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We consider 3-component records of the magnetic field strength with a time step of 1 min at 153 stations of the INTERMAGNET network for 31 years, 1991–2021. Data analysis is based on the calculation of pairwise correlation coefficients between wavelet coefficients in successive time windows 1 day long (1440 min counts). To describe the state of the magnetic field, the maxima of the average values of all pairwise correlation coefficients between stations were chosen, calculated over all detail levels of the wavelet decomposition and over all components of the magnetic field strength vector. The daily time series of such maxima is called wavelet correlation. The division of the network stations into 7 clusters is considered, and a time series of wavelet correlations is calculated for each cluster. In a sliding time window with a length of 365 days, correlation measures of synchronization of wavelet correlations from different clusters are calculated, which are compared with the strongest earthquakes with a magnitude of at least 8.5. For the global time series of wavelet correlations, the method of influence matrices is used to study the relationship between the maximum correlation responses to a change in the length of the day and a sequence of earthquakes with a magnitude of at least 7. As a result of the analysis, precursor effects are identified, and the important role of the Maule earthquake in Chile on February 27, 2010 in the behavior of the response of magnetic field for the preparation of strong seismic events is shown. [ABSTRACT FROM AUTHOR]

In Algeria, prevailing climatic conditions over the past decades have had a negative impact on water resources used for irrigation. The objective of this study is to determine its effect on irrigation water requirements for citrus cultivation in the central and upper parts of the Chlef plain, a region known for its citrus production covering an area of over 64,000 hectares. Three climatological stations (Chlef, Elkhemis INRA, and Harezza Barrage) were selected for a chronology spanning 51 years (September 1968 to August 2019). In this study, we utilized the potential of agro-climatic indices such as the Thornthwaite Aridity Index (TAI), the Standardized Agricultural Precipitation Index (aSPI), the Effective Recognition Drought Index (eRDI), and wavelet analysis to characterize monthly drought at different stages of citrus development. The results show a significant increase in drought since 1980 according to the Standardized Agricultural Precipitation Index (aSPI) on scales of 1, 3, 6, and 12 months. The energy bands of three stations (1 year, 1–2 years, 2–3 years, and 3–4 years) for the months of January, February, March, September, October, November, and December show marked changes after the year 1994. Depending on the annual development stage, citrus water demand during the period 1968–2019 is strongly correlated with the new Effective Recognition Drought Index (eRDI) at various time scales. The determination coefficients are significant over a 5-month scale between the Effective Recognition Drought Index (eRDI) and irrigation water demand anomalies for the three stations (Chlef (0.73), Harezza Barrage (0.62), and Elkhemis INRA (0.62)). Considering these results, the aSPI and eRDI indices can easily be used to monitor and manage citrus irrigation in our region. [ABSTRACT FROM AUTHOR]

This paper concerns the modeling of smart health sensors for data monitoring, where the data are eventually noisy, with correlated noise. In this work, we applied Clifford-based wavelets/multiwavelets for correlated noise in multi-sensors health data monitoring by estimating the set of sensor nodes minimizing an eventual error computed by the signal values at the selected nodes mostly caused by the correlated noise. Instead of directly minimizing the estimation error, we focused on evaluating a multi-level scheme based on multiwavelets for the estimation of the error between the parameter vector and its sub-vector of those nodes. Numerical simulations are provided with a comparison to some recent existing works. This model showed a performance and a fast time execution compared to those existing works. This model exceeds these models by the non-necessity to assume a priory structure of the data. Wavelets are capable to detect, localize, and eliminate the noise, even correlated, efficiently via the independent uncorrelated multiwavelets’ components. [ABSTRACT FROM AUTHOR]

Precipitation regionalization, serving as a foundation for extrapolating information from gauged to ungauged sites, contributes to a comprehensive understanding of the spatial distribution of precipitation. However, existing studies have focused mainly on precipitation, neglecting the influence of climate background and meteorological circulation. Moreover, there is a lack of specialized analysis of regionalization results. This study proposes a novel approach to precipitation regionalization that considers covariates in the circulation field and periodic features. The method utilizes Barnett–Preisendorfer canonical correlation analysis coupled with principal component analysis (BPCCA) to select covariates and multivariate self-organizing map (SOM) clustering for preliminary regionalization. Wavelet decomposition is further used for regional feature analysis. The methodology is empirically applied to analyze summer precipitation in Shanxi Province, identifying homogeneous regions characterized by diverse spatiotemporal distributions. The results successfully identified 12 distinct regions of precipitation, effectively capturing the influence of topographic and atmospheric factors. According to the periodic and trend characteristics of each region at different time scales, we merged the division results on the three frequencies and six regions were ultimately differentiated. Specifically, a decreasing trend was observed in the southern and southeastern parts of Shanxi, as well as in the western part of the Lüliang Mountains. They had a significant 4-yr period mode, and the decreasing trend was more significant in the southern region. In contrast, northern Shanxi showed no trend and a significant 8-yr period mode. This proposed method presents an effective strategy for enhancing precipitation regionalization and extracting valuable information from the circulation field and multiple frequencies. [ABSTRACT FROM AUTHOR]

Undoubtedly, financial markets are not only affected by common economic, financial and behavioral factors but also by other global risk shocks. In this paper, we investigate the relevance of global geopolitical risk in stock-bond relationships. Specifically, we assess the possibility and manner in which time-varying correlations of Islamic stocks and bonds (sukuk) returns are affected by geopolitical risk and whether they behave differently from their conventional counterparts. We do so by implementing a multivariate GARCH model under dynamic conditional correlations (DCCs) to daily data of the Gulf Cooperation Council (GCC) markets (2013-2019). Our outcomes unveil that geopolitical risks positively affect the dependence between Islamic stocks and sukuk, as well as their conventional counterparts. Regional rather than global geopolitical risk factors positively affect the volatility of conventional stock-bond correlation, while the volatility of Islamic stock-sukuk correlation decreases during times of high geopolitical risks. Our findings offer several prominent implications in terms of financial stability, asset allocation of portfolios and policy design. [ABSTRACT FROM AUTHOR]

The distribution of centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds is determined by their covariance operators. We consider centered GRFs given as variational solutions to coloring operator equations driven by spatial white noise, with an elliptic self-adjoint pseudodifferential coloring operator from the Hörmander class. This includes the Matérn class of GRFs as a special case. Using biorthogonal multiresolution analyses on the manifold, we prove that the precision and covariance operators, respectively, may be identified with bi-infinite matrices and finite sections may be diagonally preconditioned rendering the condition number independent of the dimension p of this section. We prove that a tapering strategy by thresholding applied on finite sections of the bi-infinite precision and covariance matrices results in optimally numerically sparse approximations. That is, asymptotically only linearly many nonzero matrix entries are sufficient to approximate the original section of the bi-infinite covariance or precision matrix using this tapering strategy to arbitrary precision. The locations of these nonzero matrix entries can be determined a priori. The tapered covariance or precision matrices may also be optimally diagonally preconditioned. Analysis of the relative size of the entries of the tapered covariance matrices motivates novel, multilevel Monte Carlo (MLMC) oracles for covariance estimation, in sample complexity that scales log-linearly with respect to the number p of parameters. In addition, we propose and analyze novel compressive algorithms for simulating and kriging of GRFs. The complexity (work and memory vs. accuracy) of these three algorithms scales near-optimally in terms of the number of parameters p of the sample-wise approximation of the GRF in Sobolev scales. [ABSTRACT FROM AUTHOR]

Self-similar and generally scaling laws are pointed out in time series issued from different types of data. The analysis of these structures has been conducted via many advanced mathematical tools such as wavelets. In this paper, we propose to exploit some self-similar type models for the modeling of time series issued from air quality and/or pollution data, by using wavelet multifractal techniques. The applied models are shown to involve self-similar, multi-scaling and also noised structures. The resulting models are applied empirically on a sample of data issued from air pollution factors in the northwestern region of Tabuk governorate in Saudi Arabia. Some of the chemicals and materials are essential components of many air pollution factors such as PM10 and PM2.5 particles. [ABSTRACT FROM AUTHOR]

We introduce a Path Shadowing Monte Carlo method, which provides the prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or ‘shadows’, the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called ‘Scattering Spectra’. This model promotes the diversity of generated paths while reproducing main statistical properties of financial prices, including stylized facts such as volatility roughness. Our method yields state-of-the-art predictions for future realized volatility and allows one to determine conditional option smiles for the S&P500 that outperform both the most recent low-parametric models and the option market itself. The code is available at https://github.com/RudyMorel/shadowing (This work is supported by the PRAIRIE 3IA Institute of the French ANR-19-P3IA-0001 program and the ENS-CFM models and data science chair.). [ABSTRACT FROM AUTHOR]

Atrial fibrillation (AF) is a life-threatening cardiac condition caused by inadequate blood flow, resulting in abnormal ECG records, blood clotting, and cardioembolic strokes. In recent years, physicians have been particularly concerned with early detection and diagnosis to overcome cardiogenic stroke. AF can be easily identified at the initial stages due to the development in computer-aided diagnosis. The performance of this method is affected by noise and the variations in pattern of the ECG, which leads to false diagnosis. Current signal processing and shallow machine learning (ML) approaches are severely limited in their ability to detect this condition accurately. Deep neural networks have been shown to be extremely effective at learning nonlinear patterns in a wide variety of problems, which include computer vision tasks. Deep learning models are computationally costly, non-explainable, and require a large quantity of data to discover characteristics. In contrast, ML approaches are explainable and require good feature extraction. In this manuscript, ML based supervised classification method is developed based on feature ensembling. ECG signals are preprocessed (mean subtraction followed by Butterworth filtering and computation of RR intervals) and subjected to feature extraction (by entropy-, wavelets-, & statistical-features). The variations due to AF are effectively captured and selective features are ensembled to perform classification by SVM and KNN. This method is experimented on five different databases (such as: PAF prediction Challenge, Long-Term AF, Intracardiac, AF termination Challenge, and MIT-BIH atrial fibrillation) and the classification performance is found to be the highest compared to the state of art. To evaluate the effectiveness of the proposed technique, AF-specific characteristics are retrieved from the ECG signal in the presence of artificially added noise and the features are fed to classifiers for classification. Performance of the proposed method is compared with the deep learning based approaches. The graphical abstract of the proposed atrial fibrillation detection method is presented. The overall accuracy of the proposed method was found to be 91.88 % and 91.99 % for wavelets-SVM and ensemble wavelet-SVM, respectively. This model attained 100 % accuracy for entropy and statistical features with SVM and KNN, respectively. [ABSTRACT FROM AUTHOR]

This paper examines the stability of the à trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under which an infinitely iterated shift-invariant filter bank is stable. Moreover, it is shown that the stability of an infinitely iterated shift-invariant filter bank guarantees that of any associated finitely iterated shift-invariant filter bank, with uniform bounds. The reverse implication is shown to hold under an additional assumption on the low-pass filter. Finally, it is also shown that the separable product of stable one-dimensional shift-invariant filter banks produces a stable two-dimensional shift-invariant filter bank. [ABSTRACT FROM AUTHOR]

The concepts of multiresolution analysis (MRA) and wavelets in Sobolev space over local fields of positive characteristic ( H s (K) ) are developed by Pathak and Singh [9]. In this paper, we constructed wavelet packets in Sobolev space H s (K) and derived their orthogonality at each level. By using convolution theory, an example of wavelet packets in H s (K) is presented [ABSTRACT FROM AUTHOR]

Mathematical models, especially complex nonlinear systems, are always difficult to analyze and synthesize, and researchers need effective and suitable control methods to address these issues. In the present work, we proposed a hybrid method that combines the well-known Takagi-Sugeno fuzzy model with wavelet decomposition to investigate nonlinear systems characterized by the presence of mixed nonlinearities. Here, one nonlinearity is super-linear and convex, and other is sub-linear, concave, and singular at zero, which leads to difficulties in the analysis, as is known in PDE theory. Linear and polynomial fuzzy models were combined with wavelets to ensure an improvement in both methods for investigating such problems. The results showed a high performance compared with existing methods via error estimates and Lyapunov theory of stability. The model was applied to a prototype nonlinear Schrodinger dynamical system. [ABSTRACT FROM AUTHOR]

Corrosion deterioration of materials is a major problem affecting economic, safety, and logistical issues, especially in the aeronautical sector. Detecting the correct corrosion type in metal alloys is very important to know how to mitigate the corrosion problem. Electrochemical noise (EN) is a corrosion technique used to characterize the behavior of different alloys and determine the type of corrosion in a system. The objective of this research is to characterize by EN technique different aeronautical alloys (Al, Ti, steels, and superalloys) using different analysis methods such as time domain (visual analysis, statistical), frequency domain (power spectral density (PSD)), and frequency–time domain (wavelet decomposition, Hilbert Huang analysis, and recurrence plots (RP)) related to the corrosion process. Optical microscopy (OM) is used to observe the surface of the tested samples. The alloys were exposed to 3.5 wt.% NaCl and H2SO4 solutions at room temperature. The results indicate that HHT and recurrence plots are the best options for determining the corrosion type compared with the other methods due to their ability to analyze dynamic and chaotic systems, such as corrosion. Corrosion processes such as passivation and localized corrosion can be differentiated when analyzed using HHT and RP methods when a passive system presents values of determinism between 0.5 and 0.8. Also, to differentiate the passive system from the localized system, it is necessary to see the recurrence plot due to the similarity of the determinism value. Noise impedance (Zn) is one of the best options for determining the corrosion kinetics of one system, showing that Ti CP2 and Ti-6Al-4V presented 742,824 and 939,575 Ω·cm2, while Rn presented 271,851 and 325,751 Ω·cm2, being the highest when exposed to H2SO4. [ABSTRACT FROM AUTHOR]

The Sun is a major source of energy for the planetary system in our solar system. The solar output shows variations in timescales from a few days (Bartel's 27-day solar rotation cycle) to several years (the 11-year solar cycle and longer timescales). This variability can be seen in the magnetic field, particle flux, and electromagnetic radiation flux behavior. Several indicators, such as the sunspot number and the Mg II index, have been used as solar activity proxies. Further, direct measurements in radio at centimeter wavelengths have been conducted since 1947 (the F10.7 index). This work uses multiscale techniques to study the relations between these solar indexes and their long-term variations through multiscale techniques. The monthly averages of these indexes from 1979 to 2022 are analyzed using wavelet scalogram, global wavelet spectrum, wavelet cross-correlation, and wavelet entropy techniques. As a result, some nonlinear multiscale aspects in the long-term variations of these solar indexes are identified. The major scales at which these indexes vary are found to be, in order of decreasing energy: sunspots (130.1, 253.9, 11.7, 5.0, and 2.0 months); F10.7 (130.1, 253.9, 39.1, 10.9, 9.9, and 5.4 months), and Mg II (132.9, 39.0, and 10.3 months). Thus, all three indexes present the nearly 11-year solar cycle period as the strongest signal. The three indexes are correlated with a coefficient higher than 0.85 and vary in phase for scales near the 11-year solar cycle, with slight and large deviations from it for longer and shorter scales, respectively. The wavelet entropy analysis shows that the F10.7 and sunspot number values are comparable, while Mg II entropy values are much lower. The entropy also indicates that the minimum values for all the indexes occur close to the solar minimum. However, after the last solar maximum in 2014, the entropy increased even in the declining phase of the cycle, during the 2015 – 2020. [ABSTRACT FROM AUTHOR]

Knowledge of the directional distribution of a wave field is crucial for a better understanding of complex air–sea interactions. However, the dynamic and unpredictable nature of ocean waves, combined with the limitations of existing measurement technologies and analysis techniques, makes it difficult to obtain precise directional information, leading to a poor understanding of this important quantity. This study investigates the potential use of a wavelet-based method applied to GPS buoy observations as an alternative approach to the conventional methods for estimating the directional distribution of ocean waves. The results indicate that the wavelet-based estimations are consistently good when compared to the framework of widely used parameterizations for the directional distribution. The wavelet-based method presents advantages in comparison with the conventional methods, including being purely data-driven and not requiring any assumptions about the shape of the distribution. In addition, it was found that the wave directional distribution is narrower at the spectral peak and broadens asymmetrically at higher and lower scales, particularly sharply for frequencies below the peak. The directional spreading appears to be independent of the wave age across the entire range of frequencies, implying that the angular width of the directional spectrum is primarily controlled by nonlinear wave–wave interactions rather than by wind forcing. These results support the use of the wavelet-based method as a practical alternative for the estimation of the wave directional distribution. In addition, this study highlights the need for continued innovation in the field of ocean wave measuring technologies and analysis techniques to improve our understanding of air–sea interactions. Significance Statement: This study presents a wavelet-based technique for obtaining the directional distribution of ocean waves applied to GPS buoy. This method serves as an alternative to conventional methods and is relatively easy to implement, making it a practical option for researchers and engineers. The study was conducted in a highly energetic environment characterized by high wind speeds and large waves, providing a valuable dataset for understanding the dynamics of marine environment in extreme conditions. This research has implications for improving our understanding of directional characteristics of ocean waves, which is crucial for navigation, offshore engineering, weather forecasting, and coastal hazard mitigation. This study also highlights the challenges associated with understanding wave directionality and emphasizes a need for further observations. [ABSTRACT FROM AUTHOR]

In this study, we propose an innovative concept that applies an AI-based approach using the random forest algorithm integrated with fractal and discrete wavelet transform features of nuclear chromatin. This strategy could be employed to identify subtle structural changes in cells that are in the early stages of programmed cell death. The code for the random forest model is developed using the Scikit-learn library in Python and includes hyperparameter tuning and cross-validation to optimize performance. The suggested input data for the model are chromatin fractal dimension, fractal lacunarity, and three wavelet coefficient energies obtained through high-pass and low-pass filtering. Additionally, the code contains several methods to assess the performance metrics of the model. This model holds potential as a starting point for designing simple yet advanced AI biosensors capable of detecting apoptotic cells that are not discernible through conventional microscopy techniques. [ABSTRACT FROM AUTHOR]

A novel morphing activation function is proposed, motivated by the wavelet theory and the use of wavelets as activation functions. Morphing refers to the gradual change of shape to mimic several apparently unrelated activation functions. The shape is controlled by the fractional order derivative, which is a trainable parameter to be optimized in the neural network learning process. Given the morphing activation function, and taking only integer-order derivatives, efficient piecewise polynomial versions of several existing activation functions are obtained. Experiments show that the performance of polynomial versions PolySigmoid, PolySoftplus, PolyGeLU, PolySwish, and PolyMish is similar or better than their counterparts Sigmoid, Softplus, GeLU, Swish, and Mish. Furthermore, it is possible to learn the best shape from the data by optimizing the fractional-order derivative with gradient descent algorithms, leading to the study of a more general formula based on fractional calculus to build and adapt activation functions with properties useful in machine learning. [ABSTRACT FROM AUTHOR]

A wavelet based finite element method (WBFEM) using B-spline wavelet on the interval is developed in this paper for modeling multi-span pipes conveying fluid with different support conditions. The pipe element is considered as a beam element which is formulated based on Euler–Bernoulli and Timoshenko beam theories. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the multi-span pipe. In comparison to the conventional finite element method, the developed WBFEM discretization scheme uses appreciably less elements for modeling the multi-span pipe. Numerical solutions are obtained and compared with some available results in the literature and those obtained by ANSYS to verify the accuracy and efficiency of the developed method. [ABSTRACT FROM AUTHOR]

Mathematical models, especially complex nonlinear systems, are always difficult to analyze and synthesize, and researchers need effective and suitable control methods to address these issues. In the present work, we proposed a hybrid method that combines the well-known Takagi-Sugeno fuzzy model with wavelet decomposition to investigate nonlinear systems characterized by the presence of mixed nonlinearities. Here, one nonlinearity is super-linear and convex, and other is sub-linear, concave, and singular at zero, which leads to difficulties in the analysis, as is known in PDE theory. Linear and polynomial fuzzy models were combined with wavelets to ensure an improvement in both methods for investigating such problems. The results showed a high performance compared with existing methods via error estimates and Lyapunov theory of stability. The model was applied to a prototype nonlinear Schrödinger dynamical system.

In this paper, it was proposed to create a new quality control chart for the single value of the Daubechies wavelet to address the problem of data contamination before creating the single value chart and comparing it with the classical Shewhart single value chart. The proposed charts are an application of wavelet shrinkage and a universal threshold estimation method with a soft threshold rule to address the contamination problem and de-noise data to obtain a more efficient chart in controlling the single value and increasing the sensitivity of the chart in detecting minor changes that may occur in the production process. Accordingly, a single chart for the Daubechies wavelet with orders (1, 2, and 3) was proposed and applied to randomly generated data (simulated) for several cases, then real data and some efficiency indicators of the proposed charts were calculated and compared with the classical chart based on the MATLAB program. The paper results showed that all proposed charts were better than the classical chart for single values for all simulation cases and real data.

Based on a data-driven kernel estimator, Lepski and Willer considered the problem of adaptive $ L^{p} $ risk estimations in the convolution structure density model in 2017 and 2019. This current paper studies the same problem with a data-driven wavelet estimator on Besov spaces, as wavelet estimations offer fast algorithm and provide more local information. Our results can reduce to the traditional adaptive wavelet estimations in the classical density model with no errors, as well as deconvolutional model.

The paper investigates the problem of the time arrow in terms of artistic creation. The statistical model of artwork signal processing is established in order to identify a duality relation between psychological and intrinsic time. The intrinsic time is linked to the time operator of wavelets, and the psychological one is metaphorically related to the spatial domain of an artwork. The increase of irreducible randomness along the timeline is formulated by the second law of thermodynamics. The dual statement concerns an increase in statistical complexity, which is the definition of self-organization. In that manner, two arrows of time which are opposed and dual to each other are recognized. The authors have indicated a link to the theory of musical forms, the originality issue, and the perspective problem. Some repercussions for art theory, neuroaesthetics, and psychophysics have also been implied. [ABSTRACT FROM AUTHOR]

We discuss a volatility functional model and show that jumps asymptotically impact the volatility estimate. This result is useful because our model shows that significant variations affect the estimation of the volatility and historically price series have structures with this type of behavior. We also discuss a method for detecting and locating jumps at different levels and show that the jumps tend to be detected by wavelet coefficients at lower resolution levels accurately. By checking the wavelet coefficients on the different levels, we can find dyadic intervals in some levels, whose corresponding absolute value of the wavelet coefficient exceeds a threshold, and is significantly higher than the others. We applied the procedure in a simulation study and to a series of Google stocks. [ABSTRACT FROM AUTHOR]

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We study the role of co-jumps in the interest rate futures markets. To disentangle continuous part of quadratic covariation from co-jumps, we localize the co-jumps precisely through wavelet coefficients and identify statistically significant ones. Using high frequency data about U.S. and European yield curves we quantify the effect of co-jumps on their correlation structure. Empirical findings reveal much stronger co-jumping behavior of the U.S. yield curves in comparison to the European one. Further, we connect co-jumping behavior to the monetary policy announcements, and study effect of 103 FOMC and 119 ECB announcements on the identified co-jumps during the period from January 2007 to December 2017. [ABSTRACT FROM AUTHOR]

Humans spend a significant portion of their time in the state of sleep, and therefore one's'sleep health' is an important indicator of the overall health of an individual. Non‐invasive methods such as electroencephalography (EEG) are used to evaluate the 'sleep health' as well as associated disorders such as nocturnal front lobe epilepsy, insomnia, and narcolepsy. A long‐duration and repetitive activity, known as a cyclic alternating pattern (CAP), is observed in the EEG waveforms which reflect the cortical electrical activity during non‐rapid eye movement (NREM) sleep. The CAP sequences involve various, continuing periods of phasic activation (phase‐A) and deactivation (phase‐B). The manual analysis of these signals performed by clinicians are prone to errors, and may lead to the wrong diagnosis. Hence, automated systems that can classify the two phases (viz. Phase A and Phase B accurately can eliminate any human involvement in the diagnosis. The pivotal aim of this study is to evaluate the usefulness of stopband energy minimized biorthogonal wavelet filter bank (BOWFB) based entropy features in the identification of CAP phases. We have employed entropy features obtained from six wavelet subbands of EEG signals to develop a machine learning (ML) based model using various supervised ML algorithms. The proposed model by us yielded an average classification accuracy of 74.40% with 10% hold‐out validation with the balanced dataset, and maximum accuracy of 87.83% with the unbalanced dataset using ensemble bagged tree classifier. The developed expert system can assist the medical practitioners to assess the person's cerebral activity and quality of sleep accurately. [ABSTRACT FROM AUTHOR]

In the general setting of long‐memory multivariate time series, the long‐memory characteristics are defined by two components. The long‐memory parameters describe the autocorrelation of each time series. And the long‐run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long‐memory, long‐run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi‐analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long‐memory and brain connectivity are inferred. [ABSTRACT FROM AUTHOR]

We propose TrendSegment, a methodology for detecting multiple change-points corresponding to linear trend changes in one dimensional data. A core ingredient of TrendSegment is a new Tail-Greedy Unbalanced Wavelet transform: a conditionally orthonormal, bottom-up transformation of the data through an adaptively constructed unbalanced wavelet basis, which results in a sparse representation of the data. Due to its bottom-up nature, this multiscale decomposition focuses on local features in its early stages and on global features next which enables the detection of both long and short linear trend segments at once. To reduce the computational complexity, the proposed method merges multiple regions in a single pass over the data. We show the consistency of the estimated number and locations of change-points. The practicality of our approach is demonstrated through simulations and two real data examples, involving Iceland temperature data and sea ice extent of the Arctic and the Antarctic. Our methodology is implemented in the R package trendsegmentR, available from CRAN. [ABSTRACT FROM AUTHOR]

Purpose – This study aims to reassess the dynamics of major cryptocurrencies sur-rounding recent economic and geopolitical events. By employing wavelet analysis and quantile regression methods, it seeks to understand the behavior of cryptocurrencies before, during, and after the COVID-19 pandemic. Research methodology – This research employs the Least Asymmetric Daubechies (LA8) wavelet function to decompose log-returns of major cryptocurrencies into various frequency scales. Additionally, it utilizes wavelet coherence and quantile-on-quantile regression techniques to analyze daily price data spanning from July 2017 to May 2024. Findings – The findings reveal a strong long-term association among cryptocurrencies, with a decline in medium-term correlations. Bitcoin exhibits synchronization with major cryptocurrencies, excluding Tether, while BTC-ETH and BTC-BNB display a rapid, interconnected behavior alongside their fundamental links. Moreover, empirical evidence indicates Bitcoin’s heterogeneous nexus with other alternatives, showcasing greater sensitivity to positive extremes over negative ones. Research limitations – The study’s scope is delimited by the selected time frame (July 2017 to May 2024) for data analysis, potentially limiting insights into longer-term trends. Additionally, the reliance on specific methodologies like wavelet analysis might introduce constraints in capturing the entirety of cryptocurrency dynamics, leaving room for alternative interpretations or unexplored aspects. Practical implications – Results suggest that understanding the varying correlations among major cryptocurrencies during different market phases could aid investors and policymakers in devising more nuanced strategies. Recognizing the sensitivity of Bitcoin’s connections with alternatives to market trends could inform risk management approaches, particularly in navigating extreme market conditions. Originality/Value – The originality of this study lies in its comprehensive examination of cryptocurrency dynamics across varying time scales, utilizing wavelet analysis and quantile regression techniques. The findings offer valuable insights into the complex interconnections among cryptocurrencies, especially in terms of their sensitivity to different market conditions, providing a nuanced perspective for investors, analysts, and policymakers navigating the crypto landscape.

Summary: Background: Electroencephalography (EEG) has a long history as a clinical tool to study brain function, and its potential to derive biomarkers for various applications is far from exhausted. Machine learning (ML) can guide future innovation by harnessing the wealth of complex EEG signals to isolate relevant brain activity. Yet, ML studies in EEG tend to ignore physiological artefacts, which may cause problems for deriving biomarkers specific to the central nervous system (CNS). Methods: We present a framework for conceptualising machine learning from CNS versus peripheral signals measured with EEG. A signal representation based on Morlet wavelets allowed us to define traditional brain activity features (e.g. log power) and alternative inputs used by state-of-the-art ML approaches based on covariance matrices. Using more than 2600 EEG recordings from large public databases (TUAB, TDBRAIN), we studied the impact of peripheral signals and artefact removal techniques on ML models in age and sex prediction analyses. Findings: Across benchmarks, basic artefact rejection improved model performance, whereas further removal of peripheral signals using ICA decreased performance. Our analyses revealed that peripheral signals enable age and sex prediction. However, they explained only a fraction of the performance provided by brain signals. Interpretation: We show that brain signals and body signals, both present in the EEG, allow for prediction of personal characteristics. While these results may depend on specific applications, our work suggests that great care is needed to separate these signals when the goal is to develop CNS-specific biomarkers using ML. Funding: All authors have been working for F. Hoffmann-La Roche Ltd.

The measured synchronous response of rotor components may be analyzed with two objectives. On the one hand, the estimation of the response amplitude is necessary for structural calculations such as the assessment of the low-cycle fatigue safety margin. On the other hand, it is used for system identification purpose with particular interest for damping. Both these tasks can be carried out efficiently and accurately using the time-frequency analysis (TFA) based on the continuous wavelet transform (WT). A major issue that limits a wide use of this tool is the lack of criteria to guide the analyst to a proper choice of the parameters involved in the wavelet transform. This paper discusses this problem from a theoretical and practical point of view and provides a criterion valid for the analysis of the response during resonance crossings. [ABSTRACT FROM AUTHOR]

In this paper we employ Sinc functions as the basis functions and call the resulting method Sinc wavelet collocation method. The main distinguishing feature of the present method, in contrast to the standard Sinc collocation method, is that we do not use a mapping to transform the Sinc functions to a finite domain on which the BVPs are defined to an infinite domain in order to apply them. This results in a much simplified algorithm which is easy to implement while maintaining the high accuracy of the traditional Sinc collocation method. We apply the Sinc collocation method to BVPs and the fractional diffusion equation. [ABSTRACT FROM AUTHOR]

Wavelets are employed to study atmospheric turbulent data of three wind components, temperature and passive scalars CO 2 and H 2 O. The multiresolution analysis (MRA) based on maximal overlap discrete wavelet transform (MODWT) is used to separate turbulent fluctuations from the mean flow. These turbulent fluctuations are further partitioned into small scales x ′ s and large scales x ′ L , and the fluxes are calculated by averaging over the given time interval. The large scales are responsible for much of the flux transport, while the small scales are fine scales consisting of non-transporting, nearly isotropic motions. The velocity spectrum for both small (non-coherent) and large scale (coherent) follow - 5 / 3 scaling, and the transfer efficiency R wa similarity laws are better satisfied for the large scales. The velocity probability distribution of partitioned signals shows a narrower distribution for small scales compared to large ones. However, the flatness factor indicates deviation from Gaussianity. The joint probability distribution for large scales is skewed, suggesting the dominance of ejections and sweeps. Despite their wave-like nature, the large scales are not linear waves as indicated by the phase spectrum. The large scales are subjected to the continuous wavelet transform (CWT) to detect and isolate the strong localized events. The Mexican Hat (MHAT) wavelet transform and zero-crossing method is used to estimate the duration, separation, and frequency of occurrence of the detected events. [ABSTRACT FROM AUTHOR]

Bridges serve as vital engineering structures crafted to facilitate secure and effective transportation networks. Throughout their life-cycle, they withstand various factors, including diverse environmental conditions, natural hazards, and substantial loads. Recent bridge failures underscore the significant risks posed to the structural integrity of bridges. Damage detection techniques, being core components of structural health monitoring, play a crucial role in objectively assessing bridge conditions. This article introduces a novel framework for identifying damage in bridges utilizing continuous wavelet analysis of accelerations recorded using two sensors mounted on a vehicle traversing the bridge. The proposed method leverages changes in the static response of the bridge, which has proven to be more sensitive to damage than its dynamic counterpart. By doing so, the method eliminates the reliance on modal parameters for damage identification, addressing a significant challenge in the field. The proposed framework also addresses key challenges encountered by drive-by monitoring methods. It mitigates the adverse effects of road roughness by utilizing residual accelerations and efficiently detects and locates damage even in the absence of corresponding data from an undamaged bridge. Numerical investigations demonstrate the robustness of the proposed method against various parameters, including damage location and extent, vehicle speeds, road roughness levels, different boundary conditions, and multi-damage scenarios. [ABSTRACT FROM AUTHOR]

Since the discovery and the development of many technological instruments such as modern communication and communication technologies, digital media has served widely from the technology, and thus intersected quasi all life's domains, by providing news, information, and also discussions of quasi all subjects. In social sciences, for example, a major part of digital media sites discusses the well-being of both individuals, and societies, especially with the presence of many challenging phenomena like pandemics, wars, and financial crises. A major concern for QoL index for example resides in whether it is a uniform stable index or on the contrary a non-uniform index depending strongly and point-wisely on the time scale. This motivates the consideration of a non-uniform QoL index based on non-uniform wavelets to take into account the influence of many factors issued from political, social, environmental, economic effects according to the time scale. The model developed is tested on Saudi Arabia QoL index case. Recall that the Kingdom of Saudi Arabia has fixed many aims in its 2030-vision plan including the quality of life as a major goal. For example, the KSA worldwide NEOM project necessitates surely a supportive environment to be realized. The second purpose of our paper is also to study the impact of digital media such as social one on the QoL. Therefore, the data collected is basically issued from a set of conversations on social media platforms. To obtain a suitable time series, we developed a backward-forward non-uniform wavelet forecasting model to extend the data sample suitably. The whole time series is by the next applied for the QoL index dynamics and interpretations. The findings showed that effectively, the QoL index is never a stable single index on the whole year, but on the contrary, the dependence on the time scale is non-uniform. Moreover, to interpret suitably and for a correct policy, the non-uniform behavior should be considered adequately. [ABSTRACT FROM AUTHOR]

Crypto currency price prediction is one of the biggest challenges for any prediction system owing to its volatility and dependence on many factors. Artificial intelligence powered by the development of sophisticated computing technology and developments in research has opened up a wide variety of applications and new possibilities to solve complicated problems. Extraction of appropriate features and input with features affecting the output is equally important in time series prediction problems. Wavelet transform is considered an effective method to split a non-stationary signal into uncorrelated components. This work attempts to extract the advantage of wavelets to extract features from an available data set and to predict the trend of the crypto price for next 16 days using the Bi-LSTM network. Historic data of crypto currencies available in Yahoo finance through the yFinance API with the python code is used as the primary data for this work. Due to the gaining importance of SHIB crypto due to its multiplication of value from its start, we have taken SHIB trend analysis as a case study with the use of a data set provided by Yahoo Finance API. The novelty of the proposed system lies largely on the combination of wavelet and deep learning system to improve the performance measures. The proposed systems evaluates the wavelet transform coefficients of the historic data available from the Yahoo Finance API and feed the wavelet transform values to the input of Bi-LSTM network to predict the wavelet transform coefficients for the next 16 days. Finally an inverse wavelet transform is used to get the price of the crypto currency for next 16 days. The results obtained shows that the model was able to estimate the trend in crypto price. The trend analysis shows whether there is an increase or decrease of prices in upcoming days and this could be useful to invest or to withdraw the funds to improve the returns. The proposed scheme resulted in lower Mean Square Error (MSE), Mean Average Error (MAE) and Root Mean Square Error (RMSE) compared with the currently available methods. The method could be useful for trend analysis of other crypto currencies as well. Though it is practically impossible to get the trend analysis from the price and volume history alone, the proposed scheme gives a reasonable estimate of the trend of the crypto price. The work may be extended in future to applications like prediction of agricultural product price, variation in climatic conditions, and availability of certain agricultural products like Onion in the market. [ABSTRACT FROM AUTHOR]

This article discusses the nonparametric estimation of a bivariate density function using copula information under right censoring. We propose an adaptive estimator based on wavelet methods and the formulae for the asymptotic mean integrated squared error(MISE) is used to get the near optimal rate on a large functional class of regular densities. In particular, the asymptotic formulae for MISE in the context of kernel density estimators is derived in the case of censoring. Finally, the consistency of the proposed estimators is established and its effectiveness is validated through a numerical simulations. [ABSTRACT FROM AUTHOR]

Gas turbines play a vital role in gas transportation and power generation, but they are prone to instability phenomena that can lead to vibrations, shorten equipment lifespan, and result in catastrophic failures. To tackle these challenges, a paper introduces an integrated approach that leverages advanced techniques like Fourier transform, Neuro-Fuzzy systems, and wavelet analysis for continuous monitoring of the MS5002C turbine's condition. The proposed method begins by collecting operational data and utilizing the Fourier transform to measure vibratory quantities, accurately representing their evolution through spectral data obtained from the analyzed signals. Adaptive inference-based algorithms of neuro-fuzzy systems are then employed to generate turbine failure indicators. This approach enables the development of a model-based fault detection method that compares the actual turbine operation with the estimated operation derived from a pre-established model, enabling the classification of detected faults. To enhance decision-making quality, evaluation, and validation of the diagnostic strategy's performance, a multi-resolution analysis based on the wavelet transform is applied. The presented results from various implementation and validation tests demonstrate the effectiveness of this intelligent diagnostic approach in detecting and analyzing gas turbine vibrations. The paper exhibits promising outcomes in real-time monitoring, ensuring the operational safety of the turbine. [ABSTRACT FROM AUTHOR]

This paper introduces a novel nothing-on-road (NOR) bridge weigh-in-motion (BWIM) approach with deep learning (DL) and non-invasive ground-based radar (GBR) time-series data. BWIMs allow site-specific structural health monitoring (SHM) but are usually difficult to attach and maintain. GBR measures the bridge deflection contactless. In this study, GBR and an unmanned aerial vehicle (UAV) monitor a two-span bridge in Germany to gather ground-truth data. Based on the UAV data, we determine vehicle type, lane, locus, speed, axle count, and axle spacing for single-presence vehicle crossings. Since displacement is a global response, using peak detection like conventional strain-based BWIMs is challenging. Therefore, we investigate data-driven machine learning approaches to extract the vehicle configurations directly from the displacement data. Despite a small and imbalanced real-world dataset, the proposed approaches classify, e.g., the axle count for trucks with a balanced accuracy of 76.7% satisfyingly. Additionally, we demonstrate that, for the selected bridge, high-frequency vibrations can coincide with axles crossing the junction between the street and the bridge. We evaluate whether filtering approaches via bandpass filtering or wavelet transform can be exploited for axle count and axle spacing identification. Overall, we can show that GBR is a serious contender for BWIM systems. [ABSTRACT FROM AUTHOR]

This article provides an expository review of the relationship between graph C ∗ -algebras and the wavelet theory. This connection was first established by O. Bratteli and P.E.T. Jorgensen in the late 90 ′ s. Various mathematicians paid attention to this connection in the past 25 years, and the area has become active and dynamic now. The major contributors include O. Bratteli, P. E. T. Jorgensen, C. Farsi, E. Gillaspy, S. Kang, J. Packer, M. Marcolli and A. M. Paolucci. Our aim is to provide an expository survey in this direction. [ABSTRACT FROM AUTHOR]

Food security is an indispensable concept because human life depends on it. Although numerous studies have examined food security in developing economies, there has been a lack of attention given to this issue in developed countries. Thus, this study investigates the influence of carbon dioxide emissions (CO2) on food security in the United States from 1965 to 2022 using Quantile Autoregressive Distributed Lag (QARDL) and Wavelet Coherence methods. Food security is proxied by the food production index (FPI), while the control variables are gross domestic product (GDP), population growth (POP), and inflation. The Quantile Autoregressive Distributed Lag results show that: (i) In the short‐run, CO2 influences FPI positively at the 0.05 quantile, while it harms food security at the 0.50 and 0.95 quantiles. However, in the long‐run, the impact is positive across all quantiles; (ii) In the short‐run, GDP harms FPI at the 0.05 quantile while it benefits FPI at the 0.50 and 0.95 quantiles. In the long‐run, GDP's impact across all quantiles is beneficial; (iii) In the short‐run, POP negatively influences FPI at 0.05 and 0.50 quantiles, while it positively spurs FPI at 0.95 quantiles. In the long‐run, POP positively influences FPI at quantiles of 0.05, whereas it negatively influences FPI at 0.50 and 0.95 quantiles; (iv) inflation positively influences FPI in the short and long‐run across all quantiles; (v) The Wavelet Coherence analysis showed a robust correlation across all frequencies. Policy suggestions and implications are discussed further. [ABSTRACT FROM AUTHOR]

With the presence of a large number of inversion algorithms for inverse heat transfer problems (IHTPs) and non-IHTPs, a need for review to have a holistic view is seen. An exhaustive literature review, with the motivation of selecting the inversion technique best fit for a given problem, was made for a general inverse problem. For ill-posedness, a classification of available regularization algorithms namely Tikhonov's regularization, Bayesian regularization, mollification method, Beck's sequential approach and Alifanov's iterative approach, has been provided. Inversion methods like singular value decomposition, truncated singular value decomposition, Tikhonov regularization and total variation regularization are explained. Optimization methods namely steepest descent method, conjugate gradient method, Newton method, Levenberg–Marquardt method, Lagrange method, adjoint method, function specification method, genetic algorithm, differential evolution and particle swarm optimization (PSO) are reviewed. Further, a technique based on neural networks is studied, and wavelet methods like shrinking and wavelet vaguelette decomposition are reviewed. Associated literature has also been listed, highlighting the gaps. The usability of various algorithms in IHTP, starting from the golden section search method, for retrieval of a single parameter, to the regularized versions of the inversion technique, for retrieval of multiple parameters with uncertainty, demonstrates real-life applications to fins in IHTP. An inversion algorithm capable to handle every kind of nonlinearity is sought in literature, whose absence raises the research question, "Is there a technique that works globally for every inverse problem?", is asked prior to, "What if the available techniques were not utilized to an extent that they should?" is posed. In lieu of this gap, a general comparative framework is developed, such that an efficient technique is selected, based on the total minimum error, which can be used in any field of interest. [ABSTRACT FROM AUTHOR]