sample, both stablecoins indicate mean reversion, with USD Coin showing marginally better efficiency. Conversely, investment tokens display persistent clusters due to retail traders and long‐term fundamental institutions. Although both tokens illustrate multifractal volatility, Ethereum unveils more essence of self‐similarity than Bitcoin. Hence, there is no evidence that Ethereum truly duplicates Bitcoin since policy‐related events differ between them, as both return series move incongruously. Conditional dynamics signify that all cryptocurrencies, except Tether, were affected by the pandemic transition of COVID‐19 and subsequent macroeconomic news. The unconditional volatility of stablecoins evinces zero‐mean errors, antithetical to investment tokens exhibiting annual cycles. The fractal geometry suggests that investment tokens simulate one‐dimensional lines, whereas stablecoins mimic two‐dimensional planes. [ABSTRACT FROM AUTHOR]

In this paper, a convolutional recurrent neural network (ConvRNN) wavelet-based kernel is proposed to improve the time–frequency localization of non-stationary signals. Time–frequency distributions (TFDs) are used to localize the power spectral density components of a signal simultaneously over the time–frequency plane. For various non-stationary signals (NSS) with different features, poor time–frequency resolution is always an inherent problem in all developed TFDs. This is mainly due to inefficient segmentation methods and improper kernel adaptation. In the current work, the fraction Bezier–Bernstein polynomial function is applied to model the NSS, and points of inflection are used for signal segmentation. From the obtained segments, statistical time–frequency features are extracted and fed to a ConvRNN for better time–frequency localization. The ConvRNN employs a convolution computation between input signal features and the proposed Newton–Raphson gradient algorithm (NRGA)-based wavelet function. The optimization of the ConvRNN network is achieved by incorporating a hybrid method that combines the principles of normalized adaptive gradient descent and momentum-based optimization, with an additional normalization step to enhance convergence and stability. The ConvRNN weights are updated in both forward and backward directions (resilient propagation) until a better correlation is achieved between signal segments and the wavelet kernel. It is observed that the proposed ConvRNN NRGA wavelet improves the time–frequency localization when compared with standard TFDs and state-of-the-art methodologies. Furthermore, the proposed ConvRNN model is compared with other CNN and RNN architectures for better practical interpretations. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an operational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black-Scholes model

Abstract This study focused on detecting the reflections of healing and change in cortex activation in full-face transplantation and lesions patients on EEG activity. Face transplant patients have facial lesions before transplantation and, to identify pre-face transplant patients' brain activity in the absence of pre-transplant recordings, we used data obtained from pre-transplant facial lesion patients. Ten healthy, four facial lesion and three full-face transplant patients participated in this study. EEG data recorded for four different sensory stimuli (brush from the right face, right hand, left face, and left-hand regions) were analyzed using wavelet packet transform method. EEG waves were analyzed for standard bands. Our findings indicate significant change in the 2–4 Hz frequency range which may be a result of ongoing or previous cortical reorganization for face lesion and transplant patients. Alterations of the delta wave seen in patients with facial lesion and face transplant can also be explained by the intense central plasticity. Our findings show that the delta band differences might be used as a marker in the evaluation of post-transplant cortical plasticity in the future.

This paper addresses the adaptive wavelet estimations for density derivatives by using data-driven methods. Based on the classical linear wavelet estimator of density derivatives, we provide a point-wise estimation under the local Hölder condition firstly. Moreover, we introduce a data-driven wavelet estimator for adaptivity and prove a point-wise oracle inequality, which does not require any assumption on the underlying function. Finally, by using the point-wise oracle inequality, the point-wise estimation under the local Hölder condition and L p -risk ( 1 ≤ p < ∞ ) estimation on Besov spaces are investigated respectively. [ABSTRACT FROM AUTHOR]

The parameters estimation through bias-to-variance ratio optimization has been suggested for various applications in literature. The explicit values of bias or variance for a "near to optimal" solution are generally not needed. However, the additional noise components vary the bias or variance randomly. This work proposes an adaptive Intersection of Confidence Intervals (ICI)-based method for the mitigation of noise component by balancing bias to variance trade-off. The presented method is a non-linear and non-parametric method of local polynomial regression (LPR). Unlike curve fitting by shrinkage or adaptation to higher harmonics representation in the wavelet transform method, the proposed technique optimized the bias of variance by estimating the signals based on smoothing parameter. The optimization in the bias or variance of estimation has a direct impact on the removal of noise components. A well-denoised signal brings precision in the local fitting of the curve in a kernel regression problem that uses the parameter obtained from ICI method. The Nadaraya-Watson kernel is used in this approach where the values of point-wise smoothing parameter is kept constant throughout regressions. The comparisons of the results of proposed method are carried out with the latest wavelet denoising to ensure its superiority in performance. The implementation complexity and memory requirements are also discussed in detail. [ABSTRACT FROM AUTHOR]

Acetonitrile, a polar molecule that cannot form hydrogen bonds on its own, interacts with solvent molecules mainly through the lone pair of its nitrogen atom and the π electrons of its CN triple bond [Correction added on 17 July 2024, after first online publication: Acetole has been changed to Acetonitrile in the preceeding sentence.]. Interestingly, acetonitrile exhibits an unexpected strengthening of the triple bond's force constant in an aqueous environment, leading to an upshift (blueshift) in the corresponding stretching vibration: this effect contrasts with the usual consequence of hydrogen bonding on the vibrational frequencies of the acceptor groups, that is, frequency redshift. This investigation elucidates this phenomenon using Raman spectroscopy to examine the behavior of acetonitrile in organic solvent, water, and silver ion aqueous solutions, where an even more pronounced upshift is observed. Raman spectroscopy is particularly well suited for analyzing aqueous solutions due to the minimal scattering effect of water molecules across most of the vibrational spectrum. Computational approaches, both static and dynamical, based on Density Functional Theory and hybrid functionals, are employed here to interpret these findings, and accurately reproduce the vibrational frequencies of acetonitrile in different environments. Our calculations also allow an explanation for this unique behavior in terms of electric charge displacements. On the other hand, the study of the interaction of acetonitrile with water molecules and metal ions is relevant for the use of this molecule as a solvent in both chemical and pharmaceutical applications. [ABSTRACT FROM AUTHOR]

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel–Lizorkin-type spaces B ˙ p , q s , τ (W) and F ˙ p , q s , τ (W) . In this article, the authors establish the molecular and the wavelet characterizations of these spaces. Furthermore, as applications, the authors obtain the optimal boundedness of trace operators, pseudo-differential operators, and Calderón–Zygmund operators on these spaces. Due to the sharp boundedness of almost diagonal operators on their related sequence spaces obtained in the second article of this series, all results presented in this article improve their counterparts on matrix-weighted Besov and Triebel–Lizorkin spaces B ˙ p , q s (W) and F ˙ p , q s (W) . In particular, even when reverting to the boundedness of Calderón–Zygmund operators on unweighted Triebel–Lizorkin spaces F ˙ p , q s , these results are still better. [ABSTRACT FROM AUTHOR]

Background. Migraine disease is the second most common cause of headaches. Despite the high prevalence, the exact etiology of migraine is yet unknown. In this study, to evaluate the behavior change of electroencephalography (EEG) signals in migraine patients, various features of the EEG signals of migraine patients and healthy controls (HCs) were extracted and compared. Methods. This cross-sectional analytical study was conducted on 21 HCs and 18 migraine patients. Various features, such as fractal dimension (FD), approximate entropy (ApEn), and largest Lyapunov exponent (LLE), were calculated from the EEG signals of migraine patients and HCs. Then different frequency sub-bands of delta, theta, alpha, beta, and gamma were extracted using the wavelet transform, and the energy of these sub-bands was computed. By calculating the mean and variance of the features and applying statistical tests, the feature changes were compared between two groups, and channels with significant differences were identified. Results. The mean of ApEn, FD and energy of all frequency sub-bands in most of the analyzed channels was higher in migraine patients than in HCs. The mean LLE was mostly lower in migraine patients than in healthy controls. According to the statistical tests, the energy of theta and delta frequency sub-bands with 36 and 35 channels was the feature with the highest number of channels, with a significant difference. In this study, P values less than 0.05 were considered statistically significant. Conclusion. Migraine patients may have a less sophisticated brain dynamic system due to an increase in irregularity and randomness, as indicated by an increase in ApEn and a decrease in FD in their EEG signals compared to HCs. Anxiety, tension, and other intense sentiments and emotions, as well as the creation of new neural circuits in the brain, can all contribute to an overall increase in energy across all frequency sub-bands in migraine patients. Practical Implications. Considering the EEG signal behavior as the response of a dynamic system, we can say that the brain function of migraine patients, even in the inter-ictal phase, leaves the definite chaotic state, which is a healthy brain behavior, and enters the random state.

The type-Silurian Cellon section in the Carnic Alps in Austria underpins much of the current Silurian conodont zonations, forming the basis for the Silurian timescale. However, the Silurian record of the Cellon section lacks radiometric and astrochronological age constraints, making it difficult to gain insights into the processes pacing Silurian (anoxic) events. To attain age constraints and investigate the pacing Silurian (anoxic) events by astronomical cycles, a cyclostratigraphic study was conducted on high-resolution pXRF (CaO, Al2O3, and Fe2O3) and induration records spanning the Ludlow and Pridoli parts of the Cellon section. Astronomical cycles ranging from precession to the 405-kyr eccentricity cycle were first recognised visually in the field and in proxy records. The visual detection of astronomical cycles served as an input for the WaverideR R package, enabling the tracking of the 405-kyr eccentricity period in each proxy's continous wavelet transform scalograms. These tracked period curves were combined with external age controls through multiple Monte Carlo simulations, generating an (absolute) age model. This age model is used to assign ages and durations and their respective uncertainties to a hiatus in the Ludfordian, conodont zones, lithological units, geochronological units and events, yielding new ages for Silurian stage boundaries (e.g., Gorstian-Ludfordian boundary at 425.92 ± 0.65 Ma, the Ludfordian-Pridoli boundary at 423.03 ± 0.53 Ma, the Silurian-Devonian boundary at 418.86 ± 1.02 Ma), and new durations for the Ludfordian at 2.89 ± 0.35 Myr and Pridoli at 4.24 ± 0.46 Myr. Furthermore, the imprint of astronomical cycles in the Cellon section itself indicates that the Linde, Klev and Silurian-Devonian boundary events all occur after a 2.4-Myr eccentricity node, indicating pacing by astronomical forcing, similar to other Devonian and Cretaceous anoxic events. The Lau event, however, does not appear to coincide with a 2.4-Myr eccentricity node. [ABSTRACT FROM AUTHOR]

Soil organic carbon (SOC) is a crucial factor for soil fertility, directly impacting agricultural yields and ensuring food security. In recent years, remote sensing (RS) technology has been highly recommended as an efficient tool for producing SOC maps. The PRISMA hyperspectral satellite was used in this research to predict the SOC map in Fars province, located in southern Iran. The main purpose of this research is to investigate the capabilities of the PRISMA satellite in estimating SOC and examine hyperspectral processing techniques for improving SOC estimation accuracy. To this end, denoising methods and a feature generation strategy have been used. For denoising, three distinct algorithms were employed over the PRISMA image, including Savitzky–Golay + first-order derivative (SG + FOD), VisuShrink, and total variation (TV), and their impact on SOC estimation was compared in four different methods: Method One (reflectance bands without denoising, shown as M#1), Method Two (denoised with SG + FOD, shown as M#2), Method Three (denoised with VisuShrink, shown as M#3), and Method Four (denoised with TV, shown as M#4). Based on the results, the best denoising algorithm was TV (Method Four or M#4), which increased the estimation accuracy by about 27% (from 40% to 67%). After TV, the VisuShrink and SG + FOD algorithms improved the accuracy by about 23% and 18%, respectively. In addition to denoising, a new feature generation strategy was proposed to enhance accuracy further. This strategy comprised two main steps: first, estimating the number of endmembers using the Harsanyi–Farrand–Chang (HFC) algorithm, and second, employing Principal Component Analysis (PCA) and Independent Component Analysis (ICA) transformations to generate high-level features based on the estimated number of endmembers from the HFC algorithm. The feature generation strategy was unfolded in three scenarios to compare the ability of PCA and ICA transformation features: Scenario One (without adding any extra features, shown as S#1), Scenario Two (incorporating PCA features, shown as S#2), and Scenario Three (incorporating ICA features, shown as S#3). Each of these three scenarios was repeated for each denoising method (M#1–4). After feature generation, high-level features were added to the outputs of Methods One, Three, and Four. Subsequently, three machine learning algorithms (LightGBM, GBRT, RF) were employed for SOC modeling. The results showcased the highest accuracy when features obtained from PCA transformation were added to the results from the TV algorithm (Method Four—Scenario Two or M#4–S#2), yielding an R2 of 81.74%. Overall, denoising and feature generation methods significantly enhanced SOC estimation accuracy, escalating it from approximately 40% (M#1–S#1) to 82% (M#4–S#2). This underscores the remarkable potential of hyperspectral sensors in SOC studies. [ABSTRACT FROM AUTHOR]

Neonatal electrocardiogram (ECG) monitoring is an important diagnostic tool for identifying cardiac issues in infants at birth. Long-term remote neonatal dryelectrode ECG monitoring solutions can be an additional step for preventive healthcare measures. In these solutions, power and computationally efficient embedded signal processing techniques for denoising newborn ECGs can assist in increasing neonatal medical wearable time. Wavelet denoising is an appropriate denoising mechanism with low computational complexity that can be implemented on embedded microcontrollers for long-term remote ECG monitoring. Discrete wavelet transform (DWT) denoising for neonatal dry-electrode ECG using different wavelet families is investigated. The wavelet families and mother wavelets used include Daubechies (db1, db2, db3, db4, and db6), symlets (sym5), and coiflets (coif5). Different levels of added white Gaussian noise (AWGN) were added to 19 newborn ECG signals, and denoising was performed to select the appropriate wavelets for neonatal dry-electrode ECG. The selected wavelets then undergo real noise additions of baseline wander and electrode motion to determine their robustness and accuracy. Signal-to-noise ratio (SNR), mean squared error (MSE), and power spectral density (PSD) are used to examine denoising performance. db1, db2, and db3 wavelets are eliminated from analysis where the 30 dB AWGN led to negative SNR improvement for at least one newborn ECG, removing important ECG information. db4 and sym5 are eliminated from selection due to their different waveform morphology compared to the dry-electrode newborn ECG's QRS complex. db6 and coif5 are selected due to their highest SNR improvement and lowest MSE of 6.26 × 10-6 and 1.65 × 10-7 compared to other wavelets, respectively. Their wavelet shapes are more like a newborn ECG's QRS morphology, validating their selection. db6 and coif5 showed similar denoising performance, decreasing electrode motion and baseline wander noisy ECG signals by 10 dB and 14 dB, respectively. Further denoising of inherent dry-electrode noise is observed. DWT with coif5 or db6 wavelets is appropriate for denoising newborn dry-electrode ECGs for long-term neonatal dry-electrode ECG monitoring solutions under different noise types. Their similarity to newborn dry-electrode ECGs yields accurate and robust reconstructed denoised newborn dry-electrode ECG signals. [ABSTRACT FROM AUTHOR]

In this paper, a new method based on the Tufts–Kumaresan (TK) algorithm is used to process nonstationary signals and extract system modes. This new algorithm for mode estimation is proposed to improve estimation accuracy under dynamic conditions. The key contribution in TK is the use of multiple orthogonal sliding windows rather than a single pair of sliding windows. Simulation results under various scenarios, such as different types of faults and load changes are used to evaluate the performance of the proposed method. The proposed method will accurately extract system modes. This method will also reduce the required memory and the calculation time of estimation in nonstationary signals. In complement to successful applications in studying the dynamic behavior of the power system, identifying and analyzing low-frequency electromechanical oscillations, and removing signal noise, this method can accurately estimate the modes of a power system. To validate the accuracy of the proposed method, the Wavelet and the Prony methods have been used for comparison. The proposed method is implemented using simulated ringdown data of standard two-area power system and real measurement data of the WSCC system breakup on 10 August 1996. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Littlewood–Paley characterization for mixed Morrey spaces and its predual spaces. The topology to converge the Littlewood–Paley decomposition for the element of mixed Morrey spaces is the weak‐∗$*$ topology. If we consider the topology of mixed Morrey spaces, we must give other characterization by using the heat semigroup. As an application, we show the wavelet characterization for mixed Morrey spaces. In particular, this characterization can be shown without the Peetre maximal operator. [ABSTRACT FROM AUTHOR]

Visual biofeedback (vFB) during quiet stance has been shown to improve postural control. While this improvement has been quantified by a reduction in the center of pressure (COP) sway, the effect on COP complexity remains unexplored. As such, 20 young adults (12 females; aged 23.63 ± 3.17 years) were asked to remain in a static upright posture under different visual biofeedback magnitude (no feedback [NoFB], magnified by 1 [vFB1], magnified by 5 [vBF5] and magnified by 10 [vBF10]). In addition to confirming, through traditional COP variables (i.e. standard deviation, mean velocity, sway area), that vFB scaling improved postural control, results also suggested changes in COP complexity. Specifically, sample entropy and wavelet analysis showed that increasing the vFB scale from 1:1 to 1:5 and 1:10 led to a more irregular COP and a shift toward higher frequency. Together, and particularly from a complexity standpoint, these findings provided additional understandings of how vFB and vFB scaling improved postural control. [ABSTRACT FROM AUTHOR]

Can technology protect investors from extreme losses? This paper investigates the short- and long-run hedging and safe haven properties of Bitcoin for the US dollar over the period 2010–2023, incorporating the COVID-19-related market turmoil. Our findings reveal that (i) Bitcoin acts as a strong hedge for all US dollar currency pairs examined, (ii) Bitcoin functions as a weak safe haven for the US dollar at short investment horizons, as indicated by a limited relationship during acute negative price movements, (iii) Bitcoin, instead of acting as a safe haven may, instead, increase aggregate risk at long horizons during periods of extreme losses. The analysis, performed using a series of horizon-dependent econometric tests, provides evidence of some US dollar risk-reduction benefits from Bitcoin but limited potential for enduring relief from long-run extreme negative US dollar rate movements. [ABSTRACT FROM AUTHOR]

This study examines the nonlinear multiscale relationships and spillovers among the main cryptocurrencies (Bitcoin, Bitcoin cash, Ethereum, Litecoin, DASH, Ripple, and Monero) using spillover index methodology and wavelet approaches to hourly and daily price data. The results provide evidences of dynamic spillovers among cryptocurrencies. News releases influence the instability of spillovers. Monero is the largest transmitter of risk, and Ethereum is the largest receiver of risk from other markets. Monero and Ripple are net contributors of spillovers, whereas Bitcoin, DASH, Ethereum, and Litecoin are net receivers of spillovers. The correlation ranks for different scales show that the correlations increase with scale, indicating higher diversification benefits at low scales. A mixed portfolio composed of Bitcoin and other cryptocurrencies offers advantages over individual Bitcoin portfolios, particularly on a lower scale. Finally, the optimal portfolio weight shows that cryptocurrencies should hold more BTC than other cryptocurrencies. [ABSTRACT FROM AUTHOR]

Proton magnetic resonance spectroscopy (1H‐MRS) is increasingly used for clinical brain tumour diagnosis, but suffers from limited spectral quality. This retrospective and comparative study aims at improving paediatric brain tumour classification by performing noise suppression on clinical 1H‐MRS. Eighty‐three/forty‐two children with either an ependymoma (ages 4.6 ± 5.3/9.3 ± 5.4), a medulloblastoma (ages 6.9 ± 3.5/6.5 ± 4.4), or a pilocytic astrocytoma (8.0 ± 3.6/6.3 ± 5.0), recruited from four centres across England, were scanned with 1.5T/3T short‐echo‐time point‐resolved spectroscopy. The acquired raw 1H‐MRS was quantified by using Totally Automatic Robust Quantitation in NMR (TARQUIN), assessed by experienced spectroscopists, and processed with adaptive wavelet noise suppression (AWNS). Metabolite concentrations were extracted as features, selected based on multiclass receiver operating characteristics, and finally used for identifying brain tumour types with supervised machine learning. The minority class was oversampled through the synthetic minority oversampling technique for comparison purposes. Post‐noise‐suppression 1H‐MRS showed significantly elevated signal‐to‐noise ratios (P <.05, Wilcoxon signed‐rank test), stable full width at half‐maximum (P >.05, Wilcoxon signed‐rank test), and significantly higher classification accuracy (P <.05, Wilcoxon signed‐rank test). Specifically, the cross‐validated overall and balanced classification accuracies can be improved from 81% to 88% overall and 76% to 86% balanced for the 1.5T cohort, whilst for the 3T cohort they can be improved from 62% to 76% overall and 46% to 56%, by applying Naïve Bayes on the oversampled 1H‐MRS. The study shows that fitting‐based signal‐to‐noise ratios of clinical 1H‐MRS can be significantly improved by using AWNS with insignificantly altered line width, and the post‐noise‐suppression 1H‐MRS may have better diagnostic performance for paediatric brain tumours. [ABSTRACT FROM AUTHOR]

Wind power is increasingly seen as a global, sustainable, and eco-friendly energy option. However, one significant obstacle to further wind energy investment is the high failure rate of wind turbines. The gearbox plays a pivotal role in turbine performance. In recent years, there has been a surge in the focus on gearbox fault diagnosis, reflecting its criticality and prevalence in the industry. Time synchronous averaging (TSA) is a primary technique to identify faults in wind turbine gearboxes using mechanical vibration signals. Generally, implementing TSA requires a device that is capable of recording the phase information of a rotary shaft. Nevertheless, there are situations in which the installation of such a device poses difficulties. For instance, gearboxes that are in use cannot be halted to allow for the installation of a device, and sealed gearboxes provide challenges while being inserted into the device. This research presents an innovative technical way to improve the TSA method without requiring a phase signal. The proposed method has the advantage of extracting the shaft rotation angle signal from the measured acceleration signal, even in non-stationary conditions where the rotational speed varies over time. The effectiveness of the proposed method is validated through measured datasets from wind turbine gearboxes with actual faults and a dataset from a gear system with variable rotational speeds. [ABSTRACT FROM AUTHOR]

Electromyography (EMG) instrumentation is essential in generating electrical signals from skeletal muscles. EMG sensors are helpful in various cases requiring the detection of human muscle contractions, neuromuscular disorders, and rehabilitation. EMG instrumentation is divided into two parts, namely, the analogue part and the digital part. The EMG instrumentation design comprises a digital-to-analog converter (DAC), instrumentation amplifier, filter, and analog-todigital converter (ADC). Meanwhile, in digital signal processing adopting the Discrete Wavelet Transform (DWT) method, frequency analysis using DWT has proven superior. It is used in various research and has exceptionally detailed coefficient features for classifying neuromuscular disease signals. Therefore, this research aims to design analogue and digital EMG instrumentation and identify features in the form of detailed coefficients. The data used are two Physionet signals from the anterior tibialis body with myopathy and neuropathy disorders. The results obtained for EMG analogue instrumentation provide the expected results until they reach the filter component stage. The resulting signal forms a block in the filter component, different from the initial EMG signal. Meanwhile, the DWT decomposition results are of the Daubechies4 wavelet type with the highest level 17, which has a high detail coefficient at low frequencies, high dilation and the result of a mixture of neuropathy and myopathy EMG signals, or in other words, at low energies, this result is by the DWT theorem. Determining the efficiency of the DWT detailed coefficient feature requires further study with the same signal subject. The DWT features obtained can then be developed for various needs in EMG signal recognition. [ABSTRACT FROM AUTHOR]

The uncertainty caused by high volatile crude oil prices and the higher level of deregulations worldwide has significant effects on the economic growth of a country. The financial markets of many developing countries experienced a severe downturn during the oil price shocks in March-April 2020. Traditional predictive approaches, which assume linearity and stationarity of time series in the long run, fail to accurately capture short-term fluctuations. This paper presents an efficient algorithm based on ARMA denoising and taking advantage of the wavelet transformation. By decomposing the time series and extracting the intricate underlying structure, wavelet denoising minimizes distortions and enhances forecasting accuracy. The results demonstrate a substantial improvement in performance compared to conventional forecasting techniques. [ABSTRACT FROM AUTHOR]

Wavelet transform is a powerful time-frequency-based analysis method often used in gear fault diagnostics. The development of wavelet transform is closely linked to the improvement of resolution. When the high-frequency resolution allows for easy observation of different frequency components, it is a symptom of damage to an individual part of the machine. This study effectively applied the Wavelet analysis technique to diagnose faulty gearboxes operated in non-stationary conditions. This is a complex problem that usual diagnostic approaches need help to solve due to its non-linear character. This work conducted a simulation and real-world testing to show that the newest wavelet analysis techniques work well, showing that they can accurately find gear faults in gearboxes in non-stationary conditions. A thorough overview of the cutting-edge applications of wavelet transform in diagnosing faults in industrial gearbox systems was also given. This work also explained in detail the mathematical ideas behind the continuous wavelet transform, discrete wavelet transforms, and wavelet packet transform. [ABSTRACT FROM AUTHOR]